# Density Matters:

Review of Approaches to Setting Organism-Based Ballast Water Discharge Standards

U.S Environmental Protection Agency 

## Henry Lee II 1 

## Office of Research and Development 

## Deborah A. Reusser 2 

## EPA/600/R-10/031 

## Melanie Frazier 1 

## April 2010 (revised August 2010)

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## Greg Ruiz 3

1: Western Ecology Division,

National Health and Environmental Effects Research Laboratory, Office of Research and Development,

U.S. Environmental Protection Agency, 2111 SE Marine Science Drive, Newport, OR 97365, U.S.A.

0 4 8 12 16 20 24 28 2: U.S. Geological Survey, Western Fisheries Research Center, 2111 SE Marine Science Drive, Newport, OR 97365, U.S.A.

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Marine Invasion Research Laboratory, Smithsonian Environmental Research Center,

647 Contees Wharf Ro ad, P.O. Box 28, Edgewater, MD 21037, U.S.A.

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0123456 01 2Disclaimer: The information in this document ha s been funded in part by the U.S. Environmental Protection Agency (U.S. EPA). The publication was subjected to review by the

National Health and Environmental Effects Re search Laboratory’s Western Ecology Division and the U.S. Geological Survey (USGS), and is approved for publication. However, approval does not signify that the contents reflect the views of the U.S. EPA. The use of trade, firm, or corporation names in this publica tion is for the information and convenience of the reader; such

use does not constitute official endorsement or approval by the U.S. Department of Interior, the USGS, or the EPA of any product or service to th e exclusion of others that may be suitable.

Acknowledgements:

The authors wish to thank the fo llowing for their contributions to this report: M.S. Minton, P.W. Fofonoff, and A.W. Miller provide d data on ballast water discharg e and historical invasion rates and insights into their interpre tation. Richard Everett, John Li shman, and Ryan Albert provided guidance through the intri cacies of IMO, national, and stat e regulations; Cheryl A. Brown provided advice on mathematical issues; John Van Sickle provided advice on statistical issues. Richard Everett, John Lishman, Ryan Albert, Jo hn Van Sickle, Nathan H. Schumaker, Scott Smith, Jody Stecher, Katharine Marko, and Robert J. Ozretich reviewed an earlier version of this document and provided insightful suggestions. Deborah Reusser was partially funded through

AMI/GEOSS IAG #DW-14-92231501-0 from the U.S. EPA. Melanie Frazier was funded through AMI/GEOSS EP08D00051.

Preferred Citation: Lee II, H., Reusser, D.A., Frazier, M ., and Ruiz, G. 2010. Density Matters: Review of Approaches to Setti ng Organism-Based Ballast Water Discharge Standards. U.S. EPA, Office of Research and Development, National Health and Environmental Effects Research Laboratory, Western Ecol ogy Division. EPA/600/R-10/031.

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### TABLE OF CONTENTS

TABLE OF CONTENTS

............................................................................................................. .. iii

LIST OF FIGURES

............................................................................................................... ........ v LIST OF TABLES

................................................................................................................ ...... vi

EXECUTIVE SUMMARY

.......................................................................................................... vii

I. INTRODUCTION

............................................................................................................... ........ 1 Objectives and Scope of Report:

............................................................................................... .. 1 Nonindigenous Species Background:

......................................................................................... 2 IMO Ballast Water Treaty and Propos ed USCG Standards Background:

.................................. 3 U.S. EPA Regulatory Background:

............................................................................................ 5 Challenges in Setting Organism-Bas ed Discharge Standards:

................................................... 6

II. PROPAGULE SUPPLY DOSE-R ESPONSE AND ALLEE EFFECTS

................................... 8

Allee Effects:

................................................................................................................ .............. 8 Propagule Supply Dose-Response:

............................................................................................. 9

III. REDUCTION IN PROPAGULE SUPPLY BASED ON EXPERT

OPINION/MANAGEMENT CONSENSUS

................................................................................ 12

Overview:

..................................................................................................................... ............. 12

Rationale:

.................................................................................................................... .............. 12 Assumptions and Limitations:

.................................................................................................. 15

Recommendations/Conclusions:

............................................................................................... 16

IV. ZERO DETECTABLE DISCHARGE

................................................................................... 18

Overview:

..................................................................................................................... ............. 18

Rationale:

.................................................................................................................... .............. 18 Assumptions and Limitations:

.................................................................................................. 19

Recommendations/Conclusions:

............................................................................................... 21

V. NATURAL INVASION RATES

............................................................................................. 25

Overview:

..................................................................................................................... ............. 25

Rationale:

.................................................................................................................... .............. 25 Calculation of Discharge Standard Ba sed on Natural Invasion Rates:

..................................... 25

Estimate of Natural Invasion Ra te on Pacific Coast:

................................................................ 26 Discharge Standards Derived from Natural Invasion Rates:

.................................................... 29

Evaluation of Natural Invasion Rate s and Adjustment Factors:

............................................... 29 Adjustment of Ballast Water Organism s Concentrations to IMO Mean

.............................. 29 Taxonomically Adjusted Natural Invasion Rate

................................................................... 29 Biogeographic Analysis of Potentia l Species Pool for Invasion

.......................................... 30 Evidence for Transoceanic Interchange:

................................................................................... 31 Assumptions and Limitations:

.................................................................................................. 32

Recommendations/Conclusions:

............................................................................................... 34

VI. REACTION-DIFFU SION MODELS

.................................................................................... 35

Overview:

..................................................................................................................... ............. 35 Application to Ballast Water Discha rges by Drake et al. (2005):

............................................. 35

Parameter Es timation:

......................................................................................................... ...... 37 Assumptions and Limitations:

.................................................................................................. 39

Recommendations/Conclusions:

............................................................................................... 40

VII. POPULATION VIABILITY ANALYSIS (PVA) MODELS

............................................... 42

iiiOverview:

..................................................................................................................... ............. 42 PVA Model Used in USCG Risk Assessment for Single Species Scenario:

............................ 42 PVA Model Used in USCG Risk Assessment for Multiple Species Analysis:

........................ 50 Assumptions and Limitations:

.................................................................................................. 52

VIII. PER CAPITA INVASION PROBABILITIES

.................................................................... 55

Overview:

..................................................................................................................... ............. 55 Calculation of Per Capita Invasion Probabilities

...................................................................... 55 Foreign Ballast Water Discharge Rates for Co astal Waterbodies and the Great Lakes:

.......... 56 Estimates of Organism Concentrations in Ballast Water:

......................................................... 56

Estimates of Historical Invasion Rates:

.................................................................................... 59

Uncertainties in Historical Invasi on Rates and Safety Factors:

................................................ 61 Among Port Patterns of Invasion Risk:

.................................................................................... 62

Coastal Patterns of Invasion Risk:

............................................................................................ 64 Assumptions and Limitations:

.................................................................................................. 65

Recommendations/Conclusions:

............................................................................................... 67

IX. EXPERIMENTAL APPROACHES

....................................................................................... 70

Overview:

..................................................................................................................... ............. 70 Assumptions and Limitations:

.................................................................................................. 70

Recommendations/Conclusions:

............................................................................................... 71

X. STATISTICAL CONSIDERATIONS IN ESTIMATING THE CONCENTRATION OF

ORGANISMS IN BALLAST WATER DISCHARGES

............................................................. 72

Overview:

..................................................................................................................... ............. 72

Rationale:

.................................................................................................................... .............. 72 Sampling Ballast Water Discharges:

........................................................................................ 73 Sampling Poisson Distributions:

............................................................................................... 74 Some Sampling Scenarios:

...................................................................................................... . 78 Aggregated Populations:

....................................................................................................... .... 83

Recommendations/Conclusions:

............................................................................................... 85

XI. COMPARISON OF APPROACHES

..................................................................................... 87

XII. REFERENCES

............................................................................................................... ...... 91 Appendix A: Overview of Human Health Microbial Standards

................................................. 106

Overview:

..................................................................................................................... ........... 106

Recommendation/Conclusions:

.............................................................................................. 106 Appendix B: Calculation of Coastal Pe r Capita Invasion Probabilities

..................................... 108 Appendix C: R Statistical Tools to Develop/Ev aluate Ballast Water Sampling Protocols

........ 113 Statistical Tools Using R:

.................................................................................................... ... 113

Random distributions

.......................................................................................................... 113 Aggregated distributions

..................................................................................................... 114

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### LIST OF FIGURES
Figure 1 : Illustrations of Allee eff ects on per capita population growth

........................................ 9 Figure 2 : Hypothetical propagule supply dos e-response curves. Potential responses include; a) exponential; b) sigmoid; c) linear; and d) logarithmic or hyperbolic.

.................... 11 Figure 3 : Relative density distributions of zooplankton (>80 micron) in unexchanged

ballast water a nd after theoretical balla st water exchange

........................................................ 14 Figure 4 : Example of relative population grow th rate based on the cubic population model from Lewis and Kareiva (1993) with and without a mild Allee effect (a = 0.01)

......... 38 Figure 5 : Enlargement of the relative population growth rate based on the cubic population model from Lewis and Kareiv a (1993) with and wit hout a mild Allee effect (a = 0.01)

......................................................................................................... ................ 38 Figure 6 : Distribution of per capita invasion probabilities (PCIPs) for the Pacific Coast based on 10,000 random simulations of organism concentrations among the 5998 ships discharging foreign ballast

......................................................................................... ...... 60 Figure 7 : Risk diagrams for the Pacific Coas t illustrating the effect of three different safety factors (1, 10, and 20)

............................................................................................ ......... 66 Figure 8 : Risk diagrams for the Pacifi c Coast based on less protective and more protective assumptions.

................................................................................................... .......... 67 Figure 9 : An example of a random distribution (A , Poisson) and two possible variations of

........................................................................................ ... 74 aggregated distributions (B and C) Figure 10 : Probability distributions for random samples of 1 m 2 for a randomly distributed population with 10 (A), 1 (B), or 0.01 (C) organisms m -2

........................................................ 77 Figure 11 : Probability of detecting an exceedance for sample volumes between 1

and 50 m 3 and a discharge standard of 0.01 organisms m -3

...................................................... 81 Figure 12 : Determining whether ballast water discharge exceeds or meets a discharge standard of 0.01 (A) and 10 (B) organisms m -3

. ....................................................................... 83 Figure 13 : Comparison of sample probabilitie s from a randomly distributed (Poisson) population vs. an aggregated population w ith a dispersion parameter of 0.1 (negative binomial) for a sample volume of 1 m 3 and concentration of 1 organism m -3

. ........................ 84 Figure 14 : Theoretical example of how the appa rent aggregation in the population differ based on the scale of aggregation rela tive to the size of the sample unit.

................................ 85

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### LIST OF TABLES

Table 1 : Existing or proposed internati onal and national ballast water discharge standards applicable to th e waters of the United States and examples of state standards

.......... 4

Table 2 : Examples of complexities and uncertainties confounding the prediction of

invasion rates via ballast water.

......................................................................................... ......... 7

Table 3 : Failure rates of the systems listed as having the “potential” to achieve the California discharge standa rd for >50 micron organisms

......................................................... 21

Table 4 : Estimates of natu ral invasion rates, resulting disc harge limits, and adjusted discharge limits

.......................................................................................................... ............... 28

Table 5 : Parameters used in the PVA models in the DPEIS.

........................................................ 44

Table 6 : Ranges in the fractional decreases (f) in initial ballast water population size generated by treatment Alternatives 2 - 4 relative to the rang e of population sizes in Alternative 1 used by the DPEIS

........................................................................................ .. 46

Table 7 : Probability of extinction (pe) expres sed as a function of the initial organism concentrations (>50 microns) in ballast water and the “biological parameter” c for a single species

...................................................................................................... .............. 47

Table 8 : Probability of extinction (pe) as a function of the initial orga nism concentrations in ballast water and the “biologica l parameter” c for a single species for 10 identical, independent discharge events

............................................................................... 48

Table 9 : Factor by which the probability of extinction would be increased compared to Alternative 1 (fe) for >50 micron organisms

............................................................................ 49

Table 10 : Mean rate of successful intr oductions for treatment alternatives

relative to Alternative 1

................................................................................................ ........... 50

Table 11 : Relative efficiencies of Alternat ives 2, 3 and 4 that no species successfully

invades from a ballast di scharge compared to unexcha nged ballast water or after ballast water exchange (BWE) .

............................................................................................ .... 52

Table 12 : Number of invaders (Nh), foreign ballast discharge volumes (Dh), and per capita invasion probabilities (PCIP) for the East, Gulf, and Pacific coasts of the United States, 17 coastal ports, and the Great Lakes

...................................................... 57

Table 13 : PCIP CI estimates based on upper 90%, 95%, 99%, and 99.9% confidence intervals around the median and 0.975 quant ile PCIP values for the 12 moderate to large estuaries in Table 12.

........................................................................................... ........ 64

Table 14 : Major assumptions of the per capita invasion probability approach to setting

ballast water discharge standards

......................................................................................... ..... 69

Table 15 : Definition of statistical terms

..................................................................................... ... 76

Table 16 : Conditions for ballast water sampling scenarios

.......................................................... 79

Table 17 : Probability of detecting ≥ 1 organism for various sample volumes (100 mL

to 100 m 3 ) and ballast water concentr ations (0, 100 organisms m -3 )

........................................ 80

Table 18 : Upper possible concentration (U PC) of organisms based on one and two tailed 95% exact confidence intervals when zero organisms are detected in a range of sample volumes

......................................................................................................... ........... 80

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### EXECUTIVE SUMMARY

As one of the major vectors by which invasive species invade the coastal waterbodies and the Great Lakes, ballast water discharges from ocean -going ships are a major environmental threat to the Nation’s waters. Recognizing the importance of ballast water as a vector for invasive species on a global scale, in February 2004 the text of an intern ational ballast water treaty was negotiated through the International Maritime Organization (IMO). The IMO has proposed organism-based ballast water discharge standards fo r different size classes of organisms (Table ES-1). While this represents a major accomplishment, there is con cern that the IMO standards are not sufficiently protective. Accordingly, the United States Coas t Guard (USCG) just released proposed Phase I (equal to the IMO standards) and Phase II ( 1000 more stringent then the IMO standards) standards for the waters of the United States (T able ES-1). Additiona lly, California and other states have implemented or have proposed state standards more stringent than those proposed by the IMO (Table ES-1).

Historically, the EPA had excluded discharges incidental to the normal operation of vessels (including ballast water) from the need to obtai n an NPDES permit. However, that exclusion from the NPDES permitting program was successfully challenged in court, and as a result, was vacated by the U.S. District Court for the Northern District of California. In light of the court decision, in December 2008 EPA issued a genera l NPDES permit (known as the “Vessel General Permit” or “VGP”) that contains , among other things, standards for ballast water discharges from

non-recreational vessels. The Office of Wate r currently is undertaking development of organism-based discharge standards for ballast wate r discharges for use in the future reissuance of the VGP. To help ensure it uses a scientific ally sound approach in that effort, the Office of Water is seeking an objective and independent scientific opinion on approaches for deriving these standards and has requested that a Natio nal Academy of Sciences (NAS) expert panel evaluate the technical merits of appro aches to generating the standards.

To assist the NAS technical revi ew, this report evaluates the po tential approaches to generating national organism-based discharge standards. Be cause of data available, we focus on the >50 micron organism class in our review. On the ba sis of ecological principles we identified six previous approaches to developing standards and developed a new one, the per capita invasion probability approach, which is described here. The approaches are: 1) Reduction in Propagule Supply Based on Expert Opinion/Management Consensus 2) Zero Detectable Living Organisms 3) Natural Invasion Rates 4) Reaction-Diffusion Models 5) Population Viability Analysis (PVA) Models 6) Per Capita Invasion Probability 7) Experimental Studies

Although not an approach to setting standards pe r se, sampling issues need to be considered when assessing the practicality of verifying that a discharge standard has b een met either in test facilities for purposes of regulat ory approval of a treatment syst em or as part of compliance monitoring of vessel discharges. Additionally, th e sampling protocol, particularly the volume of

viiTable ES-1: Existing or proposed international and national ballastwater discharge standards applicable to the waters of the UnitedStates and examples of state standards.All organism dimensions are for the “minimumdimension”. Standards for the >50 micronand >10 -<50 micron classes are for “viable” or “living” organisms. Note that Phase IIof the Coast Guard standard can beimplemented incrementally. The date for the implementation of the final California standard is 2020. The California standardsareinstantaneous standards while those for Wisconsin are daily averages. NPRM =Notice of proposed rule making. IMO = InternationalMaritime Organization. cfu = “colony forming units”Organism ClassIMO D-2StandardUSCGNPRM Phase IUSCGNPRM Phase IIWIState StandardCAInterim StandardsCAFinal StandardOrganisms >50microns<10 per m3<10 per m3<1 per 100 m3(< 0.01 per m3)<1 per 10 m3(<0.1 per m3)“No detectableliving organisms”“Zero detectableliving organisms”Organisms >10 ­<50 microns<10 per ml<10 per ml<1 per 100 ml(<0.01 per ml)<1 per 10 ml(<0.1 per ml)<1 per 100 ml(<0.01 per ml)“Zero detectableliving organisms”Organisms <10micronsNo standardNo standard<103bacteria/100 ml<104viruses/100 mlNo standard< 103bacteria/100ml< 104viruses/100 ml“Zero detectableliving organisms”Escherichia coli<250 cfu per100 ml<250 cfu per100 ml<126 cfu per100 ml<126 cfu per100 ml<126 cfu per100 ml“Zero detectableliving organisms”Intestinalenterococci<100 cfu per100 ml<100 cfu per100 ml<33 cfu per100 ml<33 cfu per 100ml<33 cfu per100 ml“Zero detectableliving organisms”ToxicogenicVibrio cholerae(serotypes O1 andO139)<1 cfu per 100 mlor1 cfu per g wet wt.zooplankton<1 cfu per100 ml<1 cfu per100 mlNo standard<1 cfu per 100 mlor<1 cfu per g wetzoological sample“Zero detectableliving organisms”viiiwater sampled, defines the actual risk level a ssociated with any standard based on “zero detectable living organisms”. Accordingly, we address the statistical considerations of the volume of water that needs to be sampled when estimating the concentrations of organisms in ballast water discharges.

The potential utility and limitations of each of the approaches to generating national discharge standards is briefly discussed be low and summarized in Table ES-2.

Reduction in Propagule Supply Based on E xpert Opinion/Management Consensus: Several of the proposed discharge standards, including the IMO standards, we re based on a combination of expert opinion and management consensus. As us ed here “expert opinion” refers to technical

recommendations for ballast water standards from experts in the areas of invasion biology and related life sciences made without the expl icit use of a quantitat ive invasion model. “Management consensus” is used to capture deci sions made utilizing th is expert opinion in additions to inputs from experts in other disciplines, such as shipping and engineering, risk managers, as well as state, national, non- governmental organization (NGO), and industry representatives. Thus, management consensu s decisions in the “real world” incorporate components of risk assessment, risk management, and lobbying.

The major advantage of expert opinion is that it is possible to address complex issues even with limited data and in the absence of quantitative m odels, which then can be evaluated in a risk management context. Expert opinion/manageme nt consensus was successful in generating the IMO organism-based standards despite the uncerta inties in the invasion process itself and the politics inherent in any international treaty. This was a “watershed” accomplishment and a critical step toward reducing new invasions via ballast discha rges. The question remains, however, as to whether the IMO standards are suffici ently protective. In part, this question arises because the expert opinion/managerial consensu s approach does not allow a rigorous evaluation of the process or how the final decisions were reached. In light of these limitations and the

continued increase in our scien tific understanding, we recomme nd that future development of standards rely more heavily on quantitative models than qualita tive expert opinion. If expert opinion is used as a major input into the develo pment of national standards, we suggest that a formal process be used to reduce the limitations or biases of expert opinion. Additionally, we suggest that experts in a dive rse range of biological, shippi ng, and engineering fields be

consulted.

Zero Detectable Living Organisms: California and other states have adopted or proposed standards with the goal of “zero detectable livi ng organisms” in ballast water discharges. California’s standards will be adop ted in two phases, with an inte rim standard of “no detectable living organisms” >50 microns in ballast discha rged from ships constructed in 2010 to 2012 and

a final standard in 2020 of “no detectable discharge” of zooplankton, phytoplankton, protists, bacteria, or viruses in ballast discharges for ships constructed beginning in 2020 (Table ES-1).

The stated rationale for the California standard was “The scientific basis for a standard of discharging no exotic organisms is that exot ic organisms, unlike conventional chemical pollutants, can reproduce and increase over time , persist indefinitely and spread over large regions. Thus, very large, widespread and long- term impacts could poten tially result from the discharge of a small number of individual organisms — in some cases as few as a single mated

ixTable ES-2: Comparison of approaches to generate national, organism-based dischargestandards for >50 micron organisms in ballastdischarges. Assessment is based on current implementation; potential modifications are identified when appropriate. “Realitycheck”is used to denote that the approach could beused to help evaluate whether predictionsfrom other approaches fall within a realisticrange. “Recommend for national standard development” is our assessment of whether the approach should be considered forgenerating quantitative organism-based discharge standards at the national level.Approach /AttributeExpert Opinion /ManagementConsensusesZero DetectableOrganismsNaturalInvasionRateReaction –DiffusionPopulationViabilityAnalysisPer CapitaInvasionProbabilitiesExperimentalCurrentimplementationgenerates quant.standardsYesYesYes(prelim. forCA)No(volumebased)No(relativecomparison)YesNoApparent range ofuncertainty instandard10,000 fold(range of conc.proposed in IMOnegotiations –0.01 to 100 org m-3)10,000 fold( upper possibleconc. w/1L vs.10 m3sample)100-fold(3 experts)or10,000-fold(our analysis)About 200 fold(approx. rangein “max. safereleasevolumes”)<2 fold (w/12 spp.in ballast) to10,000 fold(multiple voyages– our analysis)6-fold (amongcoasts)or12-fold (w/GreatLakes)NAKey data needs forgeneration of quant.standardsUnknown sincedecision process nottransparentDevelopment ofstatisticallyrigoroussamplingprotocolNaturalinvasion ratesin range ofecoregionsInstantaneouspopulationgrowth ratesfor a range oftaxaInstantaneouspopulation growthrates &instantaneousvariance of thepopulation growthrate for a range oftaxaNoneExtensiveexperimentationw/range of taxaAssumes linear doseresponseUnknown sincedecision process nottransparentNA(does not assumea dose response)YesNoNoYesNA(does not assumea dose response)Incorporates invasionrisk from multiplespecies in a dischargeYes?YesYesNo?YesYesNoIncorporates invasionrisk from multipleship dischargesYes?YesYesNoNo(modify toincorporatemultiple ships?)YesNoBased on historicalinvasion ratesNoNoYesNoNoYesNoBased on populationdynamicsNoNoNoYesYesNoYesxApproach /AttributeExpert Opinion /ManagementConsensusesZero DetectableOrganismsNaturalInvasionRateReaction –DiffusionPopulationViabilityAnalysisPer CapitaInvasionProbabilitiesExperimentalApplicable to all taxaand guildsYes?YesYes?(depends ontaxa includedin analysis)No(limited toshort-livedholoplanktonicspecies)Yes?(depends uponwhich species thepop. data can beobtained)AllNo(limited to taxaadaptable toexperiments)Separates riskassessment from riskmanagementNoNo?YesYesYesYesYesPublished in peerreviewed scientificliteratureNoNoNoYes(extensiveliterature onreactiondiffusionmodels)No(extensiveliterature on PVAmodels)No(in process)Yes(individualexperiments)Recommended fornational standarddevelopmentNo(use as “realitycheck”)NoNo(possible useas “realitycheck”)No(use as “realitycheck” forholoplanktonicspecies)Yes(if sufficient pop.data available forpredictions ofactual vs. relativerisk)YesNo(use as “realitycheck” and testassumptions)xipair, or in the case of asexually-reproducing specie s, a single individual.” From this perspective, the only biologically safe standard is no discharge of exotic organisms.

While it sounds protective, the ze ro detectable organism standard s suffer from several technical

limitations. The first is that unless the entire ba llast water discharge is sampled, it has to rely on samples of the discharge, and the degree of prot ection depends directly on the sampling protocol.

If a small volume is used to evaluate whether the discharge meets the st andard, the sample may contain zero detectable organisms, but the true concentration of organisms may be quite high. For example, even with a relatively high concentration of 100 organisms m -3 , only about 10% of 1 L samples will contain one or more organisms. The general point is that more organisms may be released in ballast discharge using a stringent standa rd paired with a poor sampling protocol than a more lenient standard paired with a stringent sampling protocol.

The second limitation is the feasibility of deve loping ballast water treatment systems that can remove all organisms while operating within the constraints of a ship. It is beyond the purview of this report to evaluate ballast water treatm ent systems; however, we did assess California’s review of existing treatment syst ems. They rated a system as having “potential” if no organisms were detected in a laboratory, land-based, or sh ip-based test if “at least one replicate in compliance with the performance standards”. In other words, a system was considered to have “potential” as long as it did not fail the standard in 100% of the replicates. A reanalysis of the data summarized by California showed that wi th the exception of one system (SeaKleen®), all systems failed a moderate to high percentage of the replicates and/or they were not tested in all three modes (laboratory, land-base d, and shipboard testing). Wh ile the results for SeaKleen® are promising, the extent of testing does not meet the minimum IMO requirements under their G8 guidelines and it has not been registered by EPA for use in treati ng ballast water under the Federal Insecticide, Fungicide, and Rodenticide Ac t (FIFRA). The general point is that approved treatment systems capable of removing all larger (>50 micron) organisms are not likely to be available in the near term, much less systems that can remove all microbes and viruses.

Because of these various issues, we recommend that the zero detectable discharge standard approach not be used at the national level. If, however, zero detectable standards are considered at the national level, it is critical to define th e sampling protocols to be used to verify ballast water treatment systems and in compliance monitoring. Without this information, the meaning of the standard is undefined, making it impossible to assess the actual risk or to enforce it in a scientifically defensible fashion.

Natural Invasion Rates: The natural invasion rate approach was proposed by Dr. Andy Cohen in an August 7, 2005, memo to the California Ballast Water Treatment Standards Committee. As noted by the California State Lands Commissi on, “this approach is based on numerous assumptions that create a high level of uncertain ty for its application to performance standards that will have regulatory impacts.” Because of these uncertainties, California did not use the natural invasion rate approach to set their state st andards. Nonetheless, the natural invasion rate approach is worth examining since it addresses generating ballast water di scharge standards in a novel way.

xiiThe rationale for the natural invasion rate appr oach is that marine/estuarine ecosystems are subject to a very small natural ra te of invasion from rare events when species drift or raft across

oceans and then become established in new locati ons. A ballast water discharge standard that resulted in an invasion rate approximately equal to the natural rate would be “reasonably close to the natural rate and possibly within the normal ra nge of variation, and thus would be reasonably protective of the environment.” To generate a di scharge standard from natural invasion rates, four parameters are needed: 1) natural invasion rate; 2) histori cal invasion rate from ballast discharges; 3) organism concentr ations in ballast water; and 4) speciation rate. Of the four parameters, the major limitation is estimating the natural invasion rate with any degree of certainty; indeed, three invasion experts at the California meeting differed by 100-fold in the their estimates of this rate. Our analysis suggest s that the full range of uncertainty could be as much as 10,000 fold in the standards dependi ng upon estimates of ballast water organism concentrations, whether additiona l taxa are included in the analysis, and whether natural invasions from other areas in the North West Pacific region are considered. Additionally, our analysis of the literature indi cated a much greater genetic ex change across the Pacific than suggested by the low estimates of natural invasion rates in the Cohen analysis. Because of these uncertainties, we do not believe the natural invasi on approach is suitable for the development of

national ballast water di scharge standards.

Reaction-Diffusion Models: Reaction-diffusion models pred ict the concentration of a “substance” that is simultaneously influenced by diffusion which di lutes it and by some type of reaction affecting its con centration. The basic assumptions of th is family of models in terms of invasions are: 1) they model continuous time a nd space; 2) there is local random movement of individuals; and 3) popul ation dynamics are deterministic. Wh en applied to ballast water, the two competing processes are the dilution of the ballast water cont aining the introduced organisms, which rarefies the populations, and the population growth rate of the organisms in the ballast discharge. If the dilu tion of the species is too fast, the population goes extinct.

The primary use of reaction-diffusion models in invasion biology has been the theoretical analysis of the pattern of inva sion spread of terrestrial invade rs. The only published example of a reaction-diffusion model applied to ballast water is that of Drak e et al. (2005). Using changes in relative population densities , Drake et al. (2005) predicte d the maximum safe volume of ballast water that could be exchanged. Because these predictions are volume based, they can not be used to generate organism-based standards. On a more general level, our analysis indicates that violation of the assumption that species are passively distributed is likely to result in a

substantial underestimation of the likelihood of establishment of a species. In particular, benthic species whose larval and/or juvenile phases ac tively settle out of the water column are much more likely to become established than predic ted from dilution models. Thus, in aquatic environments, diffusion models are primarily limited to predicting invasions of small, holoplanktonic organisms, such pelagic copepods . Because of this limitation, diffusion models do not appear to be suitable for generating concen tration-based discharge st andards applicable to the wide range of taxa found in ballast water.

xiiiPopulation Viability An alysis (PVA) Models: Population viability analysis (PVA) models are a family of population growth models commonly us ed to predict the extin ction probability of endangered species. The basic premise of PVA models is that any population undergoing stochastic growth has a certain probability of going extinct even if it is presently showing positive growth. In general, the smaller the population size, the slower the population growth rate, or the larger the variation in population growth rate, the great er the probability of extinction. When used with nonindigenous species, the objective is to predict either th e time to extinction or the probability of extinction for an invader, wher e extinction is the convers e of establishment of

a new invader.

A PVA model was used in the USCG Draft Pr ogrammatic Environmental Impact Statement (DPEIS), which we reviewed in detail because it is part of the technical analysis used by the USCG in setting their proposed rules and because it is the only study that has used a PVA model to address generating ballast water standards. Th e key parameters that need to be estimated in the form of the PVA model used in the DPEIS are the instantaneous population growth rate, instantaneous variance of the popul ation growth rate, and the cr itical population density (the threshold at which the population is considered “extinct”). The strategy taken in the DPEIS was to evaluate different discharge standards by pred icting the relative increase in the probability of

extinction based on the fractional reductions in the number of organism s per cubic meter of ballast discharge among the different standards. Th is is a relative approach and as such does not generate organism-based discharge standards. The PVA analysis was conducted both for single species and for multiple species in a ballast disc harge, though we contend that the latter, which predicts the risk of any invasi on occurring from a discharge, is the more ecologically relevant analysis.

A potentially confusing strategy in the DPEIS wa s to compare relative decreases in organism concentrations resulting from different standard s to the full range of or ganism concentrations found in unmanaged ballast water and ballast water after exchange. In se veral cases, the use of these extreme ranges obscured the long-term benefits from reducing organism concentrations. Our reanalysis suggests that the re lative reduction in risk was greater than indicated by some of the analyses in the DPEIS. Additionally, values for several of the parameters in the DPEIS were not well justified. For these re asons, and because the analysis was based on relative risks among treatment alternatives, we suggest that the DPEIS analysis should not be used to generate new national standards. However, vers ions of PVA models that predict actual (vs. relative) risk of invasion may be a viable appro ach to generating organism-based standards. The limitation to developing such models is the lack of in stantaneous population growth rates and the

instantaneous variances of the growth rates for a range of taxa. While it may be possible to estimate instantaneous population growth rate through various methods, long-term population

studies are needed to estimate the instantaneous variance of the population growth rate. To assist in generating these population vital rates, we identify a number of sources summarizing longterm population studies with marine /estuarine organisms. If new PVA are used to generate new national standards, a comprehens ive sensitivity analysis should be conducted. In particular, a range of instantaneous growth rates and instantaneous variance s in growth rate should be explored, with the ranges based on an extensive review of population dynamics.

xivPer Capita Invasion Probability: During the process of generati ng this synthesis, the authors developed a new method of generating ballast wate r discharge standards th at appears to resolve many of the limitations associated with the othe r approaches. Based on the general consensus that an increase in propagul e supply increases the likelihood of invasion, we developed a “per capita invasion probability” (PCIP) approach to estimate the likelihood of invasion based on

historical invasion rates and calcu lated ballast-associated propagule pressure. The PCIP is the per year probability that an individual non-native propagule discha rged from ballast water will become established as a new nonindigenous spec ies in a specified waterbody. Using a lineardose response assumption, the PCIP is calculated from the historical number of potential ballastmediated invasions in a specifi ed waterbody over a defined time period, the average annual total ballast discharged at that location during this time period, and the estimated organism concentration in the discharged ballast water. Once a PCIP is calculated from historical data, it can be used to predict the ra te of new ballast-associated in vasions in a waterbody with a projected ballast discharge volume and organism concentration. By altering the organism concentration, it is possible to generate risk scenarios predicting the number of new invaders for different discharge standards.

Historical invasion rates were estimated for the period from 1986 to 2005 and ballast discharge

rates were obtained from the National Ba llast Information Clearinghouse for 2005 to 2007, which represent the most complete records after mandatory ballast water reporting was

instituted. A distribution of or ganism concentrations in unma naged ballast water was obtained from published estimates and a simulation conduct ed to predict a range of possible organism concentrations. Using these inputs, an analysis was conducted for the East, Gulf, and Pacific

coasts of the coterminous United States as well as for 17 individual co astal estuaries. In addition, a preliminary analysis was carried out for the Great Lakes. Predictions across individual estuaries showed high variation, pos sibly due to secondary invasions from other estuaries or ports. The three coast-wide es timates, which eliminate the uncertainty with secondary invasions, showed only a 6-fold vari ation even with the large differences in environments, donor regions for invaders, and inte nsity of nonindigenous sp ecies surveys. Risk diagrams were then constructed that illustrate the relationship of the likelihood of invasion to organism concentrations and ballast water disc harge volumes, which allow risk managers to

assess the risk with different discha rge standards and safety factors.

As with any method, the per capita invasion rate approach makes a number of assumptions. The approach may underestimate the risk of invasion from asexual and parthenogenic species. It also assumes no change in the invasion potential of new invaders or in the inva sibility of a specific waterbody over time. These types of uncertainti es can be addressed by risk managers by adding a safety factor to the predictions . Because this approach is based on relatively well-known input values and allows risk managers to generate or ganism-based standards, we recommend that the per capita invasion probab ility be considered for the deve lopment of national standards.

Experimental Studies: Laboratory and field experiments can be used to quantify the likelihood

of invasion under controlled environmental conditi ons and dosing scenarios. Over the last decade both the number and sophistication of su ch experiments have increased using both freshwater and marine organisms. However, we conclude that it is impractical to derive discharge standards from laboratory or field expe riments because of the: 1) impracticality of

xvadequate replication to quantify rare events; 2) limitation in the number and types of species than can be experimentally manipulated; and 3) ar tificiality and simplification of laboratory experiments and, to a lesser extent , field experiments. The real pow er of these experiments is to advance the theory of propagule supply and to evaluate and parameteri ze different types of population models.

Statistical Considerations in Estimating Concen trations of Organisms in Ballast Discharges: The stringent discharge standards that have been proposed will require estimating very small concentrations of organisms in ballast water. At these low densities, very large volumes of water must be sampled to find enough organisms to begi n to estimate the actual concentration. To assess the requirements for a statistically ri gorous sampling protocol, we assumed a random (Poisson) distribution of organisms in a set of samples. We then calculated the upper possible concentration (UPC) of organi sms based on one-tailed 95% c onfidence intervals when zero organisms are detected in a range of sample vol umes. For a 1 L sample with no organisms, the UPC was almost 3000 organisms m -3 while for a 10 m 3 sample the UPC was 0.3 organisms m -3

. Thus, even if no organisms are detected in a very large sample (10 m 3 ), the actual concentration could be 30 times greater than th e USCG Phase II standard of 0.01 m -3 . As large as these volumes are, they likely underestimate the volume s needed if the organisms are aggregated or clumped.

Based on our analysis, it is apparent that instituting standardized sampling protocols is a critical component of implementing ballast discharge standards. One possi ble strategy is to require the large sample sizes required for high statistical po wer during the validation of treatment systems, in particular with land-based testing facilities . Practical considerations may limit the role of compliance monitoring to detecting gross viola tions, though detection of poor performing ships would be improved if there was a global repository of compliance test results for individual ships so as to track compliance over time with multiple samples. It is important to note that these analyses assume that the goal of discharge standa rds is to directly regul ate the concentration of organisms in ballast discharges using “averag e based sampling”. However, if “maximum instantaneous” discharge standards are used, then additional statistic al factors must be considered because the results will be very sens itive to the sample number and volume.

xvi

### I. INTRODUCTION

Henry Lee II

Objectives and Scope of Report: The U.S. Environmental Protection Agency (EPA) is currently evaluating organism-based ballast water discharge standards (= performance standa rds or effluent limits), where organism-based standards are based on the concentrations of viable organisms in the discharged ballast water. To support this effort, the objectives of this report are to: 1) summar ize approaches that have been used or proposed to establish organism-based ballast water discharge standards that prevent and/or protect aquatic ecosystems from ballast mediated invasions and 2) assess the potential utility and limitations of these methods. While not an original objective, during the process of synthesizing these approaches we developed an approach to the generation of discharge standards that we believe offers a practical alternative (Section VIII: Per Capita Invasion Probabilities). The purpose of our review is to provide the technical background for the U.S. EPA and a National Academy of Sciences (NAS) expe rt panel to evaluate the technical merits of approaches to generating effluent limits for livi ng organisms in ballast water discharges. The review focuses on organisms > 50 microns, which includes most holoplanktonic organisms (e.g., calanoid copepods), pelagic species such as fishes, and larval stages of be nthic organisms. We focus on this size class because most of the theoretical, empirical, and experimental studies have focused on these larger organisms. To the exte nt possible, we assess whether an approach is potentially applicable to organisms in the 10-50 micron size class, su ch as phytoplankton and protozoa. The human health endpoints for micr obes and viruses are beyond the scope of this document but a brief overview of the approach used to establish microbial ballast water standards is given in Appendix A. We also do not review the efficacy or practicality of various ballast water treatment systems, which have been addressed elsewher e (e.g., Lloyd’s Register, 2008; Gregg et al., 2009).

On the basis of ecological principles, we iden tified seven general approaches to generating organism-based ballast water discharge standards for organisms >50 microns, each of which is

evaluated: 1) Reduction in Propagule Supply Based on Expert Opinion/Management Consensus 2) Zero Detectable Living Organisms 3) Natural Invasion Rates 4) Reaction-Diffusion Models 5) Population Viability Analysis (PVA) Models 6) Per Capita Invasion Probability 7) Experimental Studies

Although not an approach to setting standards pe r se, sampling issues need to be considered when assessing the practicality of verifying that a discharge standard has b een met either in test facilities for purposes of regulat ory approval of a treatment syst em or as part of compliance monitoring of vessel discharges. As discussed in Section IV, the sampling protocols define the

actual risk levels associated w ith the “zero detectable living organisms” approach. Accordingly,

1we address the statistical consid erations of the volume of water that needs to be sampled when estimating the concentrations of organi sms in ballast water discharges.

Niche or species distribution models that predic t the potential distribut ion of species based on

environmental conditions are not considered. While these models can be used to predict current

and future distributions of an individual non- native species after it has invaded (e.g., Peterson and Vieglais, 2001; Herborg et al., 2007; Reu sser and Lee, 2008), they do not address the likelihood of invasion via ballast water discharges.

Nonindigenous Species Background: Introductions of nonindigenous species (NIS) 1 , also known as aquatic nuisance species (ANS), are recognized as one of the major environmental stressors in freshwaterand marine/estuarine ecosystems. Examples of individual invasive species having deleterious impacts on aquatic systems include the zebra mussel ( Dreissena polymorpha ) in the Great Lakes and other freshwater systems (Drake and Bossenbroe k, 2004) and the European green crab ( Carcinus

maenas ) on both the Atlantic and Pacific coasts (C arlton et al., 2003). Other indicators of the prevalence of nonindigenous species are their dominance in benthic communities in the San Francisco Estuary (Lee et al., 2003) and the larg e number of invaders fo und on the East, Gulf, and Pacific coasts of the United States (e.g., Ruiz et al., 2000; Wonham and Carlton, 2005). It is beyond the scope of this document to review the effects of nonindige nous species on aquatic systems, and the reader is referred to previ ous reviews on the ecologi cal, human health, and economic impacts of invasive species (e.g., McMi chal and Bouma, 2000; Pimentel et al., 2005; Lodge et al., 2006). Additionally, implications of invasions of nonindigenous species on the ability of the EPA to achieve its environmental goals and mandates as of 2000 were reviewed by Lee and Chapman (2001).

Nonindigenous species can potentially invade a quatic systems through a variety of mechanisms (Ruiz and Carlton, 2003). Of these potential ro utes, shipping, including both ballast water discharges and hull fouling, is the primary vect or for biological invasi ons in the Great Lakes (Duggan et al., 2003) and most marine/estuarine ecosystems (Ruiz and Carlton, 2003; Hewitt et al., 2009) with the notable exception of the Medi terranean where Lessepsian invasions through the Suez canal is the major invasi on mechanism (Galil and Zenetos, 2002). In the past century, the increase in shipping traffic as well as the reduced time for transoceanic voyages has increased the number and abundance of nonindige nous species arriving in new environments around the world (Ruiz et al., 1997). This increasing propagule s upply appears to have increased

the rates of invasions in a num ber of aquatic ecosystems (e.g., Cohen and Carlton, 1998; Holeck et al., 2004; but see Costello and So low, 2003 and Drake et al., 2005).

Of the sub-vectors associated with shipping, ballast water is a major source of nonindigenous species in both the Great Lakes and most mari ne/estuarine environmen ts (Carlton and Geller 1993, Carlton 1996; Fofonoff et al. 2003a; Holeck et al., 2004; Hewitt et al., 2009). When ships

1 The terms “nonindigenous species” and “non-native species” are used to denote species that were introduced via anthropogenic vectors into a novel location with no speci fic connotation of ecological , human health, or economic impacts. “Invasive species” is used to denote a nonindi genous species for which there is evidence of an adverse impact on ecological, human health, or economic endpoints. (Executive Order 13112; http://www.invasivespeciesinfo.gov/laws/execorder.shtml ).

2take on ballast water to compensate for changes in load, vast assemblages of aquatic organisms are collected and then discharged into subsequent ports. This inte rnational transfer of organisms is massive – untreated ballast discharges can contain thousands of organisms per cubic meter (Minton et al., 2005) and the total foreign ballas t discharged in the United States in 2004-2005 was over 73 million metric tons (Miller et al., 2007; also see National Ballast Information Clearinghouse (NBIC), http://i nvasions.si.edu/nbic ).

IMO Ballast Water Treaty and Proposed USCG Standards Background: The first approach to managing this vector was to implement mid-ocean ballast water exchange, where ballast was exchanged either through flow -through of the ballast or empty-and-refill. Ballast water exchange, and similar treatment for vessels declaring “No Ballast on Board” (NOBOBs), have been shown to reduce the numbe r of living organisms in ballast water tanks which are adapted to living in both freshwater and coastal/estuarine environments, thereby reducing the risk of invasion (Gray et al., 2007; Locke et al., 1993; McCollin et al., 2007; Ruiz and Reid, 2007; Cordell et al ., 2009; see summary of 4.3 in U. S. EPA, 2008a). Though ballast water exchange and saltwater flushing may reduce th e risk of invasion, a nu mber of studies have shown that ballast water exchange was not suffi ciently effective or c onsistent in reducing organism concentrations in ballast water espe cially in coastal/estuarine environments (e.g., Locke et al., 1991; see summary in Section 4.3. 2 of USCG, 2008). Additionally, in many cases,

it is not safe for vessels to conduct ballast wa ter exchange, given constraints of design and

construction.

In response to this concern, nati onal and international efforts bega n to evaluate other options for managing ballast water discharges. Ultimately, a key decision was made to base ballast water discharge standards on the concentr ation of organisms in discharged ballast water, rather than on the percentage of ballast water exchanged dur ing mid-ocean exchanges. Through the Marine

Environment Protection Committee (MEPC) of the International Maritime Organization (IMO),

an international ballast wate r treaty (“The International Convention for the Control and Management of Ships' Ballast Water and Sediment s, 2004”) was initiated to reduce the spread of nonindigenous species through ballast water tran sport (IMO, 2004a). An overview of the IMO

international convention can be found in Gollash et al. (2007). A key section of the IMO treaty (Regulation D-2) sets standard s for the maximum concentratio ns of organisms allowed in discharged ballast water based on different size groups of organi sms (Table 1). The treaty has not yet entered into force, and while recognized as a major step forward, the IMO standards are considerably above those proposed by the United States (<0.01 organisms m -3 ; IMO, 2004b). In response to concerns that the IM O standards were not sufficiently protective, a number of states, such as California and Wisconsin, have initiate d or passed more stringent discharge limits for

ballast water.

The United States Coast Guard (USCG) res ponded to this concern by preparing a draft Programmatic Environmental Impact Statement on ballast water discharges (USCG, 2008) and then proposing a two phase implementation of di scharge standards (USCG, 2009). The proposed USCG Phase I standards are equivalent to the IMO D-2 standards, while Phase II is 1000-fold more stringent (Table 1). Additionally, Calif ornia and some other states have proposed alternative standards with the ultimate goal of “no detectable” discharges of organisms in ballast water (Table 1).

3Table 1: Existing or proposed international and national ballast water discharge standards applicable to the waters of the United Statesand examples of state standards. All organism dimensions are for the “minimum dimension”. Standards for the >50 micron and >10 -<50 micron classes are for “viable” or “living” organisms. Notethat Phase II of the Coast Guard standard can be implementedincrementally. The date for the implementation of the final California standard is 2020. The California standards are from theCalifornia State Lands Commission (2009). The Wisconsin standards are from the Wisconsin Department of Natural Resources(2010). The California standards are instantaneous standards while those for Wisconsin are daily averages. NPRM = Notice ofproposed rule making. IMO = International Maritime Organization. cfu = “colony forming units”Organism ClassIMO D-2StandardUSCGNPRM Phase IUSCGNPRM Phase IIWIState StandardCAInterim StandardsCAFinal StandardOrganisms >50microns<10 per m3<10 per m3<1 per 100 m3(< 0.01 per m3)<1 per 10 m3(<0.1 per m3)“No detectableliving organisms”“Zero detectableliving organisms”Organisms >10 ­<50 microns<10 per ml<10 per ml<1 per 100 ml(<0.01 per ml)<1 per 10 ml(<0.1 per ml)<1 per 100 ml(<0.01 per ml)“Zero detectableliving organisms”Organisms <10micronsNo standardNo standard<103bacteria/100 ml<104viruses/100 mlNo standard< 103bacteria/100ml< 104viruses/100 ml“Zero detectableliving organisms”Escherichia coli<250 cfu per100 ml<250 cfu per100 ml<126 cfu per100 ml<126 cfu per100 ml<126 cfu per100 ml“Zero detectableliving organisms”Intestinalenterococci<100 cfu per100 ml<100 cfu per100 ml<33 cfu per100 ml<33 cfu per 100ml<33 cfu per100 ml“Zero detectableliving organisms”ToxicogenicVibrio cholerae(serotypes O1 andO139)<1 cfu per 100 mlor1 cfu per g wet wt.zooplankton<1 cfu per100 ml<1 cfu per100 mlNo standard<1 cfu per 100 mlor<1 cfu per g wetzoological sample“Zero detectableliving organisms”4U.S. EPA Regulatory Background: Under the Clean Water Act (CWA), the U.S. EPA has the responsibility for managing the National Pollutant Discharge Elimina tion System (NPDES) Program (see http://cfpub.epa.gov/npdes/home.cfm?program_id=45 ) . Under the NPDES Pr ogram, all facilities that discharge pollutants from any point source into waters of the United States generally are required to obtain an NPDES permit (U.S. EP A, no date; U.S. EPA, 1996; see also CWA § 301(a)). Since the early 1970’s, EPA regulations (40 C.F.R. 122.3(a)) ha d excluded discharges incidental to the normal operation of vessels (including ballast wate r) from the need to obtain an NPDES permit (see http://www.epa.gov/owow/invasive _species/ballast_water.html ). However, that exclusion from the NPDES permitting program was successfully challenged in court, and as a result, was vacated (struck down) by the U.S. District Court for the Northern District of California ( Northwest Envtl Advocates et al. v. United States EPA, No. C 03–05760–SI (December 17, 2008) (vacatur of 40 C.F.R. 122.3(a) as of February 6, 2009)). For a further description of the lawsuit, see also, Northwest Envtl. Advocates v. EPA , 537 F.3d 1006 (9th Cir. 2008). In light of the court decision, in December 2008, EPA issued a general NPDES permit (known as the “Vessel General Permit” or “VGP”) that contains, among ot her things, effluent limits for ballast water discharges from non-recreational vessels (U.S. EPA, 2008b; http://cfpub.epa.gov/npdes/home.cfm?program _id=350 ). Specifically, “The 2008 Vessel General Permit (VGP) regulates discharges in cidental to the normal operation of vessels operating in a capacity as a means of transporta tion. The VGP includes general effluent limits applicable to all discharges; general effluent lim its applicable to 26 spec ific discharge streams; narrative water-quality based effluent limits ; inspection, monitori ng, recordkeeping, and reporting requirements; and additi onal requirements applicable to certain vessel types.

Recreational vessels as defined in section 502(25) of the Clean Wate r Act are not subject to this permit. In addition, with the exception of ballast water discha rges, non-recreational vessels less than 79 feet (24.08 meters) in length, and all comm ercial fishing vessels, regardless of length, are not subject to this permit.” (U.S. EPA, 2008b)

EPA currently is undertaking development of or ganism-based effluent limits (discharge standards) for ballast water discharges for use in the future reissuance of the VGP. To help ensure it uses a scientifically sound approach in that effort, EPA is seeking an objective and independent scientific opinion on approaches for de riving these standards. As part of the effort to achieve that objective, this document synthesi zes potential approaches to generating organismbased discharge standards. This synthesis is a component of the risk assessment process. As pointed out by EPA’s Office of the Science Adviso r, “The primary purpose of a risk assessment is to inform the risk manager’s decision ma king process. The primary purpose of a risk assessment is not to make or recommend any pa rticular decisions; rath er, it gives the risk manager information to consider along with ot her pertinent information.” (U.S. EPA, 2004a). Accordingly, it is not the purpose of this doc ument to propose specific discharge standards, which is a risk management decision that inco rporates additional fact ors potentially including existing laws, social factors, economics, and feasibility.

5Challenges in Setting Organis m-Based Discharge Standards: Predicting the rate of invasion into specific wate r bodies from ballast water and/or other vectors with a high degree of accuracy is one of the most complex problems in applied ecology. The invasion process can be viewed as a series of stages, ranging fr om the initial entrainment of a potential invader in its native environment to its establishment and sp read in a novel location (e.g., Sakai et al., 2001; Ruiz and Carlton, 2003). Each of these stages is confounded with its own suite of complexities and uncertainties, with ex amples listed in Table 2 (also see Ruiz et al., 2000). The purpose of listing these complexities/uncer tainties is not to imply that the problem is insurmountable but rather to help set reasonable e xpectations about what is possible in the nearterm given the nature of the problem and the stat e of the science. Realistically, development of discharge standards will require a number of si mplifying assumptions, and the 1000 fold range in quantitative standards for the >50 micron class (Table 1) reflects, to a larg e part, differences in the assumptions made. Therefore, one of the objec tives of our review is to identify the major stated and implied assumptions of each of the approaches and whether they tend to under- or overestimate the likelihood of invasion via ballast water. Additionally, with this level of complexity we suggest that it is unrealistic to expect development of highly predictive,

mechanistic models in the foreseeable future. However, we believe it is possible to generate standards that are prot ective of the environment under most situations by making “conservative” assumptions, using safety factors similar to t hose used in ecological risk assessments for pollutants, and/or by setting the standards based on the upper confidence limits of predictions of invasions. The risk management challenge will be to set standards that balance the level of protection afforded versus their technol ogical feasibility a nd economic viability.

6Table 2: Examples of complexities and uncerta inties confounding the predic tion of invasion rates

via ballast water.

Ports, Ship Routes, and Ballast Water

● Over 100 ports in the United States and its territories, ranging from the sub-Arctic to the tropics, both receive foreign ballast water discharges and donate ballast to foreign ports.

● Over 1000 foreign ports across nearly every biogeographic ecoregion that are potential sources of ballast water discharged in the United States.

● Changes in dominant source regions as trade rout es are modified in response to changes in the economies at regional, national, and global scales.

● Ship voyages that span multiple forei gn and domestic ports a nd biogeographic regions.

● Mixing of ballast water from multiple waterbodi es and/or biogeographic ecoregions within a single

voyage.

● Changes in absolute and relative densities of species within ballast tanks during a voyage.

● Different voyage durations and effects on concentrations within ballast water tanks.

● Among-ship variation in organism con centrations and ballast discharge volumes.

Vectors and Propagules

● Stochasticity in the mix of species originally entrained in ballast water in the source waterbody.

● Species that can invade via multiple vectors (polyvectic invaders).

● Uncertainty in the nature of the propagule dose-r esponse relationship for any particular species at any place or time.

● Secondary invasions into a wate rbody from other regional waterbodies.

Invasibility of Recipient Waterbody

● Extent of environmental matching between the donor and recipient regions and uncertainty in how to quantify similarity among environments.

● Seasonal changes in invasibility within a waterbody.

● Long-term changes in invasibilit y within a waterbody due to envi ronmental trends (e.g., increase in nutrient loading).

● Long-term changes in invasibility with in a waterbody due to climate change.

● Differences in invasibility among differe nt waterbodies and biogeographic ecoregions.

● Differences in existing pool of NIS among waterbodies (resulting in whether a specific non-native species represents a “new” invader to the waterbody).

Establishment and Spread of New Invader

● Uncertainty regarding popula tion dynamics at low densities

● Competitive interactions with existing flora and fauna.

● Predator/prey interactions with existi ng flora and fauna in the invaded ecosystem.

● Feedback between existing NIS and estab lishment of new NIS (biological meltdown).

● Determining whether a NIS is actually est ablished within a waterbody or ecoregion.

Taxonomy and Sampling Biases

● Underestimation of the extent of invasion w ithin a waterbody because of taxonomic difficulties in

identification of new invaders.

● Differences in extent of invasion among water bodies or regions because of different sampling efforts and/or taxonomic expertise.

7

### II. PROPAGULE SUPPLY DOSE-R ESPONSE AND ALLEE EFFECTS

Henry Lee II and Deborah A. Reusser

Two major factors driving the li kelihood of invasion are the nature of the propagule supply doseresponse relationship and Allee effects on populati on dynamics. We first discuss Allee effects and then propagule dose-response re lationships before addressing sp ecific approaches to setting

ballast water standards.

Allee Effects: Allee effects are reductions in the per capita popula tion growth rate in sparse populations. Such depressions in individual grow th rates in rarefied populati ons may occur due to several potentially interacting mechanisms (see Stephe ns and Sutherland, 1999; Courchamp et al., 1999; Berec et al., 2006; Kramer et al., 2009) including: 1) Mate limitation (i.e., difficulty in finding a mate at low densities). 2) Genetic inbreeding a nd loss of heterozygosity. 3) Demographic stochasticity of a sma ll population, which may result from random

fluctuations in sex ratios and/or birth rates or envir onmental perturbations. 4) Increased predation due to less effective or lack of predator swamping. 5) Increased predation due to less effectiv e cooperative defense against predators. 6) Absence or reduction of cooperation in so cial species, including cooperative feeding. 7) Absence or reduction in habitat altera tion that increases fitness of recruits. 8) Increased dispersal away from areas of low density.

A distinction is made between “weak” and “str ong” Allee effects (Tay lor and Hastings, 2005; Kramer et al., 2009) (Figure 1). A weak Allee eff ect depresses the per cap ita growth rate at low densities, but the per capita growth rate remain s positive. In comparison, a strong Allee effect results in a negative per capita growth rate belo w a threshold density, refe rred to as the “critical density”. With deterministic population growth models, the population will go extinct after it falls below its critical density unless ther e is immigration of new individuals.

Allee effects are predicted to ha ve major impacts on the likelihood that an invader will become

established and on its rate of spread (e.g., Lewis and Kareiva, 1993; Drake, 2004; Taylor and Hastings, 2005). Unfortunately, there is limited empirical evidence regard ing the role of Allee effects in natural populations, or th e densities at which they might occur. In a review of Allee effects with marine organisms, Gascoigne and Lipcius (2004) found little evidence for widespread Allee effects in marine populations, though they di d find “suggestive observations” with exploited fish and shellfish populations, as well as with broadcast spawners, a common breeding type among marine/estuari ne invaders. In a more complete meta-analysis of natural populations, Kramer et al. (2009) concluded that Allee effects have been documented in a range of taxa, including mollusks, arthropods, and chorda tes (including three cla sses of vertebrates). They also concluded that there wa s evidence that these effects occu rred through at least six of the

mechanisms listed above.

8In assessing the likelihood of Allee effects in populations of non-native species introduced via ballast water discharges, it is im portant to recognize that the dens ity of any individual species will be very low given the proposed discharge sta ndards (Table 1). This density will be further reduced by dilution of the ballast water in th e receiving water. As an upper case example assume: 1) total discharge concentration of zooplankton equal to th e IMO standard of 10 organisms m -3 ; 2) the most abundant species constitutes 50% of the discharged individuals; and 3) a 10-fold dilution of the ballast water when di scharged into the receiving water. Under this scenario, the density of the most abundant species is 0.5 organisms m -3 in the receiving water. As a lower case scenario, assume: 1) a total zooplankton concentration proposed in Phase II by the USCG of 0.01 organism m -3 ; 2) the most abundant species c onstitutes 10% of the discharged individuals; and 3) a 50-fold diluti on of the ballast water. With this scenario, the density of the most abundant species is 0.00002 individuals m -3 . These two scenarios are for planktonic species, but the low discharge sta ndard concentrations and dilution in the receiving waters would

also result in low densitie s of benthic organisms.

B. Weak Allee Effect

0 Density Density C. Strong Allee EffectPer Capita Growth Rate

0 Density A. No Allee Effect

0

Critical Density

Figure 1: Illustrations of Allee effects on per capita population growth. The per capita rate declines at higher populati on densities in all three scenarios due to intraspecific interactions such as competition. Scenario A illustrates the case wh ere there is no Allee effect and the per capita

rate increases at lower densities. Scenario B i llustrates a weak Allee effect where there is a decline in the per capita growth rate at lower population densities but th e growth rate does not became negative. Scenario C illustrates a strong Allee effect where the pe r capita growth rate declines below 0 at population levels below the “cr itical density”. (Modified from Taylor and Hastings, 2005)

Propagule Supply Dose-Response: The concept that invasion risk decreases with decreasing propagule supp ly is the fundamental assumption behind the IMO and USCG ballast water performance standards. This assumption is supported by a wide body of empirical, theoreti cal, and experimental evidence showing that invasion success increases with an increase in pr opagule supply, either by a higher concentration of organisms in an inoculation and/or by an increase in the frequency of inoculations (e.g., Simberloff, 1989, 2009; Ruiz et al., 2000; Ko lar and Lodge, 2001, Ruiz and Carlton, 2003; Lockwood et al., 2005; Johnston et al., 2008). The difficulty is that the nature of the doseresponse relationship (Figure 2) is unknown, and “we cannot predict the co rresponding change in

invasion success in terms of eith er the type (general shape) of the response or the specific magnitude (slope) of the respons e” (Ruiz and Carlton, 2003).

9While it is not possible to predict the exact sh ape of the dose-response, two generalities are possible in context of generating discharge standards. First, there is likely to be a saturation dose beyond which any increase in the number of organi sms is unlikely to increase invasion success. In most cases, organism concentrations are likely to be well below this saturation value. The second generality is that the linear dose respons e is likely to be a reasonably protective first approximation for many, if not most, species and densities. At low concentrations, actual invasion probabilities are likely to be lower than that predicted from a linear dose response

because of Allee effects and stochastic events . At higher organism concentrations, response slopes that are steeper than the li near model (e.g., curves a and b in Figure 2) imply some type of positive intraspecific facilitation that increases the likelihood establishment. While there are examples of intraspecific facilitation in freshw ater and marine/estuari ne species (e.g., Leslie, 2005; Nilsson et al., 2006), they appear to be the exception rather than the rule and do not appear to be sufficiently strong to resu lt in invasion probabilities substa ntially greater than the linear

model.

There are, however, important exceptions to the generalization that establishment is unlikely at very low densities. In experime ntal studies with freshwater cladocerns, Bailey et al. (2009) found that the probabili ty of establishment of the parthenogenic Daphnia retrocurva can be >0.1 with an inoculum density of only 1 individual m -3 . Simberloff (2009) cites several cases of mammals and insects where release of just a few individuals resulted in establishment of a nonnative species. One sobering example is that all of the Indian mongooses ( Herpestes

auropunctatus ) in the West Indies were initially derived from just five females and four males. However, Simberloff goes on to cite the “Noah fallacy” proposed by Jim Ca rlton - that a single breeding pair suffices for an introduction to take hold and spread. While recognizing the cases where a minute propagule supply was responsible for a successful invasion, Simberloff concludes, “if we think probabilis tically (and invasion biology is largely a probabi listic science), the metaphor of Noah’s fallacy is correct in spirit, because for most if not all species the probability of such an event is small, even vanishingly small, and larger propagule sizes drastically increase the probability of establishmen t.” In terms of setting ballast water discharge standards, the possibility that a single mated female or part henogenic individual may result in a successful invasion needs to be acknowledged. However, the only standard that would completely eliminate this possibility is the disc harge of sterile water, which not even the “zero detectable organism” standard can provide because of the impracticality of collecting a sufficient ballast water sample to detect a zero concentrat ion with a high confidence (see Sections IV and X). Thus, all practical standards contain some risk of invasion, though to varying extents they can substantially reduce this risk as discussed below.

10

### Propagule Supply Probability of Invasion Success

Increasing number of organisms/m 3 Increasing probability



### Allee effect

Propagule Supply Propagule SupplyProbability of Invasion Success

Increasing number of organisms



### Allee effect

Figure 2: Hypothetical propagule supply dose-res ponse curves. Potential responses include; a) exponential; b) sigmoid; c) linear; and d) logarithmic or hyperbolic. Th e triangles denote the range in invasion probabilities pr edicted at a single propagule dose (X) for different response models. The exponential and sigmoid models demons trate the possible influence of Allee effects on invasion dynamics, and the double-headed arro w shows the reduction in invasion probability, relative to the linear model, due to Allee eff ects. The box on the left illustrates that the propagule doses associated with the proposed discharge standards (Tab le 1) are likely to be very low. (Modified from Ruiz and Carlton, 2003).

11

### III. REDUCTION IN PROPAGULE SUPPLY BASED ON EXPERT

OPINION/MANAGEMENT CONSENSUS

Henry Lee II

Overview: Several of the proposed discharg e standards were based on a comb ination of expert opinion and management consensus. As used here “expert op inion” refers to technical recommendations for ballast water standards from experts in the ar eas of invasion biology a nd related life sciences made without the explicit use of a quantitative invasion model. “Management consensus” is used to capture decisions made utilizing this e xpert opinion as well as inputs from experts in other disciplines, such as shipping and engineerin g, risk managers, as well as state, national, nongovernmental organization (NGO), and industry representatives. Thus, management consensus decisions incorporate components of risk assessment, risk ma nagement, and lobbying. With homage to G. E. Hutchinson (1965), the consensus process can be characte rized as a scientific opera staged by experts in a political theater.

Perhaps the apogee of a consensus driven proces s was the derivation of the IMO D-2 standards for the >50 micron and 10-50 micron size groups. (IMO standards for microbes and viruses were derived from existing human h ealth criteria and thus had a di fferent origin.) As discussed below, there were several meetings of national and international invasi on experts prior to and during the IMO convention evaluating the scientific merits of possi ble standards. At the treaty convention itself, however, the vast majority of th e delegates were not inva sion experts and, as is true of any internationa l treaty negotiation, the delegates had a wide range of agendas. Thus, the

scientific recommendations from the invasion experts were only one of a suite of factors going into deriving the IMO standards. Additionally, both national and state bills have been drafted (e.g., S. 1578 (110th Congress), “The Ballast Water Management Act of 2007;” see also, accompanying S. Rept. 110-269) with performance standards apparently reflecting an expert opinion/management consensus approach. We suggest that this includes California’s “zero detectable discharge” approach as well, though it is discussed separately because of the ambiguity regarding the exact concen trations of the standards.

It is beyond the scope of this document to a ttempt to decipher the management consensus decision making process at the IMO treaty negotiations or in the derivation of the proposed/existing national bills or state regula tions. Rather, we will address the scientific benefits/limitations of an expert opinion approach to generating recommendations for risk managers. We will also summarize the expert op inion process leading up to the IMO convention as an example.

Rationale: The major advantage of expert opinion is that it is possible to address complex issues even with limited data and in the absence of quantitative models. Additionally, expert opinion can draw upon types of knowledge and experience that is diffi cult or currently impossible to quantify in a model. Finally, decisions gene rated using expert opinion inpu ts provide a focus for guiding future research and management strategies. B ecause of all the complexities associated with

12generating ballast water st andards (see Table 2), expe rt opinion has been a key type of scientific input into the generation of balla st water standards to date.

One of the authors (HL) participated in seve ral technical workshops and IMO meetings where much of the discussion focused on estimating or ganism concentrations in unexchanged ballast water (see Figure 3 and MEPC, 2003a) and what reduction in these concentrations would be ecologically protective. The basic premise drivin g the expert decision process was that “less is better” and the greater th e reductions in propagule supply, the lower the risk of invasion. No quantitative invasion models were used, though th e expert consensus was that the discharge standard needed to be substantially below that normally achieve d through ballast water exchange. Additionally, in the U.S.-sponsored workshops, the practicab ility of achieving the expert-derived concentrations was not explicitly considered. Thus some of the values generated via expert opinion should be view ed as conceptual end-points rather than achievable near-term goals.

To document the expert opinion decision maki ng process, we will briefly summarize the sequence of events that lead up to the IMO standards (Table 1). Some of the first national and international meetings addressing ballast water standards were a pair of workshops held by the

U.S. Coast Guard on the East and West coasts in 2001 (USCG, 2002a) and an IMO GloBallast workshop in London also in 2001 (Raaymakers, 2002) . Drawing on these workshops, the USCG published the “Advance notice of proposed rulemaking; request for comments” in the Federal Register in March of 2002 (USCG, 2002b). In this notice, they listed four possible standards:

“S1. Achieve at least 95% removal, kill or inactivation of a representative species from each of six representative taxonomic gr oups ... (GLOBALLAS T PROPOSAL ‘‘A’’.)

S2. Remove, kill or inactivate all organisms larger than 100 microns in size. (GLOBALLAST PROPOSAL ‘‘B’’.)

S3. Remove 99% of all coastal holoplanktonic, meroplanktonic, and demersal zooplankton, inclusive of all life-stages (eggs, larvae, j uveniles, and adults). Remove 95% of all photosynthetic organisms ... (COAST GUA RD WORKSHOP PROPOSAL ‘‘A’’.)

S4. Discharge no organisms greater than 50 microns in size, and treat to meet federal criteria for contact recreation ... (COAST G UARD WORKSHOP PROPOSAL ‘‘B’’.)”

In 2003, an International Workshop on Ballast Water Discharge Standards was hosted by the State Department and the USCG in cooperati on with the National Sc ience Foundation (NSF) in Washington, DC. Workshop part icipants included IMO representatives and technical experts from seven countries (MEPC, 2003a). The sy nthesis suggestion from this workshop was a standard of <1 organism m -3 by 2006 for the >50 micron si ze group. The workgroup provided

two alternative recommendations for >10 – 50 micron organisms by 2015 as either “No detectable viable organisms” or “< 1 org./100 MT” (= 0.01 organisms m -3 ).

In January of 2004, the United States submitted a recommended discharge standard for zooplankton of <0.01 organisms m -3 to the IMO (IMO, 2004b). The rationale for this value was

13UnexchangedballastExchangedballastExpertOpinionUSCGPhase II

Relative Densit yFigure 3: Relative density distributions of zooplankton (>80 micron) in unexchangedballast water (blue line) and after theoreticalballast water exchange (red line). The dashed lineindicates the IMO standard of <10 organisms m-3for >50 micron organisms and thegray area indicates concentrationsthat meet the IMO standard. The “Expert Opinion” arrow pointing to the left illustrates thebasicassumption that lower organism concentrations would reduce invasion risk. The “USCG Phase II”arrow points to the proposedstandard of 0.01 organisms m-3for organisms >50 microns. (Modified from Minton et al., 2005).14based on the large number of organisms that would be discharged even at these low

concentrations and the additive densities from mu ltiple ship discharges. The example they gave was, “if the ICES figure of an average of 4.6 /l [organisms] is used, a vessel with 10,000 m 3 of ballast water would discharge 46,000,000 zooplankt on. This vessel would actually be carrying 4,600 zooplankton/m 3 , and in the absence of treatmen t would discharge a total of 46,000,000 zooplankton. Even if treated to reduce the co ncentration by 4 orders of magnitude [= 0.46 organisms m -3 ], this single vessel would still potentia lly discharge 4,600 living organisms into a harbour or estuary. Given that many ports and estuaries receive multiple vessel visits from the same regions over the course of days and week s, the cumulative number of organisms introduced will be quite a bit larger. For th ese reasons the United States ur ges the Conference to adopt less

than 0.01/m 3 as the concentration standard for zooplankton.”

In February of 2004, the IMO adopted by consen sus “The International Convention for the Control and Management of Ships’ Ballast Wa ter and Sediments, 2004” (IMO, 2004a) with the specific standards given in Annex D-2 of the C onvention as listed in Table 1. There is no

discussion in the Convention or the diplomatic conference’s Reco rds of Decision of the Plenary

as to how these values were sett led upon. The reality is that th e final IMO standards represent a negotiated compromise between the more stringe nt standards proposed by the U.S. and some other countries and the less prot ective standards (100 organisms m -3 ) proposed by several other

countries. Note that the standards in the C onvention will enter into force 12 months after ratification by 30 nations, representing 35% of th e world shipping tonnage. As of October 2, 2009, 18 countries representing 15.36% of the worl d’s shipping have ratif ied the treaty. The United States has not ye t signed or ratified.

Assumptions and Limitations: While the IMO standards were developed with input from experts, the numbers ultimately adopted reflect a negotiated outcome among th e many countries with differing views that participated in the Diplomatic Conference negoti ations. This is not unc ommon, as in general, decisions generated through an expert opinion/mana gement consensus approach tend to mix risk assessment, risk management, and politics. This makes it extremely difficult, or impossible, to parse exactly how a decision was made, which in turn, makes it difficult to update the decision based on new information, or even to identify wh at new scientific information would be required to modify a decision.

A related issue is the lack of documentation on how management consensus decisions are made. One exception is the State of California that pr ovides detailed documen tation of their process ( http://www.slc.ca.gov/Spec_Pub/MFD/Balla st_Water/Ballast_Wat er_Default.html ).

A general limitation of the expert opinion approach is that it is dependent upon which experts are involved, making it difficult to reproduce the deci sion making process. A related limitation is that one, or a few, outspoken e xperts may drive the decision maki ng process at the expense of exploring alternative ideas. This effect can be minimized or eliminated when experts respond via a questionnaire rather than within a workshop setting or with the use of an effective

facilitator.

15A group of experts restricted to a narrow field of specializatio n tend to look to at problems through the “lenses” of their partic ular expertise. Such differences not only reflect differences in the knowledge base of the individuals, but also th eir values. While such specialization is both appropriate and required, the real ity is that additional factors, including economics, feasibility, and timeliness, are likely going to be important considerations when making risk management decisions. Accordingly, we sugge st that the best approach woul d be for experts to provide a range of suggested standards accompanied with details on the ecological risks associated with

the different standards. This w ould allow the risk managers to we ight better all the cost-benefits

of different standards.

With the exception of certain structured appro aches (e.g. Delphi Method ), the decision making process is less transparent when it is based on expert opinion in comparison to models. In particular, it is difficult to capture the implicit assumptions that go into an expert’s decision,

which in turn makes it difficult to assess the valid ity of the decision or to reproduce the decision making process.

Kuhnert et al. (2009) identified ten “key heuristics, judgments or mental operations that can result in bias when eliciting information from experts” for ecological models. One example was that experts can overestimate th e accuracy of their beliefs or underestimate the uncertainty. Another type of bias referred to as “anchoring and adjustment” is the “tendency for groups to anchor around (any) initial estimates and adjust th eir final estimate from this value irrespective of the initial estimates’ accuracy.” These au thors present several methods to minimize such

biases that are summarized below.

Recommendations/Conclusions: Expert opinion/management consensus was successf ul in the face of the uncertainties in the invasion process itself and the politics inherent in any international treaty in generating the IMO organism-based discharge standards. This was a “watershed” accomplishment and a critical step toward reducing new invasions vi a ballast discharges. The ques tion remains, however, as to whether the IMO standards are sufficiently protectiv e. In part, this ques tion arises because the expert opinion/managerial consensus approach does not allow a rigor ous evaluation of the process or how the final decisions were reached. In light of these limitations and the continued

increase in our scientific unde rstanding, we recommend that future development of standards should rely more heavily on quantitative models. Use of invasion models will not remove the need for expert knowledge (e.g., what models and data to use, etc.) nor will it eliminate the need for risk managers to make difficult decisions weighing environmental risks versus other considerations. However, use of such models will make the process more transparent, more repeatable, and help to generate standards with defined levels of risk and associated uncertainty.

If expert opinion is used as a major input into the development of national standards, we suggest that the recommendations by Kuhnert et al. (2009) be considered to help formalize the process: 1) use multiple experts in a normative setting to avoid overconfidence; 2) pool expert beliefs with a mechanism for separating variability from ignorance; 3) calibrate the expert opinions to ensure that the experts report what they actually mean; 4) incorporate a feedback and comparison process that allows experts to discuss and revi se their opinions as well as comparing their assumptions of the methodology with their belief s; 5) utilize a met hodology that allows the

16experts to respond in a non-thre atening manner; and 6) design the elicitation process around the

statistical methods that will be used to analyze the data and investigate the impact of this information on the model outcomes. To this, we a dd that experts in a dive rse range of biological, shipping, and engineering fields be consulted.

17

### IV. ZERO DETECTABLE DISCHARGE

Henry Lee II

Overview: The state of California and other states have adop ted or have proposed standards with the goal of “zero detectable living organisms” in ballast water di scharges. In this assessm ent of zero detectable organisms, we will focus on the California standards as they are the best documented of the efforts (see Dobroski et al., 2009a and http://www.slc.ca.gov/Spec_Pub/MFD/Ballast_Water /Ballast_Water_Default .html ). California’s standards will be adopted in tw o-phases, with an interim sta ndard of “no detectable living organisms” >50 microns for ships constructed in 2010 to 2012, depending upon vessel size (Table 1). The proposed final standard is “no de tectable discharge” of zooplankton, phytoplankton, protists, bacteria, or viruses fo r ships constructed beginning in 2020 (Table 1). While California considered the natural invasion rate approach (described in Section V), it was not used in establishing the standards and the “n o detectable discharge” standard is a special case of the expert opinion/management consensus approach discussed in Section III.

Rationale: The principal legal authority for California to set these standards is the Coastal Ecosystems

Protection Act of 2006. As noted in th e Notice of Proposed Regulatory Action ( www.slc.ca.gov/Spec_Pub/MFD/.../Art_4-7_2009_NOPR

. doc), “Current California law requires that vessels manage ballast water to reduce the discharge of NIS into California waters. The performance standards for the discharge of ballast water prescribed by Article 4.7 are necessary to minimize the transport of NIS into and througho ut the waters of the State of California.” (Amendments to Article 4.7 entitled “Performance Standards for the Discharge of Ballast Water for Vessels Operating in California Waters”; Updated August 31, 2009).

The environmental rationale for the zero detectab le discharge standard given by the “Report and Recommendation of the California Advisory Pa nel on Ballast Water Performance Standards” ( www.slc.ca.gov/Spec_Pub/MFD/Ballast_Water/Docu ments/Appendix_A.doc ) was, “The scientific basis for a standard of discharging no exotic orga nisms is that exotic organisms, unlike conventional chemical pollutants, can reproduce and increase over time, persist indefinitely and spread over large regions. Thus, very large, widespread and long- term impacts could poten tially result from the discharge of a small number of individual organism s—in some cases as few as a single mated pair, or in the case of asexually-reprodu cing species, a single individual. Fr om this perspective, the only biologically safe standard is no di scharge of exotic organisms.” This rationale was also discussed by Cohen (2005 in Appendix 3 of the California Panel Re port). Note that this rationale implies that no organisms should be discharged (actual zero discharge), which can be substantially different than the “zero detectable discharge” of the California regul ation, which is entire ly dependent upon the sampling regime used.

Another rationale for setti ng stringent standards is to “force” tec hnology development. In a letter to

California Lt. Governor Bustamante and the California State Lands Commission, The Ocean Conservancy (TOC) stated, “Dur ing the [Ballast Water] Comm ittee’s work, TOC sought higher

18standards because the existence of such standards – combined with a competitive marketplace for ballast water treatment products – would motivate the rapid development of technology appropriate for meeting them.” ( http://www.slc.ca.gov/Spec_Pub/MFD/Ba llast_Water/Documents/Appendix_C.pdf ).

California states that their ballas t water standards should be interp reted as instantaneous standards rather than averages over the entire discharge. As a result, if any individual sample from a discharge exceeds any of the standards, this w ould be grounds for finding non-compliance and it is unnecessary to show non-compliance in multiple sa mples or in mean values (Dobroski et al., 2009a). California justifies the instantaneous standards based on the 2005 draft MEPC G2 sampling guidelines. However, the final MEPC G2 guidelines were subsequently revised to instead suggest an average method (J. Lishman, pers. comm., Nove mber, 2009). It is wo rth noting that while California cites the earlier G2 guidelin es as a justification, any zero ba sed standard is inherently an

instantaneous standard since once any sample contains an organi sm the discharge has failed the

standard.

Assumptions and Limitations: A true zero discharge of all size groups eliminates the risk of invasion via ballast water, assuming perfect compliance and no equipment failures. However, perfect compliance and no failure is practically, if not theore tically, impossible, particularly for microbiological organisms unless ballast water is discharged into a land-based treatment facil ity or ships are redesigned to eliminate the need to discharge ballast water (see Gregg et al., 2009 for discussion of ballast-free ships). Thus, ignoring all the other issues mentione d below, there will still be some level of risk associated with the proposed California standards resulting from equipment and human failure.

A major limitation with “zero detect able” discharge standards is that they are undefined in the absence of a quantitative sampling protocol, and depending upon the sampling protocol, the actual risk may be considerably higher than that associated with othe r standards. For example, as discussed in Section X, when zer o organisms are detected in a 1 liter sample, the actual ballast

water concentration could be as high as 3,000 organisms m -3 based on the 95% confidence interval (1-tailed). For a 10 m 3 sample (=2641 gallons) with no detected organisms, the ballast water concentration could be as high as 0.3 organisms m -3 (see Table 15). Thus, with a small (1 liter) sample with no organisms, the actu al concentration could be as much as 300-fold higher than the IMO standard, while for a 10,000-fold larger samp le the actual concentrat ion could be 30-fold higher than the proposed USCG Ph ase II standard. Without a stat istically-robust sampling protocol to quantify the detection limits dur ing both testing of treatment sy stems and compliance monitoring, it is impossible to conclude that the zero detect able discharge standard is actually any more stringent than the other standards.

These problems with a zero detectable discharge st andard for ballast water have been previously identified by various expert panels. For example, the summary of the 2003 “International Workshop on Ballast Water Discharge Standard s” (MEPC, 2003a) included the following two points: “Experience following passage of the United States Clean Water Act showed that an absolute standard of “zero discharge” was an unrealistic/ unworkable concept – detection limits have always been a problem.”

19“Setting a specific detection limit means that an actual concentration will be allowed for the testing protocol, therefore it might be better to specify the (acceptable) concentration as determined by the selected test protocols, rather than to use the expression “zero detectable” in the standard. This concept could be specifi ed in the testing pr otocol guidelines.”

Other major challenges are whether the putative low concentration associated with the “zero detectable” standard is economically viable and/or technologically f easible given the constraints of ship operations. These challenges are likely to be especially acute meeting the standards for microbiological organisms. It is beyond the scope of this document to conduct a review of the technical approaches to ballast water treatment methodologies but it is worth noting the scope of the challenges such systems face. Large tankers can carry in excess of 200,000 m 3 of ballast and the rates of ballasting and deballas ting can be as high as 20,000 m 3 hr -1 (NRC, 1996; Wright, 2007). Treatment systems must fit within the confined sp aces available on ships, continue to operate under the demanding conditions of ocean voyages, not be so complex that the crew can not operate them effectively, and pose no risk to th e crew or environment. As pointed out by Gregg et al. (2009), “Effectively eliminating the risk of ballast wate r mediated invasions sti ll remains a monumental technological and economical challenge.”

In evaluating the practicality of the “zero detectable” standard, the State of California conducted a

review of ballast water treatment systems using available informati on (Dobroski et al., 2009a, b) in terms of whether they presently meet the Californi a standards or showed th e potential of meeting them. They conducted a review for the >50 micron group, 10 - 50 micron size group, E. coli

, intestinal Enterococci , and Vibrio chlorae . They initially included viru ses, but concluded that there was no widely accepted technique or proxy for en umerating them and dropped them from the evaluation. They noted that their review was hampered by the lack of detailed testing data, inconsistency in the testing met hodologies, and differences in the scale and location in which the tests were conducted (e.g., lab based vs. land based vs. shipboard). They also noted that much of the available data have not been subject to a re view by an independent sc ientific organization.

Based on the January 2009 review (D obroski et al., 2009a), 15 systems were considered to have the potential to meet the California standard of zero detectable discharge for the >50 micron size class (see Table 3). In an October 2009 update to this review (Dobroski et al ., 2009b), the MH Systems was also listed as having potential. However, it is critical to note th at California listed a system as having the “potential” to meet thei r standards if it had “at least one replicate in compliance with the performance standards” (Dobroski et al., 2009a). In other words, a system was considered to have “potential” as long as it did not fail the standard in 100% of the replicates , which is the least stringent criterion possible. Failure of these syst ems could be due to several factors, such as mechanical problems, inherent variability in the efficacy of the system, the system working in one test mode but not another (e.g., working in a land-b ased testing facility but failing on a ship), or

statistical variation in the resu lts based on a inadequate sampling regime. Regardless of the cause for failures, the California criterion for “potential” is much less stringent than the criteria to meet approval through the Marine Environment Protect ion Committee (MEPC) of the IMO. The G8 MEPC Guidelines for Approval of Ballast Water Ma nagement Systems provide that to obtain typeapproval, a system needs to satisfy the IMO Regul ation D-2 standards in three consecutive valid shipboard test cycles and five consecu tive valid land-based cycles (MEPC, 2008a).

20To gain a better insight into the performance of these treatment syst ems, we analyzed their failure rates among replicate trials as presented in Appendix B1 of Dobr oski et al. (2009a) (Table 3). It was not possible to conduct this an alysis with the more limited data presented in the October update (Dobroski et al., 2009b), so the MH Systems treatment system is not included. With the exception of SeaKleen®, all systems failed a moderate to high percentage of th e replicates and/or they were not tested in all three modes (l aboratory, land-based, and shipboard testing). While the results for SeaKleen® are promising, they are only based on one laboratory test, two land-based tests, and one ship-based test, which do not meet the minimu m G8 requirements menti oned above. Additionally, there are concerns over residual toxicity from Se aKleen®, as well as its effectiveness against bacteria, resistant resting stages, and sediment-d welling organisms (Gregg et al., 2009). SeaKleen® has not been registered by EPA for use in trea ting ballast water under th e Federal Insecticide, Fungicide, and Rodenticide Act (FIFRA), and thus is not currently approved for such use in the United States. Furthermore, it has not received final type approval under G8 requirements or final approval from IMO for use as an active substanc e. We identify these issues not criticize SeaKleen® but to point out the gap between identifying a system with “potential” and having an approved system. Finally, our analysis is based only on the percentage fa ilure as reported in Dobroski et al. (2009a); it would take a detailed stat istical review of the sampling protocols used in testing these systems to ascertain the statisti cal confidence of detec ting a zero discharge (see Section X) and thus what level of confiden ce to place in the reported system successes.

Dobroski et al. (2009a) concluded based on their review that “at l east two treatment systems have demonstrated the potential to comply with Calif ornia’s performance standards. Many additional systems are close to completing system performan ce verification testing and will soon have data

available for review. Commission sta ff expects that before 2010 seve ral systems will be ready to

meet California standards.” Our assessment is not as optimistic, especially since it is now 2010 and no systems meeting the California standards have b een approved by IMO. While predictions about technology development are littered with emba rrassing prognoses (Ken Olson founder of DEC

computers: “There is no reason anyone would want a computer in their home.” ), our view is that it is unlikely that any practical ballast water treatmen t system will approach an actual zero discharge of organisms, defined here as co ncentrations substantially less than the USCG Phase II standards, in the near term, in particular for microbes and viruse s. Of course it is pos sible to achieve a “zero detectable” standard simply by using an inadequate sampling protocol with insufficient statistical power. Again, this emphasizes the need to have quantitative sampling pr otocols with adequate sample volumes and replication to qu antitatively assess these systems.

Recommendations/Conclusions: As discussed above, “zero detect able” discharge standards are undefined in the absence of a quantitative sampling protocol, a nd depending on the sampling protoc ol, the actual risk may be considerable higher than that asso ciated with other standards. Th erefore, we recommend that it not be used at the national level as an approach for deriving environmentally protective limits on concentrations of living or ganisms in ballast water.

If zero detectable discharge standards are consider ed as a possible approach for national standards, part of the technical anal ysis should include an assessment of th e relative risk associated with the zero detectable discharge standa rds versus risk associated with the USCG Phase II standards

21Table 3: Failure rates of the sy stems listed as having the “potential” to achieve the California discharge standard for >50 micron organisms (Dobr oski et al., 2009a). Failure is defined as detection of organisms in a test sample. The fa ilure rate was calculated as the percent of the replicate tests that failed the cr iterion using the data in Appendix B1 of Dobroski et al. (2009a). The Hitachi system was listed as ach ieving the California standard in Table VI-1 of Dobroski et al. (2009a) but no results were given in Appendix B1. The RWO Marine Water Tech. was tested with

Artemia cysts only. Systems that had a 100% failure rate for the >50 micron organisms may have passed the standard for another size group. The stat us of the type and active substance approval are from Dobroski et al., 2009a, D obroski et al., 2009b, and Gregg et al. (2009). The commercial names of the systems are given in parentheses. NT = not tested. NA = approval for active substance not applicable. Note that the number of samples or sample volume used in the validation testing was not reported by D obroski et al. (2009a, b).

System Failure Rate for Laboratory Testing (# Tests) Failure Rate

for Landbased Testing (# Tests) Failure Rate for Shipboard Testing (# Tests) Type Approval 1 Active

Substance Approval 2

Alfa Laval (PureBallast) 100% (1) 25% (12) 40% (5) Yes Final

Ecochlor (Ecochlor BW

Treatment

System) 0% (2) NT 0% (1) No Basic

Greenship (Sedinox) NT 0% (5) NT No Final

Hamann Evonik Degussa

(SEDNA) * 0% (2) 16% (19) 20% (5) Yes (Germany) Final

Hitachi (Clearballast) ? ? ? No Final

Hyde Marine (Hyde Guardian) 100% (1) 50% (4) 100% (4) Yes Basic

MARENCO 33% (3) NT NT No NA

Mitsui Engineering (Special Pipe) NT 100% (4) 100% (1) No Basic

NEI (Venturi Oxygen Stripping (VOS)) NT 80% (5) 75% (4) Yes (Liberia) NA

Nutech 03 Inc. (SCX 2000, Mark III) 100% (3) 67% (3) 33% (3) No No

22System Failure Rate for Laboratory Testing (# Tests) Failure Rate

for Landbased Testing (# Tests) Failure Rate for Shipboard Testing (# Tests) Type Approval Active

Substance Approval

OceanSaver (OceanSaver BWMS) NT 86% (14) 67% (12) Yes (Norway) Final

OptiMarin (OptiMarin Ballast System) 100% (1) 38% (13) 100% (7) No NA

RWO Marine

Water Tech. (CleanBallast) 0% (1) NT NT No Final

SeaKleen 0% (1) 0% (2) 0% (1) No No

Severn Trent DeNora (BalPure) NT 40% (5) NT No No

TechCross (Electro-Cleen) NT 27% (11) 0% (3) Yes (Korea) Yes

1) Type Approval: Type approval is grante d by Flags states following successful equipment performance during land based and ship board testi ng in accordance with the IMO G8 Guidelines to verify treatment system efficacy, safety, desi gn, construction, operation, and function (MEPC, 2008a).

2) Active Substance Approval: Active Substance A pproval is granted by MEPC, not the Flag state, and is required by Convention Regulation D-3 for t hose treatment systems that make use of Active Substances (biocides) to comply with the C onvention’s Regulation D-2 standards. Active Substance Approval relates to the environmental and safety aspects of the sy stem's use of biocides

and is conducted in accordance with the IMO G9 Gu idelines (MEPC, 2008b). Approval typically is given in 2 stages, first “basic” approval, and then “final” approva l. Systems subject to Active Substance Approval also must undergo type-appr oval testing by Flag states under the IMO G8

Guidelines.

* : Harmann Ag ceased work on its ballast water tr eatment system after it was discovered that the

biocide Perclean was more toxic in cold waters and in freshwater than initially assumed (Lloyd’s List, February 9, 2010).

23(USCG, 2009) and/or standards derived from the per capita invasion approach (Section VIII). This analysis should include an assessment of th e number and impacts of historic invaders in

coastal waters and the Great Lakes that the USCG or PCIP standards might not have prevented, in particular asexual and parthe nogenic invaders, in comparison to the likelihood that the zero detectable standards would have prevented th eir introduction, assuming some practical sampling protocol for the zero detectable standards.

If zero detectable standards are cons idered at the national level, it is critical to define all aspects of the sampling protocols for verification of ba llast water treatment systems and for compliance monitoring. (see Section X).

24

### V. NATURAL INVASION RATES

Henry Lee II

Overview: The natural invasion rate appr oach was proposed by Dr. Andy Cohen (San Francisco Estuary Institute) in an August 7, 2005, memo to the California Ballast Water Treatment Standards Committee, with a follow-up addendum with co rrected values. The memo and addendum are Appendix 5 and 6, respectively, in Appendix A of Falkner et al. (2006) . As noted by the California State Lands Commission (Falkner et al., 2006, page 21), “this approach is based on numerous assumptions that create a high level of uncertainty for its application to performance

standards that will have re gulatory impacts. ... The proposed approach had been neither published nor peer reviewed and was thus not known or widely accepted by the scientific community.” Because of these uncertainties, they adopted the zero detectable organism approach instead (see Section IV). Even though not adopted by California, the natural invasion rate approach is worth examining since it addres ses generating ballast water discharge standards in a novel way.

Rationale: The rationale for the natural invasion rate appr oach is that marine/estuarine ecosystems are subject to a very small natural ra te of invasion from rare events when species drift or raft across

oceans and then become established in new locati ons. A ballast water discharge standard that resulted in an invasion rate ap proximately equal to the natural rate would essentially double the

natural invasion rate but would be “reasonably close to the natural rate and possibly within the normal range of variation, and thus would be re asonably protective of the environment” (Cohen, 2005 in Falkner et al., 2006). Cohe n further assumed that such a standard would be “reasonably protective of the various environmental, recreatio nal and economic beneficial uses of California's

waters.”

Calculation of Discharge Standard Based on Natural Invasion Rates: As discussed in Appendices 5 and 6 of Falkne r et al. (2006), development of a discharge standard (= concentration standa rd) resulting in a ballast water invasion rate approximately equal to the natural rate requires that the concentrati on of organisms in ballast discharges needs to be reduced “by the ratio between the natural invasion rate and the i nvasion rate due to the discharge of untreated and unexchanged ballas t water.” This ratio is refe rred to as the Reduction Factor:

Natural invasion rate Equation 1: Reduction Factor = Invasion rate due to untreated and unexchanged BW

Where:

BW = ballast water

25Cohen assumes a linear dose-response for propagule pressure (Fig. 2, line c) so that the ballast

water standard that would result in an invasion rate approximately equal to the natural rate of

invasion is:

Concentration of organisms in Equation 2: Discharge Standard = X Reduction Factor untreated & unexchanged BW

Therefore, to calculate the discharge standa rd, three values are needed: 1) organism concentrations in untreated ballast water; 2) a rate of invasion resulting from discharge of untreated ballast water; and 3) a natural inva sion rate. For organism concentrations, Cohen

assumes concentrations in untreated ba llast water to be on the order of 10 2 -10 3 per m 3 for organisms >50 microns, 10-10 2 per mL for organisms between 10 and 50 microns, and 10 8 -10 9
per 100 mL for organisms <10 microns.

For the rate of invasion from ballast water, Cohen focused on the San Francisco Estuary for which he has extensive expe rience (e.g., Cohen and Carlton, 1995; Cohen and Carlton, 1998; Cohen 2005). From 1961 to 1995, which is prior to the California and USCG regulations requiring mid-ocean ballast water exchange, he es timated the rate of invasion as 3.7 species per year, with an increase to 5.2 species per ye ar during 1991 to 1995 (Cohen and Carlton, 1998). The fraction of these invaders assumed to have been introduced via ballast water discharges was 0.7-1.7 species per year for the period 1961 to 1995 and 1.6-3.2 species year for the period 1991 to 1995. Cohen makes the argument that these numb ers underestimate the actual rate of invasion because of: 1) new invaders that have not yet be en collected; 2) new invaders that have not yet been identified as exotic species (e.g., misidentified as a native species); and 3) species that have

been collected but whose invasion status is uncerta in (cryptogenic species). Cohen estimates that

these factors could increase the invasion rate by 50 to 100%. Cohe n is correct in asserting that these factors are likely to result in an underestimation of the true invasion rate (e.g., Ruiz et al., 2000; Carlton, 2009), and while the actual extent of underestimati on is not known, increasing the observed invasion rate by 50% to 10 0% does not seem unreasonable.

These rates only capture invasi ons into the San Francisco Estuary, and Cohen assumes that including all of California would increase the rate by at least another 50 to 100% . Implicitly this assumes that there are potentially as many unique invaders in the re st of California as have been found in San Francisco. This validity of this assumption was not assessed, though it would be possible to synthesize the existing California invasion records (e.g., http://www.dfg.ca.gov/ospr/abou t/science/misp.html ) to dete rmine how many California

invaders are not found in the San Francisco Estuary or were first reported from areas other than San Francisco. Nonetheless, based these assumptions , the invasion rate for al l of California from ballast water was estimated by Cohen as 2 to 7 species per year during the 1961 to 1995 period and 4 to 13 species per year during the 1991 to 1995 period.

Estimate of Natural Invasio n Rate on Pacific Coast: The third input value needed is the natural invasi on rate, which is the most difficult to estimate.

A natural invasion event is defined as a “marine organism that is transported across an ocean by drifting, rafting or some other natural, irregular a nd rare transport mechanism and becomes established initially as a disjunct, isolated population in waters on the other side” (Falkner et al.,

262006). In assessing the prevalence of natural invasion rates, Cohe n excluded several groups of organisms that would “inflate” th e natural invasion rate. Pelagic organisms that have “regular, natural genetic exchange between populations on opposite side s of the ocean” were excluded. Such species would include pelagic copepods, many of which have trans-Pacific or transAtlantic distributions (see http://copepodes.obs -banyuls.fr/en/index.php ). Additionally, species that have continuous ranges on both sides of the ocean (e.g., boreal species that occur from northern Japan across the Aleutians and into Br itish Columbia) were excluded. Another group that was excluded was species th at have disjunct, transoceanic populations “that are relics of formerly genetically-continuous populations”. Finally, Cohen excluded species that have teleplanic larvae, which are larvae that have a long residence times as plankton and may be transported across oceans (e.g., Scheltema, 1986; Scheltema and Williams, 1983). There is no discussion of how to identify species that co nsist of relict populations, what constitutes a continuous range on both sides of the ocean, or the larval duration defining a species as teleplanic. Thus, the taxa that potentially woul d be included in such an analysis are not well

defined.

Cohen’s equation to calculate the one-way invasion rate is:

Equation 3: Natural

invasion rate = 0.5 X The number of species common to both sides of the ocean that are thought to re sult from natural invasion The length of time it takes for isolated populations to become morphologically distinct

The natural invasion rate as defined by this form ula is for one side of the ocean and multiplying the number of species common to both sides by 0.5 inherently assumes that there is an equal natural invasion rate in both directions. The logic of dividing by time for isolated populations to evolve into separate species is not discussed but appears to be an attempt to account for species that successfully invaded but are no longer “comm on to both sides of the ocean” because they evolved into a new species. For example, give n 100 species in common a nd a speciation rate of

0.75 million years, the adjusted natural invasion ra te (for one side of the ocean) would be 66.7 invaders per million years versus 50 invaders if no adjustment for speciation had been made. [Note that for speciation rates >1 million years, the time needs to be entered into Equation 3 as years and not million of years otherwise the formula decreases the invasion rate below the observed rate.]. In any case, Cohen assumes that it takes 1 million years for isolated species to become morphologically distinct without giving any documentation.

Then based on a “review of the biogeographical literature and other re levant data”, Cohen

estimated that the number of fish and inverteb rates common to both sides of the Pacific Ocean resulting from natural invasions is ≤ 100 species per million years. Two other invasion experts, Dr. Jim Carlton and Dr. Greg Ruiz, estimated ≤ 10 species per million years and ≤ 1000 species per million years, respectively (Table 4). While it was stated that a review of the biogeographic literature was conducted, the only reference gi ven was Vermeij’s (1991) estimate that the Northeast Pacific mainland had been invaded by 11 gastropod species from the Line Islands in the Central Pacific over the last 2 million years (a one-way invasion rate). This results in a natural invasion rate of 5.5 sp ecies per million years (correct ed value from Appendix 6 of Falkner et al., 2006). The assumptions inherent in these estimates are discussed below.

27Table 4: Estimates of natural invasionrates, resulting discharge limits, and adjusted discharge limits. Adjustment factorsare theextent to which the discharge limit wouldbe increased because of the identified factor. The first three estimates are from invasionexperts who participated in the CA Advisory Panel on Ballast Water Performance Standards (Falkner et al.,2006). These estimatesare adjusted based on the mean IMO organism concentrations forzooplankton compared to that used by Cohen. The second approachto adjusting the discharge ratesis to adjust the natural invasion rate from Vermeij (1991) for gastropods from the Line Islands thatinvaded the Northeast Pacific. The reduction factors for Vermeij’s natural invasion rate are derived from Equation 1 using Cohen’srange in the estimate of yearly ballast water invaders in California. The taxonomicadjustment increases Vermeij’s rate basedon theestimated relative proportion of gastropods to total number of invertebrate and fish species. The two species pool adjustmentsfurtherincrease Vermeij’s rate based on the presumed increase in the number of natural invaders whenconsidering the entire CentralPolynesia Province or all the ecoregions within the Northwest Pacific and Indo-West Pacific. For reference, the IMO standard for >50micron size class is organisms is 10 organisms per m3while the USCG Phase II is 0.01 organisms per m3.Expert/Type of AdjustmentNumber of one-way naturalinvasions per 106years/Extent of adjustmentReductionFactorDischarge limits per m3fororganisms >50 micronsDischarge limits perml for organisms 10­50 micronsDischarge limits perml for organisms<10 micronsJ. Carlton≤1010-610-4to 10-310-5to 10-4102to103A. Cohen≤10010-510-3to 10-210-4to 10-3103to 104G. Ruiz≤1,00010-410-2to 10-110-3to 10-2104to 105Ballast water conc.adjustment to meanIMO conc.4.6 to 46 fold increaseNA4.6 10-4to 4.6 100(0.00046 - 4.6 org. m-3)NANAVermeij (1991)5.54.2 - 28 x 10-74.2 10-5to 2.8 10-4(0.00004 – 0.0003 org.m-3)NANATaxonomic adjustmentfor all inverts & fish10.6 fold increaseNA4.45 10-4to 2.97 10-3(0.00045 - 0.003 org. m-3)NANASpecies pool withinCentral PolynesiaProvince2 fold increaseNA8.90 10-4to 5.94 10-3(0.00089 - 0.0059 org. m-3)NANASpecies pool withinWestern Pacific &Indo-West Pacific10 fold increaseNA8.9 10-3to 5.94 10-2(0.0089 - 0.059 org. m-3NANA28As mentioned, the only quantitative estimate of a natural invasion rate wa s for gastropods from the Line Islands to the Eastern Pacific (U.S. P acific coast). The Line Islands are located 2,500

kilometers south of Hawaii in the central Paci fic, and the 5,400 km expanse of deep ocean

between the Line Islands and th e Clipperton Islands off western Mexico constitute the “East Pacific Barrier” (EPB), the single largest ocea nic barrier in the world (e.g., Scheltema, 1988; Collin, 2003). Thus a natural invasion rate derive d from the Line Islands presumably represents the “worst case” scenario (i.e., lowest natural invasion rates). No similar analysis was conducted to estimate natural invasion rates from subtropi cal/tropical Asia and Indo-West Pacific or the Northwest Pacific (northern China, Japan, Korea, or Russia) to the U.S. and Canadian Pacific

coasts. Natural invasion rates were not calcula ted from Europe to the U.S. East Coast.

Discharge Standards Derived from Natural Invasion Rates: Depending upon the ballast water concentrations and the natural invasion rate used, the discharge

standards based on the natural i nvasion rate for the >50 micron si ze class reported in Falkner et al. (2006) ranged from 0.1 to 0.0001 organisms per m 3 (Table 4). Natural invasion rates for smaller organisms were not addressed in Falkner et al. (2006) but the re duction factors for the >50 micron invaders were applied to 10-50 micr on and <10 micron groups, based on the implicit assumption that there had been a similar number of natural invasions for these smaller taxa. This resulted in ranges of discharge standards of 0.01 to 0.00001 organisms per ml and 100 to 10,000 organisms per ml for the two smaller si ze classes, respectively (Table 4).

Evaluation of Natural Invasion Rates and Adjustment Factors:

In this section we evaluate several of the a ssumptions inherent in estimating natural invasion rates and suggest some adjustment factors to these rates. We use these adjustment factors to first modify the range in discharge limits from th e expert estimates and second to derive a new discharge limit based on modifying the invasi on rate from Vermeij (1991) (Table 4).

Adjustment of Ballast Water Orga nisms Concentrations to IMO Mean

Cohen uses ballast water organism concentr ations in untreated ballast water of 10 2 -10 3 per m 3
for organisms >50 microns. In comparison, th e IMO baseline study (MEPC, 2003b) reported a mean zooplankton concentration of 4640 m -3 (also see Figure 3 from Minton et al., 2005). Because the calculated discharge standards increase linearly with higher organism concentrations (see Equation 2), th e estimates of 10 2 -10 3 per m 3 potentially underestim ate the lower and upper discharge limits. Adjusting the upper and lower discharge limits from the three experts by the

IMO ballast water concentration results in a range of discharge limits of 0.00046 – 0.46 organisms m -3 . The lower value is still more than an order-of-magnitude lower than the USCG Phase II standard while the upper value is almost 50-times greater than the Phase II standard.

Taxonomically Adjusted Natural Invasion Rate

The number of natural invasions will depend, in part, upon the tota l number of species available for invasion (i.e., the species pool). The natura l invasion rate from Vermeij’s (1991) work is based solely on gastropods, and thus substantially unde restimates the potential species pool. To adjust this rate to be taxonomically inclusive of all macroscopic taxa in near-coastal ecosystems,

we estimated the ratio of total num ber of gastropods to total number of near-coastal invertebrates

and fishes. The invertebrate numbers were taken from the recently revised “ The Light and Smith Manual: Intertidal Invertebrates from Central California to Oregon ” (Carlton, 2007). The

29preface (page xi) to the Light and Smith Manual states that “over 3700 species are keyed or

discussed in this fourth edition” and this value was used for the total number of intertidal and

near-shore invertebrates. A total of 376 benthic gastropods was determined by counting the number of gastropod descriptions in Light and Smith Manual exclusive of the pelagic gastropod families. While we are unaware of a total spec ies inventory for the Line Islands, a total of 281 coastal fishes have been estimated from Kiritimati, one of the Line Island s (Sandin et al., 2008).

Based on these values, gastropods constitute 10.2% of the intertidal and near-coastal invertebrate species in northern California and Oregon. Ac cordingly, Vermeij’s rate of 5.5 gastropods per million years was multiplied by 9.8 to account for all invertebrate taxa, resulting in an estimated natural invasion rate of 54.1 invertebrates per m illion years. Adding th e number of fishes estimated from Kiritimati to the total species co unt results in gastropods constituting 9.4% of the total fauna. In turn, this results in an upwar d adjustment of 10.6 fold, generating a natural invasion rate of 58.5 species per million years. Thus, Vermeij’s rate for gastropods likely

underestimates the natural invasi on rate by about 10-fold, assuming all taxa have approximately equal probability of natural i nvasion. These are approximate corrections as ideally the

invertebrate ratio would be base d on a total species list from the Line Islands, the fish estimate

would be based on all the islands within the Line Islands group, and all taxa such as macroalgae

would be included. Even with these limitations, we believe that these taxonomic adjustments more closely capture the potential species pool for natural invasion than only using the number of gastropods.

Biogeographic Analysis of Poten tial Species Pool for Invasion

The size of the potential species pool available fo r natural invasions depends not only on the taxa included in the analysis but also the geographical area consider ed to represent potential donor regions. Vermeij’s estimate is based only on the Line Islands, which contain approximately 250 known gastropod species (Vermeij, 1991). While it would take a major effort to conduct a

detailed review of the number of potential invaders in the entire We stern Pacific, it is possible to use the number of distinct biogeog raphic regions as a relative i ndicator of the number of unique species available for invasion.

In the “Marine Ecosystems of the World” (MEOW) hierarchical biogeographic schema, “ecoregions” are the smallest biogeographic br eakout which are contained within larger “provinces” (Spalding et al., 2007) . The Line Islands are part of the “Line Island Ecoregion” which is contained within the “Central Polynesi a Province”. The Centra l Polynesia Province is composed of two additional ecoregions (Cook Islands and Samoa Islands), which are approximately the same distance from the U.S. Pacific Coast as the Line Islands. The Cook Islands contain 377 extant native ga stropod species (search conducted at http://cookislands.bishopmuseum.org/ search.asp ), while the number of marine gastropods in the Samoa Islands is apparently unknown. Though there is likely some overlap of species among the three ecoregions, the total number of potential gastropod invaders within the entire Central Polynesia Province is greater than from the Li ne Islands Ecoregion al one, as indicated by the 50% greater number of gastr opods in the Cook Islands. Presumably, this increase in the available species pool would also apply to other taxonomic groups as well. In lieu of a detailed biogeographic analysis, we suggest that the tota l number of potential invaders in the entire Central Polynesia Prov ince is at least 100% greater than the Line Islands alone.

30In addition to these tropical island ecoregions, th ere have likely been na tural invasions to the

U.S. Pacific Coast from the subt ropical/tropical ecoregions of As ia and the Indo-West Pacific as well as the temperate/boreal ecoregions of th e Cold Temperate Northwest Pacific Province (northern China, Korea, Japan, a nd Russia). It is beyond the scope of this document to attempt a biogeographic synthesis of these areas, but it is suffice to say th at these regions harbor an extensive number of species. The South China Sea contains more than 3500 fish species (Kwang-Tsao et al., 2008) and more than 20,000 speci es are listed in an inventory of China’s seas (Zongguo, 2001). While the distance of these areas from the U.S. Pacific Coast may have limited the number of natural invasions migrating directly across the Pacific Ocean, it is possible that species “hop scotched”. For example, cold adapted spec ies from the six ecoregion making up the Cold Temperate Northwest Pacific Provin ce may have initially colonized the Aleutian Islands before migrating to the Gulf of Alaska and then southward to cold temperate ecoregions of Washington, Oregon, and northern California. The main point is that estimates based on only the Line Islands are likely to substantially unde restimate the total numbe r of natural invasions and thus result in artificially lo w discharge standards. The extent of this underestimate is not known, but given the small size of the Line Island Ecoregion comp ared to all the potential donor ecoregions, it is possible th at it is at least 10-fold.

Evidence for Transoceanic Interchange: Independent of the adjustments to the natural in vasion rates, there are several lines of evidence indicating that transoceanic migra tions are not as rare as origina lly hypothesized. For example, a reasonably high percentage (13%) of the gastropod species from the Line Islands has invaded offshore islands in the Eastern Pacific (Vermeij, 1991). It is possible that these species are not

found on the mainland of California and Mexico b ecause of environmental mismatches rather than an absence of dispersal. Additionally, in a review of trop ical trans-Pacific shore fishes, Robertson et al. (2004) reported 80 species that likely migrated eastward to the tropical Eastern Pacific and 22 species of shore species that likel y migrated westward fr om the tropical Eastern

Pacific.

Another line of evidence for transoceanic transpor t is the genetic similarity in a number of transPacific species. In a study of 20 reef fish morphospecies found on both sides of the Pacific, Lessios and Robertson (2006) found that 18 of the 20 had high gene tic overlap. They concluded that the similarity in these 18 trans-Pacific species was maintained by recurrent gene flow between the populations on the two sides of th e Pacific. Additionally, these authors had previously found “massive breaching of the EPB” in two species of sea ur chins (Lessios et al. 1998, 2003). Thus Lessios and Robertson (2006) conc luded that while the EPB was generally an effective barrier in separating species in the Northwest and Northeast Pacific, it should be considered a “sporadically permeable filter.” This conclusion is supported by a study of calyptraeid gastropods (slipper shel ls) (Collin, 2003). Collin found Bostrycapulus species on both sides of the Pacific Ocean, leading her to conclude that the Eastern Pacific Barrier is “somewhat permeable to some calyptraeids”. These genetic studies indicate th at there is periodic mixing of populations across the Eastern Pacific Barrier, and that such transport is not as “irregular and rare” as assumed in genera ting the natural invasi on rates in Table 4.

A final line of support for the potential for tran soceanic dispersal is the increasing appreciation of ocean dispersal as an important factor in determining organism distributions (de Queiroz,

312005) and the importance of raf ting as a transport mechanism in particular (e.g., Thiel and Gutow, 2005). As stated by de Queiroz (2005 ), “If vicariance bioge ography was a revolution, we are now in the midst of a counterrevolution, driven primarily by new evidence in favor of oceanic dispersal.”

Assumptions and Limitations: The natural invasion approach has only been described in the memo and addendum to the

California Ballast Water Treatment Standards Co mmittee. As such, the assumptions and input values have not been adequately vetted nor have they been peer reviewed. As mentioned, there is no discussion of how to identify species that consist of relict popula tions, what constitutes a continuous range on both sides of the ocean, the la rval duration defining a species as teleplanic, or documentation for assuming a spec iation rate of 1 million years.

An inherent assumption of the natural invasion rate approach is that a doub ling of this rate would be sufficiently protective. This is a centra l assumption and it needs to be supported through a review of appropriate ecological models and/or empirical studies. We caution that “argument by analogue” (e.g., comparison of the eff ects of invasive species to the effects of a two-fold increase in atmospheric CO 2 ) provides no real scientif ic support for the adequacy/inadequacy of a ballast water standard equivalent to the natural invasion rate. Furt hermore, the decision as what constitutes an adequate level of protection is a risk management issue, not a component of the risk assessment. For example, risk managers c ould decide that an inva sion rate equal to the natural rate constitutes too great a risk and set a standard base d on one-half or one-quarter the natural invasion rate. Conversely, they could decide that a rate twice the natural rate would provide sufficient protection. In any case, the role of this appr oach, and all the science-based models reviewed in this document, is to provi de risk managers with scientifically-sound and transparent estimates of the rate and/or eff ects of invasion based on different ballast water

concentrations.

Our review suggests that the an alysis by Cohen underestimated th e rate of natural invasions, which then results in an artificially low discha rge standard. Specifically, the following would all result in higher natural invasi on rates: 1) includi ng taxonomic groups in addition to gastropods; 2) including the additional potentia l invaders (species pool) from other ecoregions within the Western Pacific; and 3) using higher mean organism concen trations in ballast water. Our

conclusion that natural invasion rates were undere stimated is consistent with recent genetic studies showing that the East Pacific Barrier is “semi-permeable”. Based on these data, we suggest that the estimate of <1000 natural invasi ons per million years from Falkner et al. (2006) (Table 4) is the most defensible rate for natura l invasions, and potentially may still underestimate

the rate.

Estimating natural invasion rates is likely to have high uncertain ty as indicated by the 100-fold difference among just three invasi on experts (Table 4). With th e available evidence, it appears that this approach will not generate discharge standards wi th less uncertainty than those developed using other approaches.

The natural invasion rates used to generate the reduction factors were based on macrofaunal invaders (>50 microns). Application of thes e reduction factors to the 10-50 and <10 micron

32groups, which primarily consist of phytoplankton and protozoa, introduces additional uncertainty especially given the differences in rates and vect ors for natural dispersal of these smaller taxa especially for the microbes (e.g., Finlay, 2002). A separate analysis would have to be conducted for these groups, perhaps focusing on diatoms because of the availability of fossil records.

The natural invasion rate appro ach assumes a linear dose-response for propagule pressure. As discussed in Section II, this assumption should be adequate for many species and densities.

The approach assumes that there is an equal inva sion rate in both direct ions across the Pacific (the 0.5 multiplier in Equation 3). This assu mption seems unlikely for species transported

to/from from the Line Islands. Because of the much greater shoreline, there is a much higher probability that an eastward tr aveling propagule would encounter the Pacific Coast of the United States compared to the probability that a westwa rd traveling propagule would encounter the Line Islands, or other islands in the central Pacific.

The calculated natural invasion rate will vary in versely with the speciation rate (Equation 3). Thus, the speciation rate is a ke y factor in estimating natural invasion rates, and another source of uncertainty. However, there is no discussion of the importance of this parameter, and the onemillion year rate used by Cohen is not justified. Rather than using an unsupported value, the growing theory on evolutionary rates (e.g., Allen and Gillooly, 2006) as well as empirical studies using genetic techniques (e.g., Wares, 2001) shou ld be consulted to generate a range of scientifically-defensible rates.

The calculation of the natural inva sion rate does not account for species that successfully crossed the oceanic barrier and became established (e.g., survived for 10 generations) but eventually went extinct. A number of nonindigenous species have shown dramatic population crashes (e.g., Simberloff and Gibbons, 2004) so extinction of some fraction of the natural invaders is possible if not likely. Excluding these ex tinct invaders artificially lowe rs the natural invasion rate, and thus results in a lower discharge standard.

As with all the approaches th at rely on historic invasion ra tes, the possibility that a nonindigenous species may have invaded via seconda ry vectors and/or hull fouling or another

vector instead of ballast water potentially inflates the ballast- water invasion rate. Incorrectly assigning invaders to ballast wa ter reduces the reducti on factor (Equation 1) which in turn reduces the discharge standard.

The geographic scope of the current analysis is th e state of California, which is a political entity and is not defined by any specifi c set of biological or environm ental conditions. By the MEOW biogeographic schema, California encompasses tw o coastal provinces and three ecoregions. Thus the current analysis mixes a number of different areas whic h likely have different natural

invasion rates as well as numbers of ballast-mediated invasions.

Before the Wisconsin glacier, natural invasions in to the freshwater bodies of the current Great Lakes region were presumably minimal and less than that for the Pacific Coast. After the retreat of the glaciers, there was relatively rapid popul ation of at least some lakes and ponds (e.g., Daniels and Peteet, 1998), though it is not clear whether this w ould be considered “natural

33invasions” or a re-colonization pr ocess. Thus, it is not clear th at ecologically relevant natural invasion rates could be generated for the Great Lakes or whether th e standards resulting from an analysis of coastal regions would be applicable to the Great Lakes.

Recommendations/Conclusions: We conclude that given the lack of peer re view, high level of uncer tainty and number of unsupported assumptions, the current range of valu es based on the natural invasion approach should not be used to generate discharge st andards. Furthermore, given the inherent uncertainties with the approach, we do not believe that even a revised anal ysis should be used to generate national discharge standards. It is wo rth noting, however, that after adjusting for IMO ballast discharge rate, the upper es timate of the ballast water disc harge standard derived from the natural invasion approach is about 50-fold greater than the USCG Phase II standard.

Because the natural invasi on rate approach is the only techni que that attempts to define an ecologically acceptable invasion rate other than 0, values from a re vised analysis could be used as an informal benchmark for comparisons wi th values generated by other methods. The purpose of such comparisons would be to put re sults from other methods in context with our current understanding of natural invasion rates. Such a compar ison would require that all the techniques use similar assumptions regarding ballast water discharge volumes and organism

concentrations.

If the natural invasion rate appr oach is to be considered eith er as a formal approach to developing discharge standards or as an informal benchmark for other appr oaches, it is critical that it be further developed and reviewed not only by invasion biol ogists but also paleontologists, biogeographers, and geneticists working on conn ectivity among transoceanic populations. Any future development should address the limitation s mentioned above, especially those that are likely to reduce the discharge standards artificiall y. Such an analysis should develop estimates of uncertainty around the predictions.

Any further development should expand the geogra phic range considered. Instead of assessing invasion rates across a political entity (Californi a) it would be more ecologically relevant to generate estimates by the biogeogr aphic ecoregions making up the U.S. Pacific Coast. If each ecoregion was evaluated independently, it woul d then be possible to generate confidence

intervals around the suite of es timates. Within the north Paci fic, Hawaii provides a “natural experiment” on rates of colonization and speciat ion, and such an analys is could draw on the efforts to document the biodiversity of the Hawa iian Islands (Eldridge, 2 006) as well as their evolutionary history (Price and Clague, 2002). Additionally, natural invasion rates should be

evaluated on the East Coast ofthe United States, especially given the large number of amphiAtlantic species (e.g., Vermeij, 2005).

34

### VI. REACTION-DIFFUSION MODELS

Henry Lee II and Deborah A. Reusser

Overview: Reaction-diffusion models predict the concentration of a “substance” that is simultaneously influenced both by diffusion (dilution) and by some type of reaction affecting its concentration (e.g., chemical reaction, population growth). Their applications to biological systems have been reviewed by Okubo and Levin (2002) and Sexton et al. (2009) while their application to

invasions is discussed in Kinlan and Hastings (2005). The basic assumptions of this family of models in terms of invasions (Kinlan and Hastings, 2005) are: 1) they model continuous time and space; 2) there is local random movement of individuals; and 3) population dynamics are deterministic. The primary use of reaction-di ffusion models in invasion biology has been the theoretical analysis of the patt ern of invasion spread of terrest rial invaders, with the models usually predicting a linear rate of spread under the most common assumptions. The only published example of a reaction-diffusion model being applied to determining ballast water

standards that we are aware of is that of Drake et al. (2005).

Application to Ballast Water Disc harges by Drake et al. (2005): Drake et al. (2005) developed a reaction-diffusion model with an Allee effect to predict the probability of establishment of species based on th e volume of ballast water released. Note that this approach predicts “acceptable volumes” of ba llast water and does not di rectly use or predict concentrations of organisms in th e ballast water. Thus, it does not directly generate an organismbased discharge standard.

The form of the model used by Drake et al. (2005) to predict the change in the density of a species released via a ballast water discharge was:

 u 2 Equation 4:  D  u  f ( u )  t

Where:

u (relative density) = local popula tion density scaled by carrying cap acity (i.e., between 0 and 1)

t = time

D = diffusivity of disc harged ballast water (m 2 s -1 )

 = Laplace operator defining the spat ial gradient over two dimensions

f ( u ) = model describing local population grow th (change in relative density/time)

In Equation 4, the first set of terms is the “di ffusion” component of the model which models the

dilution of the individuals in the water column over time. The second function captures the simultaneous population growth, which is the “r eaction” component. By normalizing population

35size to carrying capacity, the model does not pr edict a population concen tration but rather changes in relative population si ze over time due to the combined effects of dilution and population growth (see Lewis and Kareiva, 1993).

Using the cubic population model from Lewis and Kareiva (1993), the local growth of a species subject to an Allee effect was modeled as:

Equation 5: f ( u )  ru (1

 u )( u

 a )

Where:

r

= intrinsic rate of population increase (day -1 )

a = Allee “critical density” (unitless).

The form of the relative population growth rate as a function of population size from Equation 5 is illustrated in Figures 4 and 5. In this model, an Allee effect occurs when 0 < a < 1, where a represents the fraction of the carrying capacity below which the detrimental effects of a low density result in negative populat ion growth (Lewis and Kareiva, 1993). As can be seen in Figure 4, inclusion of a mild Allee effect ha s a minor effect on population growth over most densities. It is only at very low relative densities (Figure 5) th at the Allee effect results in a

noticeable decrease in relative population growth. The decline in growth rate above a relative density of about 0.7 is due to ne gative intraspeci fic interactions.

Assuming a mild Allee effect and an initial popu lation density substantially above the critical density ( a ), the necessary and sufficient conditions fo r the establishment of a population of an introduced species in term s of area occupied is:

1 D Equation 6: R min  1/ 2

 a 2 r

Where:

R min = radius of the initially occupied area from the ballast discharge (m).

To convert this area into a volume, Drake et al. (2005) assumed that the ballast water was dispersed within a 10 m deep zone. Based on th is assumption and setting the radius of the cylinder to R

, they calculated V , the “maximum volume of [ballast] water that may be min max released to maintain the risk of population esta blishment at or below a level that would be specified by policy.” The risk of population establishment was calculated by utilizing different

values of r as described below.

Using the data from Figure 17 of Blueweiss et al. (1978), Drake et al . (2005) generated a regression between body mass a nd population growth rate ( r ) (their equation not given). They then estimated the maximum pe r capita population growth rate, r

max , using the upper 0.01, 0.001,

and 0.0001 confidence levels of the regression. These upper confidence levels were used as a

36method to establish a range of “risk tolerances”, which represent the prob ability that a species

would become established. Based on Le wis and Kareiva (1993), they then set r

max as approximately equal to 4  r or r  r

max 4 . Substituting r

max for r in Equation 6 results in:

2 D Equation 7: R min  1/ 2

 a 2 r

max

Based on the r

max from body size and for given “ a ” (critical density) and D (diffusivity), it is

possible to calculate R . Assuming a 10 m depth ( d ), it is then possible to calculate V , the min max maximum volume of ballast water that can be di scharged at a specified risk level (from the

confidence level of the r ):

2 Equation 8: V

max   R min d 

### V

max 

### = π R min 

### 2 d

Where:

V

max = maximum volume of ballast water di scharge for specified risk level (m 3 )

d

= depth (m)

Parameter Estimation: Drake et al. (2005) assumed an Allee effect equal to a = 0.01. With this threshold, the population experiences negative grow th from an Allee effect at <1% of its carrying capacity (Figure 5). While considered a “mild” Allee effect (i.e., “ a ” is a small fraction of the carrying capacity), it may actually be an important factor at the discha rge standards that have been proposed (e.g., 0.01 to 10 organisms > 50 microns per m 3 ).

As mentioned, a single depth (d) of 10 m wa s assumed for all ballast water discharges. V

max scales linearly with depth so th e “exact value is not hugely impor tant”. The authors used two horizontal diffusivity values in their calculations, 0.02 m 2 s -1 and 0.3 m 2 s -1 , the minimum and maximum values reported from a study of lakes. These values are substan tially lower than those found in many estuarine/marine systems, which can have diffusivities over 1000 m 2 s -1 (e.g., Banas et al., 2004; also see Figure 5 of Drake et al., 2005). Because th e probability of invasion decreases as diffusivity increases, the use of these lower values is protective of exposed marine/estuarine conditions. However, as noted by the authors, the lake diffusion values may not be protective in enclosed ha rbors which physically restrict diffusion (see their Figure 5). Note that the diffusivity values in m 2 s -1 need to be multiplied by 86,400 to convert them to m 2
day -1 so that the units are consistent w ith the intrinsic rate of growth (day -1 ) when used in Equations 6 and 7.

37Mild Allee Effect

0 No Allee Effect

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9Population Growth Rate 0.16

0.14

0.12

0.1

0.08

0.06

0.04

0.02

0

-0.02 1

Initial Relative Population Size

Figure 4: Example of relative popu lation growth rate based on the cubic population model from Lewis and Kareiva (1993) with and without a mild Allee effect ( a = 0.01). The relative population size is the population of a species at a given time in re lation to that species carrying capacity. The decrease in growth rate at high relative population is due to negative intraspecific

interactions.

-0.00005 0 0.00005

0.0001 0.00015

0.0002 0.00025

0.0003 0.00035

0.0004

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Initial Relative Population SizePopulation Growth Rate

Mild Allee Effect

No Allee Effect

Figure 5: Enlargement of the relative populat ion growth rate based on the cubic population

model from Lewis and Kare iva (1993) with and without a mild Allee effect ( a = 0.01). The population growth becomes negative below a relative density of 0.01 due to the Allee effect.

38Drake et al. (2005) use risk tole rance values of p = 0.01, p = 0.001, and p= 0.0001 to represent the “chance of establishment per introduction” to br acket different levels of protection. These

risk tolerance values are de rived from the upper confidence levels around the allometric relationship between body size and intrinsic rate of population increase ( r ). The validity of the resulting values is discussed below.

Assumptions and Limitations: The major limitation of the analysis by Drake et al. (2005) for development of discharge standards is that it generates a cceptable volumes of ballast water discharges rather than risks associated with the discharge of different organism concentrations. Therefore, it can not be used to generate organism-based discharge standards. We initially attempted to convert their analysis to a concentration basis, but th is would require, at the minimu m, estimates of carrying capacities for the species in the ballast discharge, whic h are unknown for nearly all the invertebrates and

larval fishes entrained in ballast water. However, as discussed under Recommendations/ Conclusions, it would be possible to use a different form of a reaction-diffusion model or other types of dilution models to pred ict changes in organism concentr ations resulting from dilution.

A general limitation of using reaction-diffusion models to de velop ballast water discharge standards is that they only apply to small hol oplanktonic species (such as calanoid copepods), that spend their entire adult life span in the water column and that ar e passively transported by currents. Species with pelagic larvae (e.g., most polychaetes and mollusks) that actively settle out of the water column violate several key m odel assumptions includi ng: 1) individuals are passively distributed by currents; 2) species complete their life span within the water column; and 3) population dynamics are rapid compared to redistribution thr ough diffusion. Pelagic species such as fish that remain within the water column but which actively swim violate the assumption of passive dispersal and, in nearly all cases, the assumption that population dynamics are rapid compared to diffusion. Because hol oplanktonic species make up a relatively small

fraction of the total marine/estua rine invaders (see Ruiz et al., 2000; Wonham and Carlton, 2005), this family of models can address only a subset of potential invaders in these systems. Even in the Great Lakes, zooplankton only const itutes 6 of the 37 (16%) fish and invertebrates introduced via “shipping, Ballast Water” (calculated from data at http://www.glerl.noaa.gov/res/Programs/ncrais/docs/great-lakes-list.xls ).

Drake et al. (2005) generated a range of “accepta ble” ballast water volumes for “invasion risk tolerances” of 0.01, 0.001, and 0.0001. The ri sk tolerance represents the probability of an invasion of an unknown species; so a risk of 0.0001 means that there is a 1 in 10,000 chance that

an invader will become established. These risk tolerances are the probabilities that a single species will become established. However, as discussed in more detail under the PVA model (Section VII), the key environmenta l question is not whether any pa rticular species will become established but rather whether any of the multitude of species in a ballast discharge will successfully invade. This multi-species risk is calculated as the risk of a single species not invading raised to the power of the number of species in the ballast discharge. Assuming 100 species in a ballast discharge and an individual species’ risk tolerance of 0.0001, the probability of a single species not invading is 0. 9999; when this is raised to the 100 th power, the result (0.99) is the probability of all 100 species not invading. With this multi- species scenario the probability of no species invading is about 1 in a hundred. Thus, even the lowest invasion risk tolerance

39value used by these authors results in a high ri sk of invasion when cons idering all the species potentially present in a ballast discharge.

It is not possible to use lower risk tolerances in this model because of how they were determined. The risk tolerance levels were generate d from the upper confidence limits of “ r ” from the regression of intrinsic rate of growth versus body size. For example, to establish the acceptable volume of ballast discharge at an invasion risk tolerance of 0.0001, th ey used the intrinsic rate of growth equal to the upper 0.0001 co nfidence level for the particular size of organism in Equation

7. While an innovative approach, the problem is that th e intrinsic growth ra tes associated with the upper 0.001 and 0.0001 upper confidence levels ar e unrealistically high. For example, backcalculating from their equations us ing a risk tolerance of 0.0001, we obtained an intrinsic growth rate (r) greater than 18 day -1 . This value is at least an order of magnitude greater than nearly all metazoans, and even for ciliated protozoans the highest value was 6.3 day -1 (Taylor and Shuter, 1981). Thus, this approach to setting different prot ection levels is limited to risk tolerance levels around 0.01, a very high, and presum ably unacceptable, invasion risk.

The authors state that the deriva tion of Equation 6 assumes that the original release density u 0 is “considerably above the Allee threshold a”. Gi ven the low proposed discharge standards (0.01 – 10 organisms m -3 ) it is possible that ballast water concentr ations of individual species will not be “considerably” above Allee thresholds. However, it is not clear whether this assumption is actually required for the derivation of the equation or simply that ballast discharge densities below the Allee threshold result in negative growth in Equation 2 and thus result in “relatively

little threat of invasion”.

The solution in Equation 6 “obtained from Le wis and Kareiva (1993) relies on the assumption that population dynamics are relatively fast co mpared to organism redistribution through diffusion” (Drake et al., 2005). To evaluate this assumption, the authors conducted numerical simulations to evaluate the potential effects on their results. Based on these simulations, the authors concluded that their model would underestimate the acceptable ballast water volume for larger species (= specie s with slower population growth rate s). From their Figure 3, biased estimates occur for organisms larger than about 0.05 grams, which they list as fish and ctenophores. The lower boundary of adult size for amphipods, decapods, copepods, and ostracods is listed as less than 0.05 grams, and thus have unbiased estimates. They do not state how biomass is measured, but we assume that it is wet weight.

Recommendations/Conclusions: The work by Drake et al. (2005) can not be used to generate orga nism-based discharge standards since it is based on “relative densities” to pred ict acceptable volumes of ballast discharge. However, it should be possible to generate reaction-diffusion m odels addressing ballast water discharges that utilize actual de nsities rather than relative dens ities, though this would require estimates of species specific popul ation vital rates. Alternativel y, it may be possible to link population growth models with models simulatin g dilution of pollutant discharges, such as Visual Plumes or CORMIX2 (see http://www.epa.gov/waterscience/standards/mixingzone /resources.html#models ). In this case,

the dilution models would be “tur ned on their head” and the ballast discharge would occur at the surface rather than from depth. These simulatio n models are “mature” and allow for inclusion of

40real world complications not readily captured in analytical models, such as density differences between discharged and receiving waters. Without further analysis, however, it is not clear to what extent the existing dilution mo dels would have to be modified to model ballas t discharges.

The more germane question is how much effort s hould be devoted to diffusion models in general for the generation of organism-based discharge standards. Violation of the assumption that species are passively distributed is likely to result in a s ubstantial underestimation of the likelihood of establishment of a species. In particular, benthic species whose larval and/or juvenile phases actively settle out of the water column are much more likely to become established than predicted from dilution models. Thus, in aquatic environments, diffusion models are primarily limited to predicting invasions of small, holoplanktonic organisms. Because of this limitation, diffusion models do not appear to be suitable for generating concentration-based discharge sta ndards applicable to the wide range of taxa found in ballast

water.

While not suitable as a general approach to gene rating discharge standards, results from diffusion models with holoplanktonic organisms can be us ed to help elucidate the role of population

dilution in initial establishment. Such an anal ysis may help explain why there are relatively few copepod invaders in marine/estuarine systems ev en though they make up a substantial portion of the fauna in ballast water (e.g., Lavoi e et al., 1999; Levings et al., 2004).

41

### VII. POPULATION VIABILITY ANALYSIS (PVA) MODELS

Henry Lee II

Overview: Population viability analysis (P VA) models are a family of p opulation growth models commonly

used in the conservation field to predict the extinction proba bility of endangered species (Beissinger and McCullough, 2002; Morris and Doak, 2002). The ba sic premise of PVA models is that any population undergoing stochastic growth has a certain probability of going extinct even if it is presently showing positive growth. In general, th e smaller the population size, the slower the population growth ra te, or the larger the variati on in population growth rate, the greater the probability of extinction. There ar e three general types of PVA models: 1) countbased PVA; 2) demographic PVA; and 3) spatia lly explicit PVA. The count based PVA is the simplest, and utilizes historical census data to estimate popula tion growth rate and variation assuming all individuals are identi cal. The diffusion approximation of Dennis et al. (1991) is the simplest of the count-based P VA models and is based on two pa rameters -- the instantaneous population growth rate and instantaneous variati on in the population growth rate. The diffusion approximation is most suitable when there is a lack of detailed life history information. Demographic PVA models are based on population pr ojection matrices that incorporate size- or age-specific demographic vital rates, and thus incorporate differences among age/size groups. Spatially explicit PVA models are the most co mplex and incorporate population migration and

colonization into and out of areas.

There is growing recognition that PVA models are a potential tool to predict the establishment and spread of nonindigenous species (Andersen, 2005). When used with nonindigenous species, the objective is to predict either the time to ex tinction or the probability of extinction for an invader, where extinction is the converse of es tablishment. Recently, PVA models have also been evaluated in laboratory experiments on population dynamics to gain insights into the invasion process (see Secti on IX). In this section, we examine the PVA analysis conducted in the USCG Draft Programmatic Environmental Im pact Statement (DPEIS; USCG, 2008). We detail this analysis both because it is part of th e technical analysis used by the USCG in setting their proposed rules (USCG, 2009) a nd because it is the only study that we are aware of that used PVA models to directly address ballast water st andards. However, as discussed below, the

formulation used in the DPEIS is not the only possible PVA me thodology to addressing the risks associated with ballast discharges.

PVA Model Used in USCG Risk Assessment for Single Species Scenario: The DPEIS used the diffusion appr oximation model (Dennis et al., 1991). The strategy taken in

the DPEIS was to evaluate differe nt discharge standards by predic ting the relative increase in the probability of extinction based on the fractional re ductions in the number of organisms per cubic meter of ballast discharge. This is a relative approach and it was not the objective of the DPEIS analysis to predict the actual probability of invasion associated with any specific organism.

42In their analysis, the DPEIS listed five potential treatment alternatives, which for the >50 micron size group were:

Alternative 1: No Action (no ballast water treatment is implemented and ballast water exchange is the preferred op tion if vessels can conduct it).

Alternative 2: <10 organisms m -3 (= IMO standard)

Alternative 3: <1 organisms m -3 (= 1/10 th IMO standard)

Alternative 4: <0.1 organisms m -3 (= 1/100 th IMO standard)

Alternative 5: 0 organisms (= sterilization)

Alternative 1 (No Action) was taken as the base line against which the other treatments were compared. Ranges in organism concentrati ons for both unexchanged and exchanged ballast

water were used to establish this baseline. A lternative 5 was not formally analyzed because no

invasions would occur with sterilization. The DPEIS did not analyze the USCG Phase II standards (= 1/1000 th IMO standard), but when possible we include such an analysis for the >50 micron organisms.

The remainder of this sub-section will detail th e diffusion model and input parameters used in the DPEIS for a single species analysis, which im plicitly assumes that all the individuals in a ballast discharge are of single species. The pa rameters used in the PVA model are given in Table 5, and for all population rates we assume a time unit of a day. The reader is referred to Sections 4 and 5 of Appendix A of the DPEIS fo r a more detailed derivation of the equations.

The simplest model of population dynamics incorporating stochastic variation is:

Equation 9: dX(t) = μ dt + σ dW(t)

In this model, dW(t) is a normal random vari able that adds randomness to the population dynamics. The larger the value of dW(t) and/or the larger the instantaneous standard deviation of the population, the larger the swings in population si ze, and the more likely that the population will drop to the critical population threshold (n

e ). Populations with negative growth ( μ < 0) will go extinct regardless of initi al population size (N(0)) and are not further considered. For populations with pos itive growth ( μ > 0), the probability that a popul ation with an initial size of N(0) will go extinct (i.e., reach th e critical population threshold) is:

Equation 10: p
e = exp(-2 μ ‘d’ / σ ) = e (-2 μ ‘d’ / σ )



### [ Note: Equation 10 is a direct reproduction of Equation 3 in th e DPEIS (App. 4, p. A-25); we assume this represents a typographical er ror and that the auth ors meant to write:

p e = exp(-2 μ ‘d’ / σ 2 )

This equation indeed can be rearranged to Equation 5 in the DPEIS (our Equation 11).]

43Table 5: Parameters used in the PVA models in the DPEIS.
N(0) = population size at time 0 (initial population size)

N(t) = population size at time t

X(t) = log N(t) (log of population size at time t)

μ

= instantaneous population growth rate

σ 2 = instantaneous variance of the population growth rate

σ = instantaneous standard devia tion of the population growth rate

dW(t) = normal random variable with mean 0 and variance 1 (to add random variation in population dynamics)

n e = critical population threshold at which the population is considered “extinct” (quasi-extinction). The

critical threshold is assumed to be 1 individual in th e DPEIS for the single species scenario, which is the smallest possible value.

x e = log n

e

p e = probability that a population w ith initial size N(0) will go extinct

‘d’ = X(0) – x

e = log (N(0)/n

e ) Log of the ratio of the initial population size to the critical population threshold. (Note that we put quotes around d to di fferentiate it from “delta” in the rate equations)

c = 2 μ / σ 2 = “biological parameter” (ratio of instanta neous growth rate to instantaneous variance in growth rate; see Equation 85 of Dennis et al., 1991)

exp = exponential function

f = fractional decrease in the initial population size (N(0 )) due to a ballast water treatment. f is calculated as the ratio of the total number of organisms discharged under a particular management Alternative to the number discharged under Alternative 1 (No Action option).

p e (f) = probability of extinction as a function of the fractional decrease in initial population size

f

e = fractional effect on extinction probability (p

e ) of reducing initial population size (N(0)) by the factor

f. Equal to ratio of probability of extinction with the fractional decrease (f) in initial population size to the probability without the decrease (= p

e (f) / p

e ).

f

r = the proportion of the mean rate of successful in troductions relative to that under Alternative 1 (No Action option)

DE = number of discharge events when calculati ng joint probabilities of no establishment of a single species from multiple identical discharge events

q(m) = probability that at least one species is succ essfully introduced in the multiple species scenario

44Assuming positive growth, the corrected version of Equation 10 can be rewritten as:

Equation 11: p

e = (n
e / N(0)) c Where N(0) > n e

This equation predicts the probability of extin ction (i.e., an invader not becoming established) based on the initial propagule supply (N(0) = orga nism concentration in ballast * volume of ballast discharged). However, these predictions require quantitative estim ates of instantaneous population growth and variance for th e specific species. As discusse d in the DPEIS, such values

are not available for most marine/estuarine or fr eshwater fishes and invertebrates. Additionally, the specific species composition in foreign ballast discharges is not known. The strategy taken in

the DPEIS to circumvent these limitations was to calculate relative changes in the probability of

extinction as a function of frac tional decreases (f) in the init ial population size resulting from

different levels of ballast water treatment.

To calculate the relative fracti onal reductions in initi al population size (f) by treatment type, the DPEIS first estimated the range of organism con centrations in unexchange d ballast water and the range that these concentrations would be reduced by ballast wa ter exchange. The range in concentrations in unexchanged ballast water incl udes concentrations below the IMO limit, thus the range in the percent removal from ballast ex change includes 0 (no reduction). As discussed below, ballast water concentrations below the IMO standard are considered a rare event. From these estimates, they calculated a range of initial population sizes for Alternative 1, which were used to calculate the range in fr actional decreases in initial popul ation size in the other treatment alternatives (Table 6).

Because the DPEIS used the lower and upper bou nds of organism concentrations in their analyses, there is a wide spread in the frac tional decreases for the ballast water treatment alternatives, including 1 (= no re duction). We believe more repr esentative fractional decreases for the >50 micron size group can be calculated from the relative decrease in median propagule doses from ships undergoing ballast water excha nge (BWE) versus the doses based on the IMO standards (data from Table 1 of Minton et al., 2005). Under this scenario, the IMO standard resulted in a median fractional decrease slight ly more than an order of magnitude (0.094) compared to exchanged ballast water. (A similar comparison to the dose from unexchanged ballast resulted in a fractional decrease of slightly more than 100-fold.) Based on this, we then

reduced the fractional decreases in Alternatives 3 and 4 and th e USCG Phase II standards each by an order of magnitude, repres entative of the changes in thei r ballast water concentrations (Table 6).

Estimates of the biological parameter “c” are needed to translate the fractional decreases in Table

6 to f
e , the factor by which the reduction in ini tial population size incr eases the extinction
probability. The parameter c (=2 μ / σ 2 ) is based on the ratio between instantaneous growth rate

and its instantaneous variance and is a critical variable determining the probability of extinction (see Equation 85 of Dennis et al., 1991). As pointed out in the DP EIS, the value of c can vary substantially among taxa and with environmental conditions. They address this uncertainty by using a range of 0.001 to 0.1, though they do not gi ve a detailed justification for these values. A

value of 0.1 means that the variance of the instan taneous growth rate is 20 times greater than

45Table 6: Ranges in the fractional decreases (f) in initial ballast water population size generated by treatment Alternatives 2 - 4 re lative to the range of population sizes in Alternative 1 used by the DPEIS. A value of 0.1 signifies that the initial population si ze was reduced to 1/10 th of the

size in Alternative 1 while a va lue of 1 indicates that there was no decrease relative to

Alternative 1. The bolded value for the >50 micr on size class for Alterna tive 2 is a recalculated

fractional decrease based on the re duction in median propagule dose associated with the IMO

standard versus that associated with excha nged but untreated ballast (concentrations from Minton et al., 2005). The recalculated fractional decreases for the other alternatives based on proportional decreases relative to the IMO standard are also bolded . NC = not calculated in the

DPEIS.

Alternative Fractional Decrease (f)

(10-50 micron taxa) Fractional Decrease (f)

(>50 micron taxa)

Alternative 2

(IMO) 0.1 – 1 0.001 – 1

(0.1)

Alternative 3

(1/10 th IMO) 0.01 – 1 0.0001 – 0.1

(0.01)

Alternative 4

(1/100 th IMO) 0.001 – 1 0.00001 – 0.01

(0.001)

USCG Phase II

(1/1000 th IMO) NC NC

0.0001

mean instantaneous growth rate, while a value of 0.001 means that the variance is 2000 times greater. Populations of small invertebrates can be highly variable, but without a quantitative review of their population dynami cs it is unclear whether vari ances on the order of 1000 fold greater than the mean growth ra te are representative of many or most species likely to be discharged in ballast water. The significance of these high variances (= low values of c) is that they increase the probability of extinction (Equation 11) because larger population variation

increases the likelihood that the population will drop below the cr itical population threshold (n
e ).

Once f and c are estimated, it is then possible to calculate the probability of extinction resulting

from the fractional decrease in the initial population size (f):

Equation 12: p
e (f) = f -c p e = f -c (n
e / N(0)) c

The effect of reducing the initial population size discharged under each of the treatment
alternatives on the probability of extinction can be expressed by f
e , the ratio of the extinction probability with and without the fractional decrease in initial population size resulting from the

treatment alternative:

Equation 13: f
e = f -c = p e (f)/p
e

46The DPEIS used these formulas to evaluate the se nsitivity of extinction probabilities to a range of values of c (their Table 5-2) . For small values of c they noted the relative insensitivity of extinction probability to the density of organi sms in the ballast. We have recalculated the probabilities (Table 7) and believe that the apparent insensitivity to initia l densities needs to be

re-examined. In this recalculation we used th e assumptions in the DPEI S of a critical population threshold of 1 organism and a ballast discharg e volume (used to calculate N(0)) of 10,000 m 3 . In Table 7, we report the values with three decimal places (versus two in their Table 5-2) so that it is possible to see that decreas ing organism density does in fact increase the likelihood of extinction. Additionally, the apparent insensitivity to organism density is partially due to the high extinction probabilities (>97%) w ith low values of c, so that there is not “much room” to increase the probability of extinction.

Another key point is that the “small” differences in extincti on probabilities become important when considering the joint extinction probabilitie s of multiple species (discussed below) or with discharges from multiple ships. To explore the ri sk associated with multiple ship discharges, we calculated the probability that a species would not become esta blished assuming 10 independent, identical ballast water discharges of 10,000 m 3 . The probability of extinction resulting from 10 independent discharges of the same species is calculated by raising the probability that the species did not become established in a single event to the 10th power.

Table 7: Probability of extinction (p

e ) expressed as a function of the initial organism concentrations (>50 microns) in ballast water and the “biological parameter” c for a single species. Extinction probabilities are calculate d from Equation 11 based on a single discharge event of 10,000 m 3 with a critical population threshold of 1 organism. The probability that the species becomes established is 1 minus the probability of extincti on given in the table, thus the higher the value, the lower the risk of invasion. While the probabi lities of extinction are given as actual values, the data are most appropriately analyzed as relative differences among organism

concentrations or values of c. Modified fr om Table 5-2 of the DPEIS, including adding the organism concentration for the USCG Phase II standard. Initial Organism Concentration (>50 mi crons) in Ballast Water (organisms m -3 )

c 10 -2

(USCG Phase II) 10 -1

(1/100 th

IMO) 10 0

(1/10 th
IMO) 10 1

(IMO) 10 2 10 3 10 4 10 6 10 8

0.001 0.995 0.993 0.991 0.989 0.986 0.984 0.982 0.977 0.973

0.01 0.955 0.933 0.912 0.891 0.871 0.851 0.832 0.794 0.759

0.1 0.631 0.501 0.398 0.316 0.251 0.199 0.158 0.100 0.063

The probability of the species becoming established is 1 minus the joint probabilities of extinction across the multiple voyages. This appro ach is similar to considering the risks from multiple species (discussed below), and the general formula for multiple voyages is:

Equation 14: probability of a species becoming es tablished from multiple, identical discharges
= 1 - p e DE

Where: DE = number of identical, independent discharge events of the same species.

47Results from our analysis of probability of extinction of a single species from 10 identical discharge events are given in Table 8. Considering the risk of multiple discharge events highlights the importance of reducing organism con centrations. For example, at the lowest value of c (0.001), the calculated risk of invasion at the Phase II standard is 0.045 versus 0.1087 for the IMO standard, more than a two-fold reduction in ri sk with the more stringent standard. A similar

two-fold difference in invasion risk was also seen with these sta ndards with a c value of 0.01. The key point from results give n in Tables 7 and 8 is that reductions in the organism concentrations in ballast water result in ecologica lly significant relative decreases in the invasion risk even for species and environments with a naturally low invasion probability (= species in environments with low value of c).

Table 8: Probability of extinction (p

e ) as a function of the initial organism concentrations in ballast water and the “biological parameter” c for a single species for 10 identical, independent discharge events. Extinction prob abilities are calculated from E quation 11 based on 10 discharge events each of 10,000 m 3 with a critical population threshold of 1 organism. The probability that the species becomes established is 1 minus the probability of extin ction given in the table, thus the higher the value, the lower the risk of inva sion. While the probabilities of extinction are given as actual values, the data are most appr opriately analyzed as re lative differences among organism concentrations or values of c. Initial Organism Concentration (>50 mi crons) in Ballast Water (organisms m -3 )

c 10 -2

(USCG Phase II) 10 -1

(1/100 th

IMO) 10 0

(1/10 th
IMO) 10 1 10 2 10 3 10 4 10 6 10 8

0.001 0.955 0.933 0.912 0.891 0.871 0.851 0.832 0.794 0.759

0.01 0.631 0.501 0.398 0.316 0.251 0.199 0.158 0.100 0.063

0.1 0.010 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000

The DPEIS then goes on to analyze the results as the range in the factor by which the extinction probability would be increased compared to Alternat ive 1 (versus the absolute values in Table 7).
This extinction probability factor (f
e ) was calculated from Equation 13 for Alternatives 2-4.
Their ranges in f
e for the >50 micron size class are replicat ed in Table 9 along with our analysis
for multiple voyages. For the multiple ship voyages, we calculated f
e from p
e (f)/p
e (see Equation
13). We first calculated p
e for a single voyage based on th e assumptions of an organism concentration of 1,000 m -3 after ballast water exchange, a discharge volume of 10,000 m 3 per voyage, and a critical population th reshold of 1 organism. The p
e (f) were calculated using the same assumptions and the organi sm concentration associated with each treatment. Then both
extinction probabilities for a single voyage were raised to the 10 th power and the ratio calculated. The results in Table 9 from a singl e voyage show that for the lowe st c (high variance compared to growth rate), the treatment alternatives do not increase the probability of invasion. As discussed above, this is a conseque nce, in part, of the high rate of extinction for species with a high population variance. For the species with a lower variance (higher c), the extinction rates

can increase two to three fold with the additiona l reduction of organism concentrations in the

ballast.

48Table 9: Factor by which the probability of extinction would be increased compared to
Alternative 1 (f

e ) for >50 micron organisms. The va lues in Column I represent the f
e for the range in fractional decrease values (f) and in c for a single voyage calcu lated in the DPEIS.

Column II is our calculations of f

e for 10 independent voyages using only the range in c.

Modified from Table 5-3 of the DPEIS.

Alternative c f I. Single Voyage

f

e (range in f & c) II. Multiple Voyages

f

e (range of c)

Alternative 2 (IMO) 0.001 –

0.1 0.001 –

1.0 1.0 – 2.0 1.047 – 100

Alternative 3 (1/10 th IMO) 0.001 –

0.1 0.0001 –

1.0 1.0 – 2.51 1.072 – 1000

Alternative 4 (1/100 th IMO) 0.001 –

0.1 0.00001 –

1.0 1.0 – 3.16 1.097 – 10,000

Phase II USCG (1/1000 th IMO) 0.001 –

0.1 - - 1.122 – 100,00

With multiple voyages using the median reduction in concentration, ther e is a relatively small increase in the extinction rate, a bout 5% to 12%, with the low valu es of c. However, with the high values of c, the extincti on rate increased by orders of magnitude, 100 to 100,000 times, compared to concentrations associated with exchanged ballast water. This result suggests that the importance of decreasing organism concentr ations in the ballast becomes increasingly important when there is a like lihood of multiple ships discharging the same organisms within a port. The analysis of the multiple voyages was not part of the DPEIS and we consider these results preliminary. Nonetheless, they suggest that further analys is of the risk of invasion from multiple voyages is warranted.

The final analysis in the DPEIS fo r single species was to calculate f

r , the mean rate of successful

introductions for a treatment relative to Alte rnative 1. Recalling th at the probability of introduction is 1- probability of extinction, f

r is calculated as:

Equation 15: f

r = 1- p

e (f) 1- p

e

The numerator in this equation is the probability that invaders will become established with the organism concentration associated with the treat ment alternative while the denominator is the extinction probability under A lternative 1. As before, the extinction probabilities were calculated assuming a criti cal population threshold (n

e ) of 1 organism, a ballast discharge of 10,000 m 3 , and range of values for c and organi sm concentrations. The ranges in f

r for the two size fractions from the DPEIS are given in Tabl e 10. We also analyze the ratio of successful invaders using the p

e calculated using a c oncentration of 1000 m -3 , the approximate modal organism concentration after ba llast water exchange (from Figur e 2 in Minton et al., 2005).

49Table 10: Mean rate of successful introductions fo r treatment alternatives relative to Alternative

1. The ranges in the first two columns are fr om the DPEIS and were derived from a range of both organism concentrations in unexchanged or exchanged ballast water and a range of c values (Table 5-4 of the DPEIS). To better focus on long-term trends, we compared the treatment alternatives to a single or ganism concentration of 1000 m -3 for ballast water exchange (BWE) and a range of value for c. The smaller the valu e, the greater the relative reduction in invasion risk compared to Alternative 1 or BWE.

Alternative Single Voyage: 10 – 50 micron organisms (DPEIS range) Single Voyage: >50 micron organisms (DPEIS range) Single Voyage: >50 micron organisms (Comparison to BWE)

Alternative 2 (IMO) 0.92-1.0 0.50-1.0 0.71 – 0.85

Alternative 3 (1/10 th IMO) 0.67-1.0 0.50-1.0 0.57 – 0.75

Alternative 4 (1/100 th IMO) 0.67-1.0 0.41-1.0 0.43 – 0.62

Phase II USCG (1/1000 th IMO) - - 0.29 – 0.46

The conclusions in the DPEIS from their values in Table 10 are:

“The reduction in the mean rate of successful introductions is the comp lement of the ranges of values presented above. As a result, th e reduction in the mean rate of successful introductions, as compared to th e No Action Alte rnative under:

• Alternative 2 is expected to range betw een no reduction and an 8% reduction, and no reduction and a 50% reduction for smaller and larger organisms, respectively;

• Alternative 3 is expected to range betw een no reduction and a 33% reduction, and no reduction and a 50% reduction for smaller and larger organisms, respectively;

and

• Alternative 4 is expected to range betw een no reduction and a 33% reduction, and no

reduction and a 59% reduction for smaller and larger organisms, respectively.”

As mentioned above, we believe the use of the medi an reductions in concentrations compared to exchanged ballast water rather than the ranges in the DPEIS give a more representative picture of the long-term improvement due to the treatment alte rnatives. For Alternatives 2-4, the use of the median organism concentrations indicates a 15% to 57% reduction in the introduction rate of >50 micron organisms. For the USCG Phase II standa rd, the predicted relati ve reduction in invasion

rate is 54% to 71%.

PVA Model Used in USCG Risk Asse ssment for Multiple Species Analysis: The analysis detailed above predicts the relativ e effects of the alternat ive treatment options on the invasion probability of a single species disc harged in ballast water. The DPEIS also

50conducted a multiple species scenario, which addr essed the probability of invasion by any of the multiple species in a ballast discharge. In other words, this analysis asks “What is the probability that at least one of the species in a ballast discharge will succ essfully invade?” Similar to the calculation of the probability of establishment for a single species with multiple discharges (Equation 14), the simplest equation to predict th e probability that at least one of the multiple species discharged from a single ballast event is introduced is:

Equation 16: probability th at at least one species becomes established = 1 - p

e n

Where: n = number of species introduced in a single ballast water di scharge that are not already successfully establis hed in the waterbody.

This equation assumes that all species are independent and that they all have the same extinction probability. The second of these assumptions w ould nearly always be violated because of different densities of species. The more realistic equation used in the DPEIS is:

n Equation 17: q ( m )  1

 

##  p j ( m )

j  1

Where: q(m) = probability that at least one species is su ccessfully introduced (= becomes established)

p

j (m) = probability that species j is not successfully introduced in a single ballast water discharge under treatment option m based on the density of species j

To address the different densitie s of species, the DPEIS calculated the relative abundances of the n species using a geometric model. Additionally, because many of the species may be rare, and

thus close to the critic al population threshold, they compared the probability of extinction with n

e = 1 and n

e = 100. Finally, in this section they al so considered differe nt organism population sizes resulting from unexcha nged and exchanged ballast.

For brevity sake, we will not detail the steps in this analysis, and the reader is referred to Section 5 of Appendix A of the USCG Draft Programmatic Environmen tal Impact Statement (USCG, 2008). Rather we will present the final relative treatment efficiencies for Alternatives 2-4 compared to initial organism populations equiva lent to unexchanged and exchanged ballast water discharges. From these populati on sizes and the assumption of 12 different species within the ballast discharge, they calculated the probability (q

m ) of at least one succe ssful introduction of a species from the ballast discharge. Probabiliti es that no species would successfully invade for

the treatment alternatives were then determined relative to those with unexchanged ballast water or exchanged ballast water (Table 11).

51Table 11: Relative efficiencies of Alternatives 2, 3 and 4 that no speci es successfully invades from a ballast discharge compared to unexchanged ballast water or after ballast water exchange (BWE). The analysis assumes 12 unique species in the ballast discharge. The critical population threshold (n

e ) is equal to 1 or 100 organisms. M odified from Table 5-9 in the DPEIS.

n e = 1 n e = 100

Alternative Unexchange d BWE Unexchanged BWE

2 (IMO) 52% 37% 78% 63%

3 (1/10 th IMO) 73% 64% 94% 90%

4 (1/100 th IMO) 88% 85% 100% 100%

The conclusion that the DPEIS draws from this analysis is, “The speci fic reduction depends upon the alternative selected and the size class of the organism consid ered, but the modeling results for multiple species support the conclusion that more stringent treatment alternatives will substantially reduce the likelihood of new ballast water introductions” (DPEIS, page A-42). This analysis also emphasizes the importance of evalua ting the total risk for the multiple species in ballast discharges. Finally, th e reduced risk at the higher cr itical population threshold value illustrates the importance of this value in drivin g the results from PVA models, at least at the very low population densities that will be associated with the pr oposed ballast water standards.

Assumptions and Limitations:

Use of PVA models are not wit hout their critics (e.g., Ludwig , 1999; Fieberg and Ellner, 2000; Coulson et al., 2001). Coulson et al. (2001) “doubt the general clai m that they can be accurate in their ability to predict the future status of wild populations.” Mo re optimistically, in a review of 271 time series representing 46 taxa, Holmes et al. (2005) conc luded that diffusion approximations did a reasonably good job at predicting proportional and severe population declines. They were not as good at predicting true extin ction. Some of th e criticisms of PVA

models are blunted when the PVA models are used to evaluate relative differences among

treatment alternatives rather than to predict quantitative extinction probabilities, as was noted in the DPEIS (USCG, 2008). However, analyzing relative differences prec ludes the use of the models to directly develop organi sm-based discharge standards.

Values for several of the parameters in the DPEIS are not well justified, in particular the values for c and the critical population threshold. These are critical parameters that drive the conclusions, and any future PVA modeling effort needs to justify the input values better.

The multi-species scenario was only run for the > 50 micron size class in the DPEIS. As data become available, a similar analysis should be attempted with the 10-50 micron size class. Additionally, the importance of the number of species used in the analysis should be explored, as the assumption of only 12 unique taxa in th e DPEIS seems low given the diversity of phytoplankton and zooplankton found in ballast water (e.g., Choi et al., 2005; Cordell et al., 2009).

52In several cases, the use of extreme ranges for in put parameters in the DPEIS analysis obscured the long-term benefits from reducing organism concentrations. In particular, in the single species analysis, the ranges in organism concentr ations of Alternative 1 bracketed the treatment concentrations, resulting in the erroneous conclu sion that the treatment alternative would offer no improvement. It is true that some ships may have essentially no organisms in their ballast but this is a rare event (see Minton et al., 2005), an d on the average ballast water treatment will substantially reduce organism c oncentrations, and hence risk. While the DPEIS notes this in their multi-species analysis, it was not apparent in the tables or in the discussion in the single species scenario.

The greatest practical limitation in developing P VA models for marine/est uarine organisms is deriving high quality values for the instantane ous population growth rates and variation from long-term population trends. Diffusion models have primarily been applied to birds and mammals based on 10+ years of population monitori ng. Such long-term population data for the marine/estuarine organisms lik ely to be discharged in ba llast water (e.g., phytoplankton, holoplanktonic zooplankton, and be nthic species with pelagic larv ae) are rare. Even when longterm monitoring data are availa ble, population estimates for ma rine/estuarine organisms may display a higher sampling variability than f ound with birds and mammals, which can affect parameter estimation (Holmes et al., 2005; Holmes, 2004).

Recommendations and Conclusions:

Given the current state of the sc ience and data availability, PVA diffusion models are appropriate

tools to estimate the relative effect iveness of different ballast water treatment alternatives. While recognizing the substantial insight s into relative treatment effi ciencies provided by the DPEIS (USCG, 2008), we recommend that any new effort s using PVA models should begin anew rather than building upon the models in this document. We make this suggestion, in part because of the difficulty we had in following some of the specific procedures in the DPEIS and because presenting the results in terms of the total range of ballast water organism concentrations tended

to obscure the benefits of the treatment altern atives. Additionally, an independent assessment may suggest a modified approach.

The use of PVA models to generate quantitative predictions of invasi on success (versus relative treatment efficiencies) is less clea r. The advantage of such mode ls is that they would provide quantitative invasion risks for proposed discharge standards. The greatest limitation is the current lack of quantitati ve population vital rates. Accordingly, before initiating any quantitative PVA modeling study, we recommend that a dedicate d effort be undertaken to extract estimates of population growth rates and variances from lo ng-term studies of marine/estuarine species.

One obvious source are the commercial catch st atistics, but this w ould require separating population variability from variabi lity due to fishing related mortal ity and/or changes in fishing effort. There are, however, other data that w ould not have these confounding effects. Eckert (2003) synthesized 570 population time series fo r 170 invertebrate species, with the durations ranging from one to 39 years wh ile Eckert (2009) collected 786 population time series greater than 2 years for 226 species in the Gulf of Al aska. Desmond et al. ( 2002) report on an eleven year record of fish and invertebrates in S outhern California. We are less familiar with zooplankton, but even a cursory s can of the literature suggested th at long-term records exist for several estuarine and marine cope pod species (Jossi et al., 2003; Pershing et al., 2004). Not all

53these studies will be suitable for deriving vital rates, but with sufficient effort it should be possible to generate ecologically realistic ranges for population growth and va riability for a suite of species across a range of taxa and habitats.

Whether assessing relative treatment efficiencies or quantitative risk probabilities, any future PVA analyses should focus on multiple species scenar ios rather than modeling a single species. That is, the analysis should a ddress the question “what is the likelihood of any species from a ballast discharge becoming established?” rather th an “what is the likelihood of any particular species becoming established?” The former is the critical ecological and regulatory issue.

A comprehensive sensitivity analys es should be part of any new P VA modeling. In particular, a range of instantaneous growth rates and instantaneous variance s in growth rate (the “c” parameter as used in the DPEIS formulation) sh ould be explored, with the ranges based on the review of population vital rates mentioned above . Another important f actor that should be evaluated is the critical populat ion density. While a full range of values should be used for all the input parameters, it is critical that the inte rpretation of the results explicitly consider the likelihood of particular values so as not to obscure the general tre nds with rare events, such as ships with organism concentrations below the proposed standards.

Any new PVA modeling should evalua te the full range of potential discharge standards including the proposed USCG Phase II standards. Sin ce the USCG may implement more stringent standards in an incremental fashion, we suggest that standards equivalent to 1/10 th and 1/100 th of the IMO standards (e.g., standard s of 1 and 0.1 organisms per m 3 for the >50 micron class) also

be evaluated.

54

### VIII. PER CAPITA IN VASION PROBABILITIES

Deborah A. Reusser, Henry Lee II, Melanie Frazier, and Greg Ruiz

Overview: As discussed in Section 2, ther e is a general consensus that an increase in propagule supply

increases the likelihood of invasion. Based on this premise, we de veloped a “per capita invasion probability” (PCIP) approach to estimating th e likelihood of invasion based on historical

invasion rates and calculated ballast-associated propagule pressures. The PCIP is the per year probability that an individual non-native propagule discharged from ballast water will become established as a new nonindigenous species in a specified waterbody. Using a linear dose response assumption, the PCIP is calculated from the historical number of potential ballastmediated invasions in a specifi ed waterbody over a defined time period, the average annual total ballast discharged at that location during th is time period, and the estimated organism concentration in the discharged ballast water. We focus on the >50 micron size class because

sufficient data are available to calculate the PCIPs for multiple waterbodies and coasts, though the approach can be applied to the 10-50 micron size class if the data are av ailable. We calculate

coastal estimates of PCIPs for th e East, Gulf, and Pacific coasts of the coterminous United States

as well as individual PCIP values for 17 coastal es tuaries. Additionally, we include a PCIP value for the Great Lakes as a preliminary assessm ent of whether standards developed for the marine/estuarine systems would be protective of freshwater systems.

An advantage of this approach is that it can be used to generate quantita tive discharge standards because it directly relate s the risk of invasion to ballast wate r organism concentrations. It is important to note, however, that because of the complexities involved with the invasion process (Table 2), our objective was not to find a highly predictive relationship between the calculated propagule supply and site-specific invasion rates. Rather, our obj ective was to “cut through” the complexities to develop an approach to allow ri sk managers to generate discharge standards based on defined assumptions and risk levels.

Calculation of Per Capita Invasion Probabilities: The per capita invasion probability (PCIP) is calculated as:

Equation 18 : PCIP = N h / (D h * C h )

Where: PCIP = per capita invasion probability (new invading species * organism -1 )

N h = historical annual invasion rate of potential ballast-associ ated invaders for a waterbody (new invading species * year -1 )

D h = historic annual foreign ballast discharge rate into a waterbody (m 3 year -1 )

C h = historic concentration of organisms in ballast water discharged into a waterbody (organisms

* m -3 )

As mentioned, the PCIP is the probability that an individual propagule, or organism, discharged

in ballast water will become established as a new nonindigenous species within the waterbody.

55For example, if one new nonindigenous species became established within a waterbody in which a total of a million individual organisms were discharged in a year, the per capita invasion probability would be 10 -6 . Because the PCIP only accounts for new invaders, it does not address the issue of multiple invasions of currently existing nonindigenous species into a waterbody.

This model assumes a linear dose-response, with the number of invaders increasing proportionally with larger ballas t water organism concentrations and/or greater volumes of ballast water discharged. Accordingly, after calcul ating a PCIP from a hist orical invasion rate, it is possible to predict the number of new, unique invaders per year for a given ballast water organism concentration and ballast water volume:

Equation 19: N p = PCIP * D p * C p

Where:

N p = predicted annual invasion rate of potential ballast-associated invaders for a waterbody (new invading species * year -1 )

D p = predicted annual foreign ballast discharge rate into a waterbody (m 3 year -1 )

C p = predicted concentration of organisms in ballast water discharged into a waterbody (organisms * m -3 )

Foreign Ballast Water Discharge Rates for C oastal Waterbodies and the Great Lakes: Historical average annual fore ign ballast discharge rates (D h in Equation 18) were used to calculate the total propagule suppl y. Discharge rates for coastal waterbodies were obtained from the Smithsonian Institution ballast water database (see the National Ballast Information Clearinghouse, http://invasions.si.edu/nbic/search.html ). Estimates for the contiguous East, Gulf, and Pacific coasts were generated from discharge records from all ships discharging foreign ballast into coastal ports on the respective coasts. Only ballast identified as coming from a foreign source was included. Th e values in Table 12 are the aver age of the yearly rates for the period 2005 to 2007, which was chosen because it occurs after the implem entation of mandatory ballast water reporting and represen ts the most complete discharge records available. Average annual foreign discharge rates were also calc ulated from 2005 to 2007 for 17 coastal ports, representing a cross section of small to large ports. Because the foreign ballast was calculated on a per tank basis, the movement of undischarged foreign ballast among ports can be estimated. That is, by following foreign ballast by tank it is possible to account fo r foreign ships that initially entered one port but did not discharge their ballast until they visite d another port. Foreign discharge values for multiple ports within a waterbody were summed for a total discharge volume for a waterbody, including freshwater ports in larger systems (e.g., Columbia River). For the Great Lakes, the National Biol ogical Invasion Shipping Study (Reid and Carlton, 1997) reported a total annual foreign ballast wate r discharge into the Great Lakes of 1,395,461 metric tons in 1991. This is before mandatory ballast water exchange, wh ich was initiated in the

Great Lakes in 1993.

Estimates of Organism Concen trations in Ballast Water: Organism concentrations in ballast water discharged in coastal waters (C h in Equation 18) were estimated from Minton et al. ( 2005), who reported zooplankton (> 80 microns) concentrations in

56Table 12: Historical number of invaders (Nh), foreign ballast discharge volumes (Dh), number of ships discharging foreign ballast, andper capita invasion probabilities (PCIP) for the East, Gulf, andPacific coasts of the United States, 17 coastal ports, and theGreatLakes. The number of coastal invasions isthe number of non-native invertebrates and macroalgae >50 microns first reported from1981 to 2006 that were possibly introduced via ballast water and consideredestablished. The total number of invaders in the coastalports includes marine, brackish, and freshwater species, while the total without freshwater excludes the freshwater invaders.Theforeign ballast discharges for the coastal waterbodies are the annual averages of 2005 to 2007 and include marine, brackish, andfreshwater ports within the waterbody.Per capita invasion probabilities for the coastal waterbodies are given for a range ofpossiblevalues, including the lower quantile (0.025), median, and upper quantile (0.975), based on the simulation estimates of organismconcentrations among the ships discharginginto a waterbody. The number of invadersfor the Great Lakes is given for bothmacrofauna and phytoplankton for the period 1960 to 1988, while theballast water discharge volume is for 1991. The sum of thedischarge volumes and number of ships from the 17 ports is lessthan the coastal averages becauseall ports were included in thecoastal values. FW = freshwater.WaterbodyTotal #Invaders /Total # w/oFW speciesAverage AnnualForeign BallastWater DischargeVol.(m3year-1)# Ships withForeignBallast Water2005-2007PCIP(lower 0.025quantile)PCIP(median)PCIP(upper 0.975quantile)East Coast407,407,83212,8604.00E-114.31E-114.64E-11Charleston13/12281,1605633.05E-103.70E-104.46E-10Chesapeake17/143,011,98213153.85E-114.51E-115.28E-11Jacksonville14/13130,2967917.48E-108.58E-109.83E-10Miami4/4578,48225155.04E-115.51E-116.02E-11Narragansett Bay13/1321,030192.38E-095.41E-091.35E-08Portsmouth9/96,377103.26E-091.54E-086.16E-08Gulf Coast1819,605,34011,8216.98E-127.31E-127.67E-12Corpus Christi5/51,254,8456212.65E-113.18E-113.84E-11Galveston4/4748,1367783.53E-114.28E-115.22E-11Pensacola3/31,12188.72E-092.45E-087.88E-08Tampa Bay7/1734,7189235.37E-116.54E-117.88E-11Pacific Coast6714,788,36959983.41E-113.61E-113.83E-11Columbia River22/125,533,61817592.89E-113.17E-113.47E-11Coos Bay22/22583,517872.18E-103.04E-104.40E-10Humboldt Bay29/295,539101.42E-085.24E-081.85E-0757WaterbodyTotal #Invaders /Total # w/oFW speciesAverage AnnualForeign BallastWater DischargeVol.(m3year-1)# Ships withForeignBallast Water2005-2007Per CapitaInvasionProbability(lower 0.025quantile)Per CapitaInvasionProbability(median)Per CapitaInvasionProbability(upper 0.975quantile)Los Angeles / LongBeach31/312,676,87416938.20E-119.23E-111.05E-10Puget Sound23/213,960,43811674.12E-114.64E-115.23E-11San Diego Bay23/2131,2711124.20E-095.92E-098.52E-09San FranciscoEstuary53/451,548,11610152.33E-102.74E-103.22E-10Great Lakes –Macrofauna171,395,461UnknownNA9.10E-11NAGreat Lakes –Phytoplankton141,395,461UnknownNANANA58unmanaged ballast water in 354 ships of various types (see Figure 3). Similar values were reported in a survey of 429 ships of multiple vessel types that had no ballast water exchange or treatment (MEPC, 2003b). Both of these studies showed that organism concentrations in untreated ballast water can vary by orders of ma gnitude among ships. For example, about 3.8% of the ships reported by Minton et al. (2005) had organism c oncentrations le ss then 10 m -3 while about 1.1% of the ships had con centrations greater than 50,000 m -3 . Thus, the actual propagule dose a waterbody receives will de pend on the distribution of organism concentrations among the ships discharging within the system.

Because the distribution of organism concentratio ns in ballast water of is highly skewed, the mean concentration may over or underestimate the true propagule pre ssure depending upon the concentrations in the specific se t of ship discharging within the waterbody. Consequently, rather than estimating PCIP values using the mean concentration of organisms we performed a simulation to estimate PCIP values from a range of possible propagule pressures. The simulation was performed by randomly assigning each ship di scharging foreign ballast in a waterbody a concentration of organisms, selected from the distribution of values reported by Minton et al. (2005; their Figure 3a). The randomly selected concentration was then multiplied by the volume of foreign ballast discharged by that particular ship (see Tabl e 12 for number of ships in each waterbody). The values for each ship within a waterbody were summed, generating a total propagule dose from which the PCIP value was calculated. This process was repeated 10,000

times to create a distribution of PCIPs for each waterbody from which the lower (0.025), median, and upper (0.975) quantile values were determined (Table 12). Figure 6 shows the range of PCIPs for the Pacific Coast genera ted with this method. Using a range of possibl e PCIP values allows us to make predictions that do not undere stimate the risk of invasion, which might occur if only the mean concentration of organisms is us ed. (Note that with a fi xed historical invasion rate, higher PCIP values result from lower disc harge values since the same number of invaders occurred with a lower propagule pressure.) Becau se we did not have individual ship records for the Great Lakes during 1991, we could not generate the PCIP distributions and instead used the mean ballast water organism concentr ation from the IMO baseline study (4640 m -3 , MEPC, 2003b) to calculate the PCIP for the Great Lakes.

Estimates of Historical Invasion Rates: The total numbers of invaders reported be tween 1981 and 2006 were synthesized for the contiguous United States Pacific Co ast, East Coast, and Gulf Coast as well as for 17 individual coastal waterbodies (Table 12). The 1981 to 2006 time period is before the implementation of mandatory mid-ocean ballast water exchange fo r coastal waterbodies, allowing the use of the estimates of organism concentrations in unexchang ed ballast. A 25 year time period was chosen

to smooth out short term variations in invasion rates as well as vari ations in monitoring efforts. A longer time period also helps to mitigate effects of the lag be tween an actual invasion event and when the species is first discovered (e.g., Costello and Solow, 2003).

The number of invaders is based on non-native invertebrates and macroa lgae >50 microns; fishes and vascular plants were not included. Besides being reported in each coas t or waterbody within the 25 year window, the species included in the an alyses had to be considered established and potentially introduced via ballast water. The coas tal invaders were classified into three salinity tolerance regimes: marine/estuari ne (>20 psu), brackish (0.5-20 psu) , and freshwater (<0.5 psu).

This broad classification allows an evaluation of the importance offreshwater invaders in riverdominated estuaries such as the Columbia River. Because of the poor resolution between native

59versus nonindigenous phytoplankt on species in coastal waters (Carlton, 2009), no attempt was

made to estimate the number of invaders in the 10-50 micron size class. The number of invaders was generated from the Smithsonian Institution invasive species databa se (Fofonoff et al. 2003b) and the majority of the East, Gulf, and Pacific in vaders and their vectors are listed in Appendix A of Ruiz et al. (2000).

The 1960 to 1988 time period was chosen for th e Great Lakes because it is before the implementation of mandatory ballast water exchange in 1993. Duri ng this interval, a total of 17

macrofaunal ballast-associated invaders was reported ( http://www.glerl.noaa.gov/res/Programs/ncrais/d ocs/great-lakes-list.xls , accessed September 26, 2009), resulting in an invasion rate of 0.58 invaders per year. Th is rate is based on all shippingrelated invaders as well as th ree macrofaunal invaders with u nknown vectors. The invasion rate for phytoplankton was similar (Table 12), resulting in a tota l rate of slightly more than 1 invader per year which is similar to that reported by Ricciardi (2006).

Figure 6: Distribution of per capita invasion prob abilities (PCIPs) for the Pacific Coast based on 10,000 random simulations of organism con centrations among the 5998 ships discharging foreign ballast. The red lines indicate th e lower 0.025 quantile and the upper 0.975 quantile while the blue line indicates the median. Approx imately 95% of the values fall between the red

lines.

60Uncertainties in Historical Invasion Rates and Safety Factors: Of the three parameters going into the calculation of a PCIP, the historical invasion rate has the greatest uncertainty and it is wort h exploring both the sources of this uncertainty and whether it

tends to over or underestimate future invasion rate s. One source of this uncertainty is that many coastal nonindigenous species can potentially inva de through multiple vectors, such as both ballast water and hull fouling (e.g., Fofonoff et al., 2003a). Inclusion of these “polyvectic” invaders (Ruiz and Carlton, 2003) in the historic invasion numbers in Table 12 potentially inflates the ballast-associated invasion rate, resu lting in an artificially high PCIP. Because of differences in the relative importance of different vectors among estuaries, uncertainty related to multiple vectors is probably greater when comp aring among estuaries than for the coast-wide estimates. For example, San Diego Bay, which has a high invasion rate relative to the ballast discharge volume, is the home to the largest naval base on the Pacifi c Coast consisting of approximately 54 naval ships. Ballast discharg es from military ships are not included in the volumes in Table 12, but most naval ships tend to discharge relatively small amounts of ballast (see Table 2 in Appendix A of U.S. EPA, 1999) , which suggests a higher propagule pressure from hull fouling in San Diego. Hull fouling ma y also be relatively more important in smaller ports that have low ballast discharge rates but a relatively large number of commercial fishing and recreational boats with no foreign ballast.

Secondary invasions could also infl ate estimates of historical ball ast-associated invasion rates in

individual waterbodies. Afte r the primary invasion and establishment of a new NIS into a biogeographic region, the invader may spread wi thin the biogeographi c region via secondary invasions from the initially esta blished population. Likely mech anisms for secondary invasions include ballast water discharges and hull fouli ng via intracoastal commercial traffic emanating from the infected waterbody (e.g., Simkanin et al., 2009; Cordell et al., 2009) as well as hull fouling on recreational boats. Secondary invasions may also occur via natural dispersal mechanisms, such as currents and rafting, as suggested by occurrence of soft-bottom NIS in

Pacific Northwest estuaries with no ballast discharges or oyster aquaculture (Lee et al., 2006; Lee, unpublished data).

An important source of uncertain ty that could result in underes timating PCIP values is the

underestimation of historical invasion rates. Ca rlton (2009) identified 12 s ources of error leading

to invader underestimation incl uding unknown, unreported, misclassi fied, and rare invaders. In some parts of the world, such as Denmark, S outh Africa, and Chile wher e no invasions prior to mid-nineteenth century are recognized, the num ber of known invaders could be underestimated by as much as 5 to 10 times (Carlton 2009). Fo r California, Cohen (in Falkner et al., 2006) suggested that unrecognized invade rs could increase the invasion rate by 50% to 100%. A recent analysis of California invaders lists 457 cryptogenic spec ies versus 358 nonindigenous species (California Dept. of Fish and Game, 2009); the California invasi on rate would more than double if all these cryptogenic species were actually nonindigenous. While some of these cryptogenic species are likely unrecognized native sibling species (e.g., Know lton, 1993), the high number of cryptogenic species in California suggests th at the reported number of invaders may underestimate actual numbers by 50% to 100% within the United States.

Other sources of uncertainty could also cause us to underestimate the risk of introducing new invaders through ballast discha rges: the relations hip between propagule pressure and the

61probability of invasion could be steeper than the proportional relationship we assume, in particular at very low concentr ations (curve d in Figure 2); su rvival in ballast tanks could improve if voyage durations decrease due to faster ships; and wa terbodies may become increasingly susceptible to inva sion due to climate change or other environmental changes. While it is not possible to quantify the total uncertainty from these various sources, safety factors on the order of 5 to 20-fold have been proposed when calculating the risk to endangered and threatened species from exposure to pesticides (U.S. EPA, 2004b), and similar ranges could be used in the generation of discha rge standards (see Equations 20 and 21). We strongly suggest using a single safety factor rather than multiply ing a string of individual safety factors for each source of uncertainty, which quickly results in unrealistic values (see Chapman et al., 1998).

Among Port Patterns of Invasion Risk: There is considerable range in the PCIP values among the 17 indi vidual ports both along a single coast and across coasts (Table 12). The largest difference is between the Humboldt Estuary and Columbia River, a more than 1600-fold differen ce. We suspect these among-estuary differences

are due to a suite of non-exclusiv e factors. Part of this range may reflect differences in the invasibility among waterbodies, whether due to differences in biotic resistance or local environmental drivers. For example, the lowe r invasion probability in the Columbia River compared to other large Pacific Coast ports may be partially explained by wide seasonal and tidal salinity fluctuations (e.g., Hickey et al ., 1998) that largely limit estuarine invaders to euryhaline or freshwater species.

One pattern observed on all three coasts is that th e smaller ports had more invaders than expected from the amount of foreign ballast water, which re sulted in higher PCIP values. Humboldt Bay, a small port in northern California, had only ten ships discharging foreign ballast from 2005 to 2007 (Table 12). Even with this small ballast input, Humboldt ha d the third largest number of invaders of the 17 estuaries, only exceeded by the San Francisco Estuary and the Los Angeles/Long Beach port. It is possible that thes e smaller ports have a greater invasibility than larger systems, but we suggest secondary inva sions and invasions via mechanisms other than foreign ballast water discharges are relatively more important in these systems, which inflate the PCIP values. In particular, Humboldt Bay’s proximity to the San Francisco Estuary and the prevailing northward oceanographic currents al ong the coast from Sa n Francisco Estuary (particularly in El Niño years) may provide one mechanism of secondary invasion (Grosholz, 1996; Behrens Yamada et al., 2005) in a ddition to intracoas tal shipping.

We evaluated the potential eff ect of polyvectic species and se condary invasions on the invasion rate in Humboldt by removing NI S from the Humboldt list if they: 1) had been observed in

Pacific Coast estuaries that do not receive ballast water discha rges; 2) were found on the outer coast; and/or 3) had a potential vector other than ballast water. Of the 29 potential ballast-water invaders reported from Humbol dt between 1980 and 2005, the introduction of only two could not be explained by mechanisms other than foreign ballast water discharges in Humboldt. The corresponding PCIP value (median = 3.58E-09) with the reduced inva der list is only about 5% of the value when all potential invaders are include d. We suspect that secondary invaders and polyvectic invaders also inflate the PCIP values in the other small ports. Another issue for estimating invasion probabilities in small estuaries is the large statistical variability in estimates

62based on small sample sizes. Consequently, port s with small amounts of ballast discharge will have high PCIP values even with the occurren ce of a single ballast associated invader.

Because of these factors, we be lieve the PCIP values for the m oderate to large ports are more reliable, with moderate/large ports defined as th ose having an average annual foreign discharge

volume of > 100,000 m 3 . This threshold was chosen because of a distinct break in ballast discharge volumes that occurs between 31,271 m 3 (San Diego) and 130,296 m 3 (Jacksonville). The 12 moderate/large ports contribute 99.67% of the total ballast from the 17 estuaries. The range in PCIP values among these moderate to la rge ports is only about 28-fold compared to the more than 1000-fold range when the small ports are included.

Discharge standards can be generated for i ndividual ports by rear ranging Equation 19 to calculate the organism concentration in ballast water (C p ) associated with a projected ballast discharge volume (D p ), acceptable risk as represented by th e number of new invaders per year (N p ), PCIP value from Table 12 or otherwis e calculated, and a safety factor:

Equation 20: C p = N p /(D p * PCIP * Safety Factor)

Safety factor = number > 1 (unitless)

What value to use for the PCIP in Equation 20 is a risk management decision. The 0.975 quantile represents an upper probability that a propagule discharged from ballast water will

become established as a new invader based on the distribution of organism concentrations in the ships discharging into the port/estuary. The median represents an “average” probability of establishment based on the “average” organism c oncentration in the ships. Similarly, the inclusion and size of any safety factor is also a risk management decision. Because it is in the dominator, the safety factor is set to 1 if no adjustment is made for uncertainties.

Because of the uncertainties surrounding invasion rates for single estuaries, we believe a better

alternative is to base the sta ndard on a specified confidence in terval (e.g., upper 95% CI) around the PCIP values for the 12 moderate/large ports. An advantage of this approach is that it incorporates the among estuary variation in PCIP values in the calculation of the discharge standard. Using this approach, the formula to calculate the discharge standard is:

Equation 21: C p = N p /(D p * PCIP CI * Safety Factor)

PCIP CI = probability that a single propagule from ba llast discharge will become established as a new invasive species; calculated for a given c onfidence interval estimat e of PCIP for the 12 moderate to large ports.

PCIP values for 12 individual ports can be base d on the 0.5 (median) or 0.975 quantile estimates from the simulations of organism concentration for each ship, or some other quantile value from the randomization. Additionally, different confidence levels can be used for PCIP CI . Table 13 gives the 90%, 95%, 99%, and 99.9% upper confid ence intervals generated for the 12 moderate and large ports around the median and 0.975 quantile values . These are two-tailed confidence intervals so, for example, 5% of the values are larger than th e 90% confidence interval values.

63Assuming a doubling of the annual ba llast water discharge rate on the Pacific Coast to 30 million

m 3 (see Table 12), an acceptable risk as represen ted by an invasion rate of one new invader per thousand years, the upper 99.9% confidence interv al value for the 0.975 quantile PCIP for the Pacific Coast, and a 10-fold safety factor, the discharge standard becomes:

Equation 22: C p = (1x10 -3 invader/yr) / (30x10 6 m 3 ballast water/yr * 5.90x10 -10
invader/organism * 10) = 0.006 organisms m -3

The resulting discharge sta ndard of 0.006 organisms m -3 is similar to the USCG Phase II standard for >50 micron organisms (0.01 organisms m -3 ). The value derived from Equation 22 is based on a number of protective assumptions, including doubling the cu rrent Pacific Coast ballast discharge volume, using the 0.975 quantile for the estimate of PCIP, using the upper 99.9% CI value, and including a 10-fold safety factor. Modifying the assumptions changes the discharge standard to varying degrees, and one wa y to visualize the “regul atory landscape” is to plot the invasion probabilities as a contour plot, or “risk diagram” , as a function of ballast water discharge volumes and organism concentrations. (Note that while the risk diagrams include long-range predictions, invasion ra tes for 1000 to 10,000 years in the future are best interpreted as indicating a very low probability of invasion ra ther than quantitative predictions.) Figure 7 shows the risk diagrams for the Pacific Coast ba sed on three different safety factors (1, 10, and 20), using the PCIP value for the 99.9% confiden ce interval of the 0.975 quantile value from the 12 moderate/large estuaries. We consider these risk diagrams as a complement to Equation 21, and the R code (R Development Core Team, 2008.) to generate these diagrams based on different input values is given in Appendix A.

Table 13: PCIP CI estimates based on upper 90%, 95%, 99%, and 99.9% confidence intervals around the median and 0.975 quantile PCIP values for the 12 moderate to la rge estuaries in Table

12. Upper 90% CI Upper 95% CI Upper 99% CI Upper 99.9% CI

Median 3.48E-10 3.77E-10 4.41E-10 5.34E-10 0.975 quantile 3.71E-10 4.05E-10 4.80E-10 5.90E-10

Coastal Patterns of Invasion Risk: Due to the significant potential for secondary in vasions, we believe the best alternative to developing discharge standards is to use Equa tion 20 with PCIP values derived from the aggregated data for an entire coast. The aggr egated coastal data eliminate the uncertainty associated with secondary invaders as the hist orical invasion rate is based on the number of unique invaders to a coast so no invader is counted more than on ce. This approach is supported by the small variance in PCIP valu es among the coastal regions. In particular, there is only a

19% difference between the East and Pacific coasts (Table 12). The Gulf Coast PCIP is less than 6-fold smaller than the East or Pacific coasts, while the PCIP value for macrofauna for the Great Lakes is about 2-fold larger than those for th e East and Pacific Coasts. Thus, even when comparing across three different coasts and the Great Lakes, there is only slightly more than a 12-fold range in the PCIP values. This relatively small range across diverse environments with different ballast discharge volumes and donor regions indicates that the analysis at this spatial scale captures many of the sources of variation.

64We focus our analysis on the Pacific Coast becau se the extensive research on the distribution of NIS in this region (e.g., Cohen a nd Carlton, 1995; Cohen et al., 2001; Lee et al., 2003: deRiveria et al., 2005; California Dept. Fish Game, 2009) pr oduces the most complete historical invasion rate. Using the same inputs for an acceptable ri sk level, ballast water discharge volume, and safety factor as for the estuary calculati on (Equation 22), and the upper 0.975 quantile PCIP value specific to the Pacific Coast, the discharge standard becomes:

Equation 23: C p = (1x10 -3 invaders/yr) / (30x10 6 m 3 ballast water/yr * 3.83 10 -11
invaders/organism * 10) = 0.087 organisms m -3

Based on this set of assumptions, the discharg e standard for >50 micron organisms would be approximately 100-fold lower than the proposed IMO standard, about 9-fold higher than the Phase II USCG standard, and about 10-fold higher than the standard derived from the multiple estuaries (Equation 22). As another example we set the acceptable risk at one new invader per 100 years, the safety factor to 2, and use the me dian PCIP value instead of the upper quantile. With these less protective assumptions , the standard is 4.6 organisms m -3 , about 2-fold lower than the IMO standard. Both of these predictions are illustrated as risk diagrams in Figure 8.

Assumptions and Limitations: The approach described here has no t been subject to peer review. However, we have a draft of a paper and our goal is to submit it to a peer-reviewed journal in 2010.

As with any approach used to establish ballast water discharge standards, the per capita invasion probabilities make a number of assumptions. We list the major assumptions in Table 14 along with an assessment of how they affect the calc ulation of the PCIPs and the discharge standard derived from these probabilities.

The PCIP values for the smaller ports are subs tantially higher than those for systems with moderate to large ballast discharge volumes. As discussed, we believe this is largely a result of secondary invasions inflating th e presumed ballast-associated i nvasion rate. However, if the higher invasion rates are actually a result of the smaller ports having a greater invasibility, the standards generated from the coas t values or the moderate/large ports would not be protective of these systems. Another way that the present an alysis could underestimate risk is by failing to account for the introduction of species that can be come established with a single or very small number of individuals, such as a parthenogenic species. As discussed in Section II, the only absolute protection against such invaders is a true zero discharge standard.

Our analysis is limited to organisms >50 micr ons, though the PCIP appro ach is theoretically applicable to smaller size classes. The pr actical limitations, however, are the difficulty in distinguishing native from nonindigenous prot ozoa, phytoplankton, and microbes and the corresponding lack of data on hist orical invasion rate s. As pointed out by Carlton (2009), “no introduced diatoms, dinoflagellates, or other phyt oprotists are recognized in San Francisco Bay, at either the morphospecies or genospecies level” despite the abundance of phytoplankton in ballast water. However, it would be possible to conduct an analysis fo r the Great Lakes given the reported historical invasion rate for phytoplankton (Table 12) if an estimate for the historical ballast water phytoplankton concentr ations can be obtained.

65Figure 7: Risk diagrams for the Pacific Coast illustrating the effect of three different safety factors (1, 10, and 20). Calculations are based on the99.9% confidence interval of the0.975 quantile value of PCIP from the 12 moderateto large estuaries. A safety factor of 1 means that there was noadjustment for the uncertainties.66Figure 8: Risk diagrams for the Pacific Coast based on less protective (left diagram) and more protective (right diagram) assumptions. The ri sk diagram on the left is based on the median PCIP for the Pacific Coast and a safety factor of 2. The diagram on the right is based on the upper 0.975 quantile PCIP value a nd a safety factor of 10.

By using past invasion rates to predict future rates, fundamental assumptions of the per capita probability approach is that neither the invasion pot ential of any new invade rs or the invasibility of the waterbody itself will change in the future. Actually, these assumptions apply to nearly all the approaches (e.g., use of previously measur ed population vital rates in PVA models) but the issue is more apparent when using historical rates. If the best co lonizers tended to invade first,

then the PCIPs derived from these historical data would over predict the nu mber of new invaders for a given propagule pressure. However, the appa rent increase in the rate of invasion in a number of aquatic ecosystems (e.g., Cohen and Carlton, 1998; Holeck et al., 2004) is the opposite of what would be expected if there had been a general decrease in the virility of new invaders. Changes in the invasi bility of aquatic ecosystems are more difficult to assess. In particular, environmental change associated with climate change is a “wild card” for all the approaches to setting discharge standards. Deve lopment due to port expansion could also change the invasibility of a system. Probably the only practical near-term solution is to incorporate a safety factor in anticipation of such changes. Over a longer-term, it is possible to periodically

evaluate PCIP values for a coast to determine if there have been any substantial changes.

Recommendations/Conclusions: The per capita invasion probability approach atte mpts to cut through the “Gordian Knot” of uncertainties associated with predicting ballast water invasions, and E quations 20 and 21 and the

67risk diagrams (Figures 7 and 8) can be used to set organism-based discharge standards. As with all approaches, however, there are a number of assumptions (see Table 14). Accordingly, our strategy was to develop an appro ach that allows risk managers the option to develop discharge

standards with different risk levels based on di fferent sets of assumptions. Specifically, the following inputs can be set: 1) acc eptable invasion risk as meas ured by an invasion rate; 2) ballast water discharge volume; 3) use of PC IPs based on median ballast water organism concentration or upper quantile values; 4) medi an or an upper confiden ce interval around the PCIP with the among-port analysis; and 5) magnitude of any safety factor.

The uncertainty around the parameters going into the per capita invasion probability model is relatively small. Even with the historical inva sion rate, the uncertainty is only on the order of 2­ fold for the Pacific Coast. In comparison, our analysis suggests that there are much greater levels of uncertainty in the popul ation vital rates that are need ed for reaction-diffusion or PVA models. Additionally, the model does not have to be parameterized for each species or type of species as with the population m odeling approaches. Finally, th e data going into the per capita probability approach are readily understandable by managers and th e public, which is beneficial in gaining acceptance for any ballast water discharge standard.

Of the three approaches to setting discharge st andards (PCIP from individual estuaries; values based on upper confidence intervals from distribu tions of PCIPs about individual estuaries; PCIP values based on aggregated coastal values), we suggest that the coastal approach has the lowest inherent uncertainty. Furt hermore, since most invaders spre ad along the coast, analysis at this scale is ecologically appropr iate. Because of the extensive effort in documenting invaders on the Pacific Coast, the PCIP values for the Pacific Coast are the most reliable and we recommend using this coast to generate discharge standards for marine and estuarine ports within

the United States.

The PCIP value for macrofauna for the Great Lakes is about 2-fold larger than those for the East and Pacific coasts, suggesting that there may be a greater likeli hood of any individual propagule becoming established as a new invader in the Grea t Lakes. However, less complete data were available for ballast discharge volume and orga nism concentrations, and we consider the calculations for the Great Lakes a preliminary analys is. While there is the complicating factor of mandatory ballast water exchange after 1993, it ma y be possible to generate more up-to-date data for an analysis using the PCIP approach with a detailed study on the Great Lakes. As mentioned above, a study focused on the Great Lakes may al so allow an analysis on phytoplankton invasion

rates.

Secondary invasions appear to be an important source of uncertainty. To understand the role of secondary invasions better, futu re surveys for nonindigenous sp ecies should not only focus on the larger ports but should also include smaller ports and estuarie s with no foreign ballast input. Additionally, further studies of the role of intrac oastal shipping and ballast discharges are needed to help elucidate their role in spreading invaders into smaller ports with minimal foreign ballast water discharges.

68Table 14: Major assumptions of the per capitainvasion probability (PCIP) approach tosetting ballast water discharge standards.AssumptionEffect on Estimate of Per CapitaInvasion ProbabilityEffect on Discharge standardMitigation ApproachesLinear dose-responseLikely over estimates invasionprobability for many sexual species dueto Allee effects; potentially underestimates for asexual and parthenogenicspecies.Protective against most sexualinvaders; possibly under protectivefor asexual and parthenogenicspecies.Use upper bound estimatesfor input values and/orsafety factor to account forcases when dose-response ismore than linear.Secondary invasions did notcontribute to historical invasionrate.Inflates PCIP to the extent that invadersdid not invade via foreign ballast waterdischarged into the waterbody.Erroneously results in too lowdischarge standard.Exclude small ports fromanalysis and/or conductanalysis on a coastal scale.Polyvectic invaders actuallyinvaded via ballast water.Inflates PCIP to the extent thatpolyvectic invaders were introduced viasome vector other than foreign ballast.Erroneously results in too low adischarge standard.Analysis on coastal scalewould correct if speciesinvaded via ballast wateranywhere on coast.Exclusion of small ports fromacross-port calculations.Generates more accurate PCIPs ifinvasions in small ports from secondaryvectors. Artificially decreases PCIP ifactual primary invasions into the smallports.Depends whether invasions insmall ports are from primary orsecondary vectors.Conduct analysis on acoastal scale so that all portsand invaders included.No change in the invasionpotential of new invaders overtime.Decrease in viability of new invadersresults in PCIPs based on historical ratesover predicting new invasions.Erroneously results in too low adischarge standard. .No adjustment unless furtherdata indicates actual changein invader viability.No change in invasibility ofwaterbody over time.Either increases or decreases PCIPdepending upon type & magnitude ofenvironmental changes in waterbody.Protective or under protectivedepending upon the type &magnitude of changes.Use upper bound estimatesfor input values and/orsafety factor to account forchanges in environment.69

### IX. EXPERIMENTAL APPROACHES

Henry Lee II

Overview: Laboratory and field experiment s can be used to quantify th e likelihood of invasion under

controlled environmental conditions and dosing scenarios. Such experiments may represent the cutting edge in invasion scienc e, at least in the Popperian sense, and the frequency of experiments has increased over the last decade (see review of extinction st udies in experimental populations by Griffen and Drake, 2008) . It appears that freshwater studies have primarily used laboratory experiments while field experiments are used more frequently with marine/estuarine species. Examples of laboratory experiments wi th freshwater organisms include those by Drake and his collogues (e.g., Drake and Lodge, 2004; Drake, 2006; Griffen and Drake, 2008; Drake and Griffen, 2009). An example of a freshwater field experiment is Bailey et al. (2009) who used field enclosures to para meterize and evaluate the diffu sion approximation PVA model. Their results indicated that the proposed IMO standards for >50 micron organisms would reduce the probability of establishment of certain parthenogenic specie s by three fold. Examples of marine/estuarine field experiments include the studies on the recruitment of native and nonindigenous bryozoans (Clark and Johns ton, 2005; Piola and Johnston, 2009).

Assumptions and Limitations: The successful introduction of any specific species is a rare event. For example, it took the green crab about another century to invade the Pacifi c Coast after invading the East Coast (Carlton and Cohen, 2003). Quantifying the probability of such rare events is gene rally impractical using experiments. The main problem is that the num ber of samples becomes prohibitively large when attempting to quantify probabilities of events with likelihoods of 10 -3 to 10 -6 . This is the classic problem when attempting to determine the carc inogenic potency of a compound using laboratory

exposures.

Some of the experiments have us ed high propagule doses, which bi ases the results to the right side of the propagule supply curve (Figure 2). Experimentally testing the recruitment of a species into an established community at the density in the USCG Phase II standard (0.01 organisms m -3 ) will prove especially challenging.

Most marine/estuarine species as well as many freshwater species are difficult to culture and spawn in the laboratory. This limits the experi ments to the aquatic “white rats” (e.g., use of Daphnia magna in Drake and Griffen, 2009). Such sp ecies are often “oppor tunistic” and thus are unlikely to be representative of the full br eadth of potential invaders in foreign ballast.

All the freshwater experiments that we are aware of have used planktonic organisms, presumably because of the ease of culture and manipulation. Many of the marine experiments have used bryozoans or barnacles. We are unaware of any studies that have evaluated propagule supply with soft-bottom species, such as polychaetes. This taxonomic limitation potentially biases the results from experiments.

70The main advantage of experiments, the tightly controlled environmenta l and biotic conditions, is also one of its main limitations. The world is much more complex than can be simulated in a

beaker or even in a field enclosure. This “dum bing down” of nature in experimental studies may be why “Results from laboratory experiments often conflict with field studies” (Griffen and Drake, 2009).

Recommendations/Conclusions: We believe it is impractical to derive discha rge standards using the experimental approach because of the: 1) impracticality of adequate replication to quantif y rare events; 2) limitation in the number and types of species than can be expe rimentally manipulated; a nd 3) artificiality and simplification of laboratory experiments and, to a lesser extent, field experiments.

The real power of the laborator y and field experiments is to advance the theory of propagule supply, test the assumptions of the various invasion models, and para meterize the population models that predict the probability of invasion. The recent work by Bailey et al. (2009) and Britton-Simmons et al. (2008) are good examples of how experimental studies can be coupled with population models.

71

### X. STATISTICAL CONSIDERATIO NS IN ESTIMATING THE

CONCENTRATION OF ORGANI SMS IN BALLAST WATER

DISCHARGES

Melanie Frazier, Henry Lee II, and Deborah A. Reusser

Overview: In the previous sections, we evaluated the potenti al utility and limitations of several approaches for generating ballast water discharge standards; he re we address the statistical issues associated with monitoring organisms at very low concentra tions. This is not an approach for setting standards; however these issues must be consider ed when assessing the practicality of verifying a discharge standard either in test facilities or as part of comp liance monitoring. The stringent discharge standards that have been proposed by various agencies will require estimating very small concentrations of organisms in ballast water. This will be challenging due to the inherent stochasticity of sampling. Furt hermore, at low densities, very large volumes of water must be sampled to find enough organisms to begin to estimate concentration. Understanding the limitations and requirements of sa mpling will help inform the development of protocols that ensure discharge standards are adequately implemented.

Stringent discharge standards are environmentally appealing because they are very protective; however, they present challenges because it is difficult to estimate low concentrations through sampling. The U.S. Coast Guard recently proposed a Phase II discharge standard of <0.01 organisms m -3 for organisms >50 μm, a standard 1000 times more stringent than the IMO’s (USCG proposal is currently in the Federal Register, 74 Fe d. Reg. 44632, August 28, 2009). Some states, such as New York and Californi a, have proposed discharge standards of “zero detectable organisms” (Dobroski et al., 2009a). We explore some of the statistical issues that must be considered for either ship-board testing in the field or type-approv al testing of treatment systems in controlled facilities. We do not address the logistics of sampling ship ballast water,

which are described in references such as Lemie ux et al. (2008) and Wri ght (2007). We also use a “best-case-scenario” approach: we limit our focu s to organisms > 50 μm in size, which are the easiest to quantify; we assume no human or equipm ent error, such that all organisms in a sample volume are counted; and for most scenarios, we assume organisms are randomly distributed in the ballast discharge.

Rationale: Currently, a great deal of effort is being devoted to selecting a discharge st andard that adequately protects against invasive species. An important aspect of testing whether ballast discharges meet these standards, during either the testing of treatment systems or compliance monitoring of individual ships, is developing sampling protocols that are adequa te for a discharge standard. For example, a standard of “zero detectable organisms” may seem very protective, but in reality, the degree of protection depends on the sampling prot ocol. If a small volume is used to evaluate whether the discharge meets a standard, the samp le may contain zero organisms, but the true concentration of organisms may be quite high. For example, even with a relatively high concentration of 100 organisms m -3 , only about 10% of 1 L samples will contain one or more organisms. Furthermore, even if zero organisms are detected in a 1 L sample, the upper possible

72concentration, based on a 95% confiden ce interval, is about 3,000 organisms m -3 . More information about these calculations is presente d below. The general point is that more organisms may be released in ballast discharge using a stringent standa rd paired with a poor sampling protocol than a more le nient standard paired with a st ringent sampling protocol. For these reasons, some researchers claim that “par t of establishing the cr iteria is defining the required sampling plan” (Jarvis, 2000).

The current lack of consistent sampling protocols makes it diff icult to compare among existing and proposed standards. Even if a single disc harge standard is adopted, without consistent sampling protocols the outcome of different ballast management programs will vary dramatically. Furthermore, the efficacy of di fferent ballast treatment technologies cannot be compared without consistent samp ling protocols (Phillips, 2005). In this chapter, we explore some of the statistical aspects of estimating the c oncentration of organisms in ballast discharge based on techniques that involve counting the living organisms in a random sample volume. In Appendix C, we describe some tools that can be used to develop statistically sound sampling protocols.

Sampling Ballast Water Discharges: Given current methodologies, it is not possible to count every single organism in a ballast discharge (i.e., the “population”); consequently, we must use sampling techniques to estimate the

true concentration. Due to the stochastic natu re of sampling, multiple samples taken from the same population will have varying numbers of orga nisms due to random chance. However, if we know how organisms are distributed in their enviro nment, this uncertainty can be estimated and taken into consideration during the development of sampling protocols. A sample taken from a ship’s ballast discharge may have a higher concentration than the standard even though the true concentration of organisms is less than the standard. In this situation, if we failed to take into account the inherent stochasticity of sampling, sh ips that do not violate the standard would be unfairly penalized. Conversely, a sample may ha ve a lower concentration than the discharge standard even though the true concentration of the discharge exceeds the standard. In this situation, if sampling protocols are inadequate then many ships th at exceed the standard would

not be detected.

Two questions that must be answered to devel op adequate sampling prot ocols, are 1) how many organisms must we observe in a sample before we feel reasonably confident that we can identify ships in violation of the standard ; and 2) how few organisms must we observe before we can feel reasonably confident that a ship does not violat e the standard? The answers will depend on the size of the sample, the true concentration of orga nisms, the discharge standard, and the definition

of “reasonable confidence”.

The answer also depends on how organisms are dist ributed in the discharged ballast water. The best-case scenario, from a sampling perspective, is a random distributi on (Figure 9A), meaningthat organisms occur independently of one another. A random distribution will occur in wellmixed ballast water. This distribution may be unlikely because organisms are often aggregated

to some extent in their environm ent. There are several biological reasons for this phenomenon. Organisms may be responding to similar environmen tal cues, resources or physical forces, such as gravity (Figure 9B); they may be actively s eeking conspecifics (Figures 9B and C); or, for

73organisms with fast population growth rates, reproduction may occur at a faster rate than diffusion or convection away from each other (Fi gure 9C). Different mechanisms can lead to varying patterns of aggregation, which can have different consequences for sampling. Murphy and colleagues (2002) have shown that the abund ance of zooplankton varies with depth in the ballast tanks, indicating that at least one type of aggregation in ballast discharges is likely.

Rando m A g g re gat ed

A B C

Figure 9: An example of a random distribution (A, Poisson) and two po ssible variations of aggregated distribut ions (B and C).

For most of the analyses in this report, we a ssume that organisms are randomly distributed in ballast tanks and the discharges. From a practic al perspective, this was the only option because we do not possess data that can be used to estimat e the degree of aggregation in ballast water. Furthermore, Elliott (1971) argues that assuming a random distribution is a reasonable starting point because the Poisson is the default, or nu ll, hypothesis, and theref ore, should be assumed until rejected by testing. Ellio tt also makes the point that for benthic organisms low density populations are effectively randomly distributed in regard to sa mpling, and therefore a random

distribution is often a suitable hypothesis. Whether this applies to organisms discharged in ballast water is unclear. The values presented in this chapter are probably optimistic because: 1) almost all organisms demonstrate at least some aggregation; and 2) for aggregated populations, larger volumes must be sampled to obtain reliable estimates of concentration.

Further, we assume that the samples are “taken from the discharge line, as near to the point of discharge as practicable, during ballast water discharge whenever possible”, as recommended in the final MEPC G2 ballast water sampling guidelines (MEPC, 2008c), and as such are representative of the actual con centrations discharged. Important aspects of developing sampling protocols may be determining the extent that organisms are aggreg ated in ballast discharges and whether samples of ballast water discharges are re presentative of the tota l number of organisms discharged. We discuss some aspects of sampling aggregated populations later in this chapter.

Sampling Poisson Distributions: For randomly distributed populations, the Poisson distribution can be used to determine the probability that a given number of individuals will occur in a sample given the true concentration of organisms (see Table 15 for definitions). This information provides th e statistical basis of sampling protocols for randomly distributed populat ions. A defining characteristic of the Poisson

74distribution is that it is defined by a single parameter, λ , which describes both the mean and variance of the expected counts pe r unit of sampling effort, thus λ = μ = σ 2 . Lambda can be a real number, and in regard to ballast sampling, it can be interpreted as the true concentration of organisms in the ballast discharge.

For a randomly distributed population the variance increases at exactly the same rate as the

mean. This differs from the normal distribut ion which has two parameters, the mean and variance, which can vary independe ntly of one another. The expected mean and variance scale isometrically with sampling effort. If sample volume doubles, the expected mean and variance of the sample will also double. For these reasons, ten 1 m 3 samples do not provide more information than a single 10 m 3 sample when a population is ra ndomly distributed. However, the first sampling scenario (i.e., ten 1 m 3 samples) provides the data for independently estimating variance, which can be used to determine whet her a population is randomly distributed versus aggregated. If the population is randomly distri buted, then the mean and variance from multiple samples should not be significantly different from one another (see Elliott, 1971, for more information). An increase in sampling effort, either by taking more sample units or increasing sample volume, improves the average estimate of λ . Ultimately, if all the discharged ballast water was sampled the concentration would equal λ

.

Given λ , the probability of N organisms occurring in a sampling unit (individual sample of ballast discharge) is

   N e Equation 23: P ( N )  N !

For example, for a true concentration of 15 organisms m -3 , the probability of getting 10 organisms in a sampling unit (i.e., 1 m 3 ) is

 15 10

 7 11 e (15) (3.06  10 )  (5.77  10 ) 176399 P (10)     0.0486 10! 10  9  8  7  6  5  4  3  2  1 3628800

Although the true concentration of organism s in the ballast tank is 15 organisms m -3 , there is a

4.9% chance that a 1 m 3 sample unit will contain 10 organisms (there is about a 12% chance that the sample unit will contain ≤ 10 organisms). The estimate of parameter λ is represented by the

statistic m , which, in this sample, equals 10 organisms m -3 . This estimate of λ is low given the true concentration of 15 organisms m -3 . As the sample volume increases, the sampling statistic,

m , will on average provide a better estimate of λ

.

In the above example, the probability of N even ts occurring in a sampling unit is determined by λ which represents the average number of events expected to occur per sampling unit. By assuming a constant sampling unit, λ represents an average count with no associated units.
However, λ is often expressed as a concentration (organisms m -3 ) by dividing the average expected count by the volume of the sampling un it. An alternative parameterization of the

Poisson distribution can be used which expresses probabilities in terms of the number of events per sampling effort rather than sampling unit. In this case, λ is replaced by the true concentration of organisms, c , times the sample volume, v ,

75 cv N e ( cv ) Equation 24: P ( N )  N !

This equation is more flexible because it allows the volume of the sample to vary, and it emphasizes that even with a constant populati on density the Poisson distribution of sample counts can change by sampling larger or smaller volumes (Bolker, 2008).

Table 15: Definition of statistical terms. Population In this case, all the >50 μm organi sms in the entire volume of a ship’s ballast discharge.

Sample In this case, a random sample of a sh ip’s ballast discharge in which all >50 μm organisms are counted.

Count Number of organisms in a sa mple. This value is an integer.

Poisson A distribution that describes the probability of a given number of “events” (counts, individuals, arrivals, etc) occurri ng in a unit of time/ space if the events are independent of each other. A defining ch aracteristic of the Poisson is that the mean and variance of the exp ected sample counts are equal ( λ = μ = σ 2 ). If organisms in a ballast tank are randomly di stributed, then sa mpling probabilities can be modeled using the Poisson.

λ Lambda, the single parameter of the Po isson distribution, which is a rate describing the average number of events e xpected to occur per unit of time/space. In this case, it also describes the true c oncentration of organisms in the discharged ballast water. This parameter is a real number.

m

Negative

Binomial A statistic estimating λ , calculated from the average number of events observed during sampling. In this case, m is an estimate of the true concentration of organisms in the discharged ballast water based on sampling.

A probability dist ribution often used to mode l aggregated populations ( σ 2 > μ).

θ Theta, dispersion parameter for the ne gative binomial distribution. Highly aggregated populations have smaller θ values, and as θ approaches infinity, the negative binomial approximates the Poisson distribution.

Taylor’s

Power Law An alternative to the negative bi nomial for modeling aggregated populations

76

### A

0.1 2 10 o r g m -2

0.1 0

0.0 8

0.0 6ProbabilitProbability

0.0 4

0.0 2

0.0 0

0 4 8 1 2 1 6 2 0 2 4 2 8



### B 1 m

0.3 5 1 or g m -2

0.3 0

0.2 5ty

0.2 0abili

0.1 5Probabilityob

0.1 0

0.0 5

0.0 0 0 1 2 3456



### C

0. 01 o r g m -2

0.8

0.6

0.4

0.2

0.0

0 1 2
Num ber of o r ga n i sm s in s a mp le

Figure 10: Probability distributions for random samples of 1 m 2 for a randomly distributed population with 10 (A ), 1 (B), or 0.01 (C) organisms m -2 . Red squares represent random samples. The data are displayed in terms of area with units of m 2 , but the probabilities are the same for volumes. Plots on the right indicate the probability that a 1 m 2 sample will contain a given number of organisms. At low concentratio ns, the concentration of organisms is likely to be estimated as 0 organisms m -2 , unless very large volumes are sampled.Probability

77From equations 23 or 24, probability distributions can be obtained that describe the probability of a sample containing a specifi c number of organisms given λ and the sample volume (Figure 10). If 1 m 3 of ballast is sampled from the discharge with a concen tration of 10 organisms per

m 3 , the sample could theoretically contain any number of organisms from zero to positive infinity (or in the case of a finite volume such as a ballast discharge, the total number of organisms in the discharged ballast), but about 95% of samples will contain 4 to 17 organisms (Figure 10A).

The shape of the Poisson probability distributio n, for a fixed sample volume, changes with λ

. For a concentration of 10 organisms m -3 and a sample volume of 1 m 3 , the probability distribution for the number of organisms in a ra ndom sample is very similar to a normal distribution (Figure 10A, right). However, there are some key differences between the Poisson

and normal distribution. For the Poisson distribu tion: 1) the model is bounded at 0, indicating there is zero probability of a ne gative count; 2) when the mean number of organisms in a sample is small (less than 10 or so organisms) due to low concentrations or relatively small sample volumes, the frequency distribution is skewed, with a tail to the right; and 3) the variance can not vary independently of the mean. As the con centration decreases, th e frequency distribution becomes increasingly skewed (Figure 10 from A to C) and the probability of obtaining a sample with zero organisms becomes very likely. For concentrations of 1 organism per m 3 , the probability of a 1 m 3 sample volume containing 0 organi sms is 36.8% (Figure 10B). For a concentration of 0.01 organisms per m 3 , the probability is about 99% (Figure 10C). One of the general challenges of sampling at low concentrations is a large number of samples will have zero detects. In these cases, the estimated concentration will likely remain at zero until enormous volumes of ballast discharge are sampled.

Some Sampling Scenarios: In this section, we translate the information fr om the theoretical probab ility distributions into specific sampling scenarios. We hope to illustrate some of the challenges inherent in sampling, as well as to aid in the development of sampli ng protocols that meet th e goals of regulatory agencies. For the following analyses, we use the conditions pres ented in Table 16.

78Table 16: Conditions for ballast water samp ling scenarios (unless otherwise stated). 1) We interpret the ballast performance st andards as establishing the allowable concentration of organisms in the entirety of the ballast discharge. Based on this interpretation, the purpose of sampling is to estimate the concentration of organisms in the whole ballast discharge (i.e. “average-base d sampling”). An alternative interpretation (Dobroski et al. 2009a) is that the standards are “instantaneo us” and consequently, a ship is non-compliant if any samples exceed the disc harge standard. These two interpretations of the enforcement of performance standards are equivalent only in the case where the standard is zero detectable organisms. Sampling protocols based on “instantaneous sampling” must consider additional statistical factors because the results will be sensitive to the number and volume of the samples. 2) Sampling probabilities can be modeled usi ng the Poisson distribution either because organisms are randomly distributed in ballast discharge, or alternatively, continuous integrated sampling is used to obtain the sa mple (method used by the land-based testing facilities of the U.S. Coast Guard). 3) We assume ALL organisms in a sample are co unted with no human or equipment error. Therefore any variation among the samples from the same population is due to the natural stochasticity of sampling. 4) For current ballast sampling techniques, th e “sample volume” can be obscured by the steps required to collect and c ount the organisms. The sample volume must be calculated

from the total volume of ballast that is f iltered (i.e., concentrated) and the volume of filtrate that is subsampled. The specific steps for sampling can vary, but one technique (Lemieux, 2008) involves filtering a known quan tity of ballast water through a net to capture > 50 μm organisms (Gollasch, 2006). The organisms are then rinsed from the net and resuspended in 1 L of water. From this diluted filtrate, several aliquots of 1 mL are

collected to enumerate the num ber of organisms. If 100 m 3 of ballast is filtered, then the filtrate is diluted with 1 L of water, and the organisms from 20 – 1 mL aliquots are counted, then the total sample volume is 2 m 3 (20 mL of aliquot /1000 mL filtrate × 100

m 3 filtered ballast = 2 m 3 ), not 100 m 3

. 5) Sometimes we report organism counts and samp le volumes rather than concentration. These can be converted to concentration by di viding the total number of organisms by the total volume of the sample.

One of the primary problems of sampling low density populations is that large volumes of ballast discharge must be sampled to have a reasonable probability of detecting any organisms. From equation 24, the probability of gett ing 0 organisms in a sample is e -cv , and therefore, the probability of getting 1 or more organisms is 1- e -cv . We used this expression to calculate the probability of detecting ≥ 1 organism for a series of concentr ations and sample volumes (Table 17). For a concentration of 0.01 organisms m -3 about 300 m 3 of ballast must be sampled to have a 95% probability of detecting at least one orga nism. For relatively small sample volumes, the probability of detecting an organism is low even at relatively high concentrations. If a 1 L sample is taken from a population with a concentration of 100 organisms m -3 , organisms will be detected in fewer than 10% of the samples.

79Table 17: Probability of detecting ≥ 1 organism for various sample volumes (100 mL to 100 m 3 ) and concentrations (0 to 100 organisms m -3 ). Gray boxes indicate probabilities of detection ≥

0.95. True concentration (organisms per m 3 ) Sample volume, m 3 0 0.001 0.01 0.1 1 10 100

0.0001 (100 mL) 0 <0.001 <0.001 <0.001 <0.001 0.001 0.01 0.001 (1 L) 0 <0.001 <0.001 <0.001 0.001 0.01 0.095 0.01 (10 L) 0 <0.001 <0.001 0.001 0.01 0.095 0.632 0.1 (100 L) 0 <0.001 0.001 0.01 0.095 0.632 >0.99

1 0 0.001 0.01 0.095 0.632 >0.99 >0.99

5 0 0.005 0.049 0.393 >0.99 >0.99 >0.99

10 0 0.010 0.095 0.632 >0.99 >0.99 >0.99

25 0 0.025 0.221 0.918 >0.99 >0.99 >0.99

50 0 0.049 0.393 >0.99 >0.99 >0.99 >0.99

100 0 0.095 0.632 >0.99 >0.99 >0.99 >0.99

300 0 0.259 0.950 >0.99 >0.99 >0.99 >0.99

This analysis demonstrates that even when 0 organisms are detected in a sample, the true concentration may be large. A discharge standa rd of “zero detectable organisms” may appear very protective; however, the true degree of prot ection depends on the sample volume. From the Poisson distribution, the upper possible concentr ation (UPC, upper 95% c onfidence interval) of organisms can be estimated based on the number of organisms in a sample. We calculated the UPC (Appendix C) when zero organisms were de tected in sample volumes ranging from 100 mL

to 100 m 3 (Table 18). In this report, we primaril y focus on confidence intervals from 2-tailed sampling probabilities, but in the case of zero detects, the lower estimate is always zero which is not very informative. For this reason, c onfidence intervals based on 1-tailed sampling probabilities may be preferred when there are zero detects. If zero organisms are detected in 1

m 3 of ballast, the true concentration could be as high as 3.7 organisms m -3 . Given the inherent challenges of sampling ballast water, especially on board a ship, a more realistic sample volume may be around 1 L. For a 1 L sample, the uppe r concentration could be >3,500 organisms m -3

even with zero detects.

Table 18: Upper possible concentration (UPC) of organisms based on one and two tailed 95% exact confidence intervals when zero organisms are detected in a range of sample volumes. Upper possible concentration, org m -3

Sample volume, m 3 one-tailed two-tailed

0.0001 m 3 (100 mL) 29,960 36,890

0.001 m 3 (1 L) 2,996 3,689

0.01 m 3 (10 L) 299.6 368.9

0.1 m 3 (100 L) 29.96 36.89

0.5 m 3 (500 L) 5.992 7.378

1 m 3 2.996 3.689

10 m 3 0.300 0.369

100 m 3 0.030 0.037

800 2 5 0 5 0

. 7 5 0

. 9 0

. 9 5

0

. 2 5 0

. 5 0

. 7 5 0

. 9 0

. 9 5 In an ideal world, we would alwa ys detect ballast water with c oncentrations of organisms that exceed the discharge standard. In reality, this is not possible with cu rrent methodologies. The probability of detecting an exceedance depends on: 1) the volume of ballast that is sampled; 2) the stringency of the discharge standard; and, 3) the magnitude of the exceedance. To demonstrate the relationship am ong these variables, we estimated the likelihood of detecting an exceedance for a discharge sta ndard of <0.01 organism m -3 when the sample volume ranged

from 1-50 m 3 and the true concentration ranged from 0.01 to 1 organism m -3 . For each combination, we simulated 10,000 random samples ( rpois function in R statistical program; R Development Core Team, 2008) and calculated the percen tage of samples that were correctly identified as exceeding the discharge standard (Figure 11). Ideally, none of the samples would pass inspection because in all cases the con centration of organisms exceeds the discharge standard. However, as the concentration approa ches the discharge sta ndard, increasingly large

volumes of ballast must be tested to confid ently detect an exceedance. When the true concentration of organisms is 0.75 m -3 (75x the proposed U.S. Coast Guard Phase II standard) approximately 4 m 3 of ballast water must be sampled to detect this exceedance 95% of the time (Figure 11A). When the true con centration of organisms is 0.1 m -3 (10x the standard) approximately 30 m 3 of ballast water must be sampled (Figure 11B). For perspective on the magnitude of these sample volumes, a Volkswag en Transporter bus has a volume of about 14

3 m

.

50

0. A B

9 5

0. 9

40

0. 7 5Samplevolume,m3

30 30

0. 5

20

0. 2 5

10

4

1 0

. 2 5 0 5 0. 75 0

. 01 0

. 2 0

. 4 0. 6 0 .8 1

. 0 0 .0 1 0 .0 5 0

. 1 0 0

. 1 5 0 .2 0 0

. 2 5

Tr ue c once n t r at i on, or g a nism s m -3

Figure 11: Probability of de tecting an exceedance for sample volumes between 1 and 50 m 3 and a discharge standard of 0.01 organisms m -3 . The true concentration ranges from (A) 0.01 to 1 organisms m -3 or, (B) 0.01 to 0.25 organisms m -3 , all of which fail to comply with the discharge standard. The legend describes the proportion of samples in which the exceedance is detected: white regions of plot indicate a >95% probability of detecting the exceedance; the darkest red regions indicate a <25% probability of detecting th e exceedance. See text for information about specific examples identified by the blue lines.

81The examples thus far have been theoretical b ecause we begin with a kno wn concentration that exceeds the discharge standard and we calculate the probability of detecting the exceedance given a specific sample volume. These examples are useful because they demonstrate the power and limitations of specific sampling protocols. They are less useful from the perspective of actual sampling, because in reality the true c oncentration is unknown and must be estimated using sampling techniques. Ultimately, the goal of sampling is to determine whether a ballast discharge exceeds or meets the discharge standard with some pre-established degree of confidence. Two obvious verdicts of sampling are: 1) Statistically Non-compliant : The number of organisms in the sample is large enough that the true c oncentration likel y exceeds the discharge standard; 2) Statistically Compliant : The number of organisms in the sample is small enough that the true concentration likely meets the discharge standard. However, there is also a third, indeterminate outcome due to the inherent stochastic ity of sampling. For these samples, it is statistically unclear whether the discharge is statistically compliant or not. A random sample of ballast discharge may have a concentration th at exceeds the discharge standard, but the true concentration may actually be le ss than the discharge standard. For example, if the true concentration of the discharged ballast water is 7 organisms m -3 and a volume of 1 m 3 is sampled, about 17% of samples will have 10 or mo re organisms, and will appear to exceed the

current IMO standard of ≤ 10 organisms m -3 . The possibility of getting an indeterminate result increases as the sample volume decreases and as the desired level of certainty increases.

We calculated the total number of organisms that must be observed in a range of sample volumes

to determine – based on two-tailed 95% confidence intervals – whether the true concentration is statistically compliant or non-co mpliant with a discharge standard of either <0.01 or <10 organisms m -3 (Figure 12). For a very stringent discha rge standard, such as the <0.01 organisms

m -3 proposed by the U.S. Coast Guard, only a few organisms must be observed before a ship’s discharge is statistically non-complia nt with the standard. If a si ngle organism is detected in a sample volume of ≤ 2 m 3 then we can be fairly confident th at the standard has been exceeded (Figure 12A, red region) given that the lower probable concentration, based on the 95% confidence interval (0.0125 to 2.786 organisms m -3 ), is greater than the standard. On the other hand, very large amounts of water must be sampled before we can be equally confident that a ship’s discharge is statistically compliant with the standard. For a disc harge standard of <0.01 organisms m -3 , approximately 370 m 3 of ballast water must be sampled, with zero detects, before a ship’s discharge is statistically compliant w ith the standard (Figure 12A, green region). Another way to think about this is that the probability of detecting 0 organisms in a 370 m 3
sample must be <2.5% (based on two-tailed test). Of course, the discovery of a single organism

in a 370 m 3 sample does not suggest the true concen tration exceeds the standard, in fact the ballast discharge in question is more likely to comply with the standard than not. However, based on this result we can not distinguish w ithin our desired confid ence whether the sample complies with the discharge standard given that the upper probable concentration, based on the 95% confidence interval (0.000068 to 0.015 organisms m -3 ), exceeds the standard (Figure 12A, white region). For the IMO discha rge standard of <10 organisms m -3 (Figure 12B) nearly 0.4 m 3
of ballast discharge must be sampled before it’s possible for ballast discharge to be statistically compliant with the standard.

82Noncompliant

Compliant IndeterminateTotal observed organisms

0 5 10 15 20 25

Log 10 Sample volume, m 3

0.01 0.1 1 10 100 1000 A Discharge standard < 0.01 org m -3 B Discharge standard < 10 org m -3

0 20 40 60 80 100

0.01 0.1 1 10Total observed organisms

0 5 10 15 20 25

Log 10 Sample volume, m 3

0.01 0.1 1 10 100 1000 A Discharge standard < 0.01 org m -3 B Discharge standard < 10 org m -3

0 20 40 60 80 100

0.01 0.1 1 10Total observed organisms

0 5 10 15 20 25

Log 10 Sample volume, m 3

0.01 0.1 1 10 100 1000 A Discharge standard < 0.01 org m -3 B Discharge standard < 10 org m -3

Noncompliant

Compliant 0 20 40 60 80 100

0.01 0.1 1 10 Indeterminate

Figure 12: Determining whether ballast water discha rge exceeds or meets a discharge standard of

<0.01 (A) and <10 (B) organisms m -3 (note: axes have different sc ales). Red regions indicate total organism counts that would be statistically non-compliant with the standard. Green regions indicate total organism counts that would be st atistically compliant with the standard. White regions indicate indeterminate resu lts that are not statistically compliant or non-complaint with the discharge standard based on two-tailed 95% confidence intervals around sample counts.

Aggregated Populations: Sampling aggregated populations, also known as clumped or contagious populations, is more complicated than sampling randomly distributed popul ations. One of the defining characteristics of aggregated populations is that the sample variance is greater than the mean ( σ 2 > μ, recall that

for Poisson distributions σ 2 = μ). As variance increases, the true concentration becomes increasingly difficult to accurately estimate b ecause the number of organisms in a random sample becomes increasingly unpredictable. C onsequently, aggregated populations must be sampled more intensively to estima te concentration confidently.

Aggregation results from many di fferent ecological and physical pr ocesses, making it difficult to apply a single probability distribut ion to the diverse array of possi ble patterns of aggregation. Although many distributions have been used to model aggregated populations, the negative binomial is probably the most useful of th ese models (Elliott, 1971). Like the Poisson distribution, the negative binomial can be used to predict the probability of observing a specific number of organisms in a sample. Unlike the Poisson distribution, the negative binomial is defined by two parameters, the mean (μ) and the dispersion ( θ , also called the size parameter). The dispersion parameter is related to the spatial distribution of organisms in their environment. More aggregated populations have smaller disper sion parameters. As the dispersion factor approaches positive infinity, the negative binomial approximates the Poisson distribution. The dispersion parameter of the negative binomial is related to both the mean and the variance (Bolker, 2008). An approximate es timate of this relationship is: θ = μ 2 /( σ 2 - μ).

830 1 2 3 4 5 6 7 8 Poisson Aggregated

Number of organisms in sampleProbability

0.0 0.2 0.4 0.6

0 1 2 3 4 5 6 7 8 Poisson Aggregated

Number of organisms in sampleProbability

0.0 0.2 0.4 0.6

Figure 13: Comparison of sample probabilities from a randomly distributed (Poisson) population vs. an aggregated population with a dispersion para meter of 0.1 (negative binomial) for a sample

volume of 1 m 3 and concentration of 1 organism m -3 . The probability that a sample will contain 0 organisms is greater for the aggregated population than for the Poisson distributed population.

As mentioned, one of the general challenges of sampling at low concentrations is the fact that a large number of samples will contain zero organisms. This problem can be compounded when organisms are aggregated. For example, if a 1 m 3 sample of ballast is taken from a randomly distributed population with a true concentration of 1 organism m -3 , about 37% of the samples will contain 0 organisms. In contrast, for an aggregated population with a dispersion parameter of 0.1, about 79% of samples will contain 0 or ganisms (Figure 13). Conversely, the probability of obtaining samples with large numbers of organism s, relative to the true concentration, also increases. For the randomly distributed population, the probability of a sample unit containing > 3 organisms is 1.9%, whereas, for the aggregated population, the probabilit y is 8.3%. If large sample volumes are not taken from aggregated p opulations, then estimates of concentration are likely to be much lower or higher than the true concentration.

There are several ways to determine whether a population is aggregated , all of which require multiple sample units from a popula tion to estimate both parameters of the negative binomial distribution (see Elliott, 1971). Th is is complicated by the fact that estimates of aggregation depend upon the scale of the aggregation pattern relative to the size of the sampling unit (Figure 14). One pattern of aggrega tion occurs when organisms form clumps that are randomly distributed throughout the environment. In this case, the population can be highly aggregated but if the sample volume is relatively small, such that most sample units contain 0 or 1 organisms, then the population will appear randomly distribute d or only slightly aggregated. As the volume of the sample unit increases, the variation in the nu mber of organisms will increase relative to the mean, peaking at the point when the sample vol ume is about equal to the volume of a single cluster. As sample volume increases beyond this point, the variance will decline relative to the mean because a sample unit will include severa l clusters. Given these and other issues, the

84Taylor power law (Taylor, 1961) is an alternative to the negative binomial for modeling aggregated populations that may be applicable for a wider range of distributions than the negative binomial (Elliott, 1971; Downing et al., 1987).

A B C

A B C σ 2 = μ (Poisson)

σ 2 < μ (regular) σ 2 > μ (aggregated)variance / meanIncreasing aggregation

A B C

A B C σ 2 = μ (Poisson)

σ 2 < μ (regular) σ 2 > μ (aggregated)variance / meanIncreasing aggregation

Figure 14: Theoretical example of how the appa rent aggregation in th e population will differ based on the scale of aggregation relativ e to the size of the sample unit.

Recommendations/Conclusions: Instituting standardized sampling protocols is a critical component of implementing ballast discharge standards.

The degree of statistical certainty desired for ball ast testing may differ according to the situation. For stringent discharge standards, such as the <0.01 standard pr oposed by the U.S. Coast Guard, a large quantity of water must be sampled to know with 95% confidence that the true concentration of organisms is less than the di scharge standard (Figure 12A, counts in green region are acceptable, counts in red regions are unacceptable, and because counts in white regions are ambiguous they may be classified as unacceptable if a high degree of confidence is desired). This level of certaint y is important when testing the performance of ballast treatment systems; however, it may be less critical during co mpliance monitoring, especially if the primary goals are to detect gross failures or to generate compliance records for individual ships so as to flag those that appear to have poor compliance. For compliance monitoring, one approach may be to employ a three class sampling criteria, such that ships with organi sm counts in the green region of Figure 12 are acceptable, counts in the red region are unacceptable, and counts in the white region are marginally acceptable.

In situations where indeterminate results are classi fied as acceptable or marginally acceptable it

is critical to ensure that th e upper possible concentr ation of organisms is reasonable from a regulatory perspective. For samples with counts that fall in the intermediate category, the possible concentration of organisms could be qu ite high depending on the sample volume. This can be true even if zero organisms are detect ed during sampling (Table s 17 and 18). If zero organisms are detected in a 1 L sample, the upper possible concentration could be nearly as high as 3,000 organisms m -3 based on the upper 1-tailed 95% conf idence interval. Given this, for

85ballast discharge standards of “zero detectable organisms” the sample volume must be large enough to ensure that the detection limit is ecologically protective.

Given the current challenges of ship-board tes ting and the stringency of the current and proposed discharge standards, it will be difficult to samp le large enough volumes of ballast discharge to detect ballast discharges that do not meet the standard, even if th e concentration of organisms is 1-3 orders of magnitude greater th an the discharge standard. Cons equently, the quality control to assure that ballast treatment systems are designed to adequately control the introduction of nonindigenous species may be best achieved primarily through ri gorous type-approval of ballast water treatment systems in controll ed testing facilities, rather th an from after-the-fact compliance ship-board sampling.

Despite the limitations of compliance monitoring in the field this technique may still play an important role in the regulation of ballast discharge standards. Th is type of testing can detect gross exceedences of the discharge standard, whic h can be used to identify treatment system failures and problematic ships. Until new samp ling technologies are developed, however, ship board testing using existing sampling methods ar e likely to be inad equate for accurately distinguishing among concentrations in the range of 0.001 to 10 organisms m -3 . However, it

would be useful to institute a global repository of compliance te st results for individual ships through the IMO in order to incr ease the probability of detect ing troublesome patterns. For a discharge standard of <10 organisms m -3 , a single 1 m 3 sample containing 15 organisms does not necessarily indicate a ship’s treatme nt system is failing to meet the discharge standard (95% CI:

8.4 to 24.8 organisms m -3 ). If, however, the same pattern is observed at subs equent discharge events, there is mounting evidence that the treatm ent system may not be adequately reducing the concentration of organisms in the ballast discharge.

Aggregation may be a significant source of error in many sampling protocols, and estimating the extent of aggregation could be an important aspe ct of accurately estimating the concentration of organisms in ballast discharge. The extent that a population is aggregated must be determined empirically by taking many replicate samples. The problem is mitigated in the land-based testing facility in Key West, Florida (Lemieux et al., 2008) by continuously sampling throughout the ballast tank. This is achieved by removing all the water from the ballast tank while continuously diverting a relatively small portion of it for testing. This appr oach is currently not practical for ship-board testing.

In these analyses, we assume the goal of disc harge standards is to directly regulate the concentration of organisms in ballast discharges using “average based sampling”. However, if “maximum instantaneous” discharg e standards are used instead then additional statistical factors must be considered because the results will be very sensitive to the sample number and volume. For example, if an IMO discharg e standard of <10 organisms m -3 is enforced using instantaneous sampling, then a ship discharging ballast wi th a true concentration of 5 organisms m -3 will fail about 3.2% of the time based on a single sample of 1 m 3 . However, as the number of samples increases the probability of a false failure increas es, assuming failure is defined as one or more

of the 1 m 3 samples having a concentration of ≥ 10 organisms m -3 . If five 1 m 3 samples are taken from a ballast discharge event, about 15% of th e ships will have at least one sample with ≥ 10 organisms m -3

.

86

### XI. COMPARISON OF APPROACHES

Henry Lee II, Deborah A. Re usser, and Melanie Frazier

It is difficult to compare the approaches that ha ve been used to determine the risk of ballastassociated invasions because they do not use a c onsistent set of input values for ballast water discharges, organism concentrations , or historical invasion rates. Nonetheless, to assist in seeing the “forest from the trees”, we present a comparison in Table 19. This comparison summarizes

attributes related both to the scie ntific rigor of the approaches a nd to their applicability to risk management decisions, in particular as they re late to the development of a national discharge standard. A table can not capture all the nuan ces or reasoning behind our assessments, and the

reader is referred back to the individual sections for more detailed information. Definitions for

the attributes in Table 19 are:

Current implementation genera tes quantitative standards: Does the approach as reviewed in this document actually generate quantitative organism -based discharge standards? A particular approach may not generate quantitative standards, at least as currently im plemented, because it is not based on organism concentrations, because th e data are not currently available, or because the approach is inherently unsuitable to generate an actual estimate of risk (e.g., it is a relative evaluation among treatments).

Range in uncertainty in standard: What is the apparent range in uncertainty in the discharge standard? This is an estimate of the range in th e standard itself, and does not attempt to capture all the potential sources of uncerta inty of the input parameters going into the approach. Because the actual organism concentration generated fr om the zero detectable organism approach is dependent upon the sampling protocol, we compar ed the upper possible organism concentration from the 95% confidence interval (one-t ailed test) for 1 liter sample to a 10 m 3 sample (Table 18). Note that this type of uncertainty would also apply to other approaches.

Key data needs for generati on of quantitative standards: These are the most important types of data required to generate a nationa l discharge standard via the identified approach. This is not necessarily a complete list of the data required.

Assumes linear dose response: Does the approach that the invasi on rate from ballast discharges is directly proportional to the propa gule supply? Note that appro aches based on historical invasion rates may actually incorporate Al lee effects if the invasion succe ss of historical invaders was dependent upon them exceeding some cr itical population threshold.

Incorporates invasion risk from multiple species in a discharge : Does the approach assess the risk of invasion from all the species c ontained within a ballast discharg e or does it inherently assume that all the discharged indivi duals are of a single species?

Incorporates invasion risk from multiple ship discharges: Does the approach assess the risk of establishment from discharges of the same species from multiple ships discharging within the same waterbody?

87Based on historical invasion rates: Does the approach directly use historical invasion rates to generate a standard? The uncertainty in these methods will depend, in part, upon the accuracy of

these historical invasion rates as well as the extent to which past invasion rates are predictive of

future rates.

Based on population dynamics: Does the approach directly use population dynamics, such as growth rates, in predicting invasion risk? The uncertainty in these methods will depend, in part, upon the accuracy of these population vital rates as well as whether they represent the breadth of

taxa found in ballast water.

Applicable to all taxa and guilds: Is the standard applicable to all taxonomic groups and guilds? For example, is the standard applicable for hol oplanktonic species, such as calanoid copepods, as well as benthic species with a pelagic larval stage or nektonic species, such as fish?

Separates risk assessment from risk management: Does the approach separate the scientific assessment of invasion risk from the risk manage ment decisions, or are the two intermingled? Intermingling the two makes it difficult to evalua te the decision making process rigorously or to

determine what new information is re quired to improve the predictions.

Published in peer-reviewed scientific literature: Has the approach been published in the scientific peer-reviewed literature? Most government reports undergo independent peer review – nonetheless, publication in the pe er-reviewed literature indicate s some level of acceptance by the broader scientific community. There is an extensive literature on PVA models in general, but the application to ballast water discharges in the DPEIS (USCG, 2008) has not been published in the

scientific literature. In addition to the specific Drake et al . (2005) paper on the application of reaction-diffusion models to ballast water, there is an extensive literature on this type of model. Individual experimental studi es are generally published in the scientific literature.

Recommended for national standard development: This is the authors’ evaluation of whether the approach is potentially suitable for the developmen t of national discharge standards. It is meant to promote further technical review, and we reco gnize that other evaluations are possible based on the different weighting of the factors. The key factors used in our evaluation include an assessment of the scientific rigor of the approach, the apparent uncertainty in the standards, and whether the current implementation of the appro ach, or some foreseeable modification, could generate organism-based standards. We also co nsidered whether the approach applies to the full suite of taxa and guilds and can address the combined risk from discharges from multiple ships.

88Table 19: Comparison of approaches to generate national organism-based discharge standards for >50 micron organisms in ballastdischarges. Assessment is based on current implementation; potential modifications are identified when appropriate. “Realitycheck”is used to denote that the approach could beused to help evaluate whether predictionsfrom other approaches fall within a realisticrange. “Recommend for national standard development” is our assessment of whether the approach should be considered forgenerating quantitative organism-based discharge standards at the national level. Seethe text for explanations of the attributes.Approach /AttributeExpert Opinion /ManagementConsensusesZero DetectableOrganismsNaturalInvasionRateReaction –DiffusionPopulationViabilityAnalysisPer CapitaInvasionProbabilitiesExperimentalCurrentimplementationYesNoNogeneratesYesYes(prelim. for(volume(relativeYesNoquantitativeCA)based)comparison)standardsApparent range ofuncertainty instandard10,000 fold(range of conc.proposed in IMOnegotiations –0.01 to 100 org m-3)Uncertain sincedetectable conc.in samples havenot yet beendefined - couldbe as much as10,000 fold( upper possibleconc. w/1L vs.10 m3sample)100-fold(3 experts)or10,000-fold(our analysis)About 200 fold(approx rangein “max. safereleasevolumes”)<2 fold (w/12 spp.in ballast) to10,000 fold(multiple voyages– our analysis)6-fold (amongcoasts)or12-fold (w/GreatLakes)NAKey data needs forgeneration ofquantitativestandardsUnknown sincedecision process nottransparentDevelopment ofstatisticallyrigoroussamplingprotocolNaturalinvasion ratesin range ofecoregionsInstantaneouspopulationgrowth ratesfor a range oftaxaInstantaneouspopulation growthrates&instantaneousvariance of thepopulation growthrate for a range oftaxaNoneExtensiveexperimentationw/range of taxaAssumes linear doseresponseUnknown sincedecision process nottransparentNo(assumes a singleindividual canbecomeestablished)YesNo(canincorporateAllee effects)No(can incorporateAllee effects)YesNA(can be used todetermine natureof a doseresponse)89Approach /AttributeExpert Opinion /ManagementConsensusesZero DetectableOrganismsNaturalInvasionRateReaction –DiffusionPopulationViabilityAnalysisPer CapitaInvasionProbabilitiesExperimentalIncorporates invasionrisk from multiplespecies in a dischargeYes?YesYesNo?YesYesNoIncorporates invasionrisk from multipleship dischargesYes?YesYesNoNo(modify toincorporatemultiple ships?)YesNoBased on historicalinvasion ratesNoNoYesNoNoYesNoBased on populationdynamicsNoNoNoYesYesNoYesApplicable to all taxaand guildsYes?YesYes?(depends ontaxa includedin analysis)No(limited toshort-livedholoplanktonicspecies)Yes?(depends uponwhich species thepop. data can beobtained)YesNo(limited to taxaadaptable toexperiments)Separates riskassessment from riskmanagementNoNo?NoYesYesYesYesPublished in peerreviewed scientificliteratureNoNoNoYes(extensiveliterature onreactiondiffusionmodels)No(extensiveliterature on PVAmodels)No(in process)Yes(individualexperiments)Recommended fornational standarddevelopmentNo(use as “realitycheck”)NoNo(possible useas “realitycheck”)No(use as “realitycheck” forholoplanktonicspecies)Yes(if sufficient pop.data available forpredictions ofactual vs. relativerisk)YesNo(use as “realitycheck” and testassumptions)90

### XII. REFERENCES

Allen, A.P. and Gillooly, J.F. 2006. Assessi ng latitudinal gradients in speciation rates and biodiversity at the global s cale. Ecological Letters 9: 947–954.

Andersen, M. 2005. Potential applications of popul ation viability analysis to risk assessments for invasive species. Human and Ecological Risk Assessment 11:1083-1095.

Bailey, S.A., Velez-Espino, L.A., Johannsson, O.E., Koops, M.A., and Wiley, C.J. 2009. Estimating establishment probabilities of Cladocera introduced at low density: an evaluation of the proposed ballast water discharge standa rds. Canadian Journal of Fisheries and Aquatic Sciences 66:261-276.

Banas, N.S, Hickey, B.M., and MacCready, P. 2004. Dynamics of Willapa Bay, Washington: A highly unsteady, partially mixed estuary. Journal of Physical Oceanography 34:2413-2427.

Beissinger, S.R., and McCull ough, D.R. (eds.) 2002. Population Viability Analysis . University of Chicago Press, Chicago, IL. 577 pp.

Behrens Yamada, S., Dumbauld, B.R., Kalin, A., H unt, C.E., Figlar-Barnes, R., and Randall, A. 2005. Growth and persistence of a recent invader Carcinus maenas in estuaries of the

northeastern Pacific. Biol ogical Invasions 7:309-321.

Berec, L., Angulo, E., and Courchamp, F. 2006. Multiple Allee effects and population management. Trends in Ec ology and Evolution 22:185-191.

Blueweiss, L., Fox, H., Kudzma, V., Nakash ima, D., Peters, R., and Sams, S. 1978. Relationships between body size and some life history parameters. Oecologia 37:257-272.

Bolker, B.M. 2008. Ecological Models and Data in R . Princeton University Press, Princeton, NJ. 408 pp.

Box, G.E.P. and Draper, N.R. 1987. Empirical Model-Build ing and Response Surfaces . John Wiley and Sons, New York, NY. 424 pp.

Boyd, M.J., Mulligan, T.J., and Shaughnessy, F.J. 2002. Non-Indigenous Marine Species of Humboldt Bay, California: A Re port to the California Department of Fish and Game. 118

pp. ( http://dscholar.humboldt.edu:8080/dspace/bitstream/2148/463/1/non_indigenous_marine_b oyd_etal_2002.pdf)

Britton-Simmons, K.H. and Abbott, K.C. 2008. S hort and long term effects of disturbance and propagule pressure on a biological inva sion. Journal of Ecology 96:68-77.

California Department of Fish and Game. 2009. California Aquatic Non-Native Organism Database (CANOD). ( htt p://www.dfg.ca.gov/ospr/about/s cience/misp.html )

91California State Lands Commission. 2009. Perfor mance Standards for the Discharge of Ballast Water for Vessels Operating in California Waters. ( http://www.slc.ca.gov/Regulations/Documents/Article_4.7.pdf )

Carlton, J.T. 1996. Pattern, process, and pr ediction in marine invasion ecology. Biological

Conservation. 78:97-106.

Carlton, J. T. 2001. Introduced Species in U.S. Coasta l Waters: Environm ental Impacts and Management Priorities . Pew Oceans Commission, Arlington, VA. 36 pp.

Carlton, J.T. (ed.). 2007. The Light and Smith Manual: Interti dal Invertebrates from Central California to Oregon. 4 th Edition. University of Califor nia Press, Berkeley, CA. 1001 pp.

Carlton, J.T. 2009. Deep Invasion Ecology and the Assembly of Communities in Historical Time. In: Rilov, G. and Crooks, J.A. (eds.) Biological Invasions in Marine Ecosystems: Ecologial, Management, and Geographic Pe rspectives (Ecological Studies) . SpringerVerlag, Berlin. pp. 13-56.

Carlton, J.T. and Cohen, A.N. 2003. Epis odic global dispersal in shallow water marine organisms: the case history of the European shore crabs Carcinus maenas and C. aestuarii

. Journal of Biogeography 30:1809-1820.

Carlton, J.T. and Geller, J.B. 1993. Ecologica l roulette: the global tr ansport of nonindigenous marine organisms. Science 261:78-82.

Carlton, J.T., Reid, D. and van Leeuwen, H. 19 95. The role of shippi ng in the introduction of nonindigenous aquatic organisms to the coastal wa ters of the United States (other than the Great Lakes) and an analysis of control opti ons. US Coast Guard. Technical Report No. CGD11-95, Washington, DC. 373 pp.

Chapman, P.M., Fairbrother, A., and Brown, D. 1998. A critical evaluation of safety (uncertainty) factors for ecological risk assessment. Environmental Toxicology and Chemistry 17:99-108.

Choi, K.-H., Kimmerer, W., Smith, G., Ruiz, G.M., and Lion, K. 2005. Post-exchange zooplankton in ballast water of ships enteri ng the San Francisco Estuary. Journal of

Plankton Research 27:707-714.

Chonsuvivatwong, V. 2008. epicalc: Epidemiol ogical calculator. R pack age version 2.8.0.1. http://CRAN.R-project.org /

Clark, G.F. and Johnston, E.L. 2005. Manipula ting larval supply in the field: a controlled study of marine invasibility. Marine Ecology Progress Series 298:9-19.

Cohen, A.N., Berry, H.D., Mills, C.E., Milne, D., Britton-Simmons, K., Wonham, M.J., Secord, D.L., Barkas, J.A., Bingham, B., Bookheim, B., Byers, J.E., Chapman, J.W., Cordell, J.R., Dumbauld, B., Fukuyama, A., Harris, L.H ., Kohn, A.J., Li, K., Mumford, T.F., Radashevsky, V., Sewell, A.T., and Welch., K. 2001. Report of the Washington State

92Exotics Expedition 2000: A Rapid Assessment Su rvey of Exotic Spec ies in the Shallow Waters of Elliot Bay, Totten and Eld Inlets, and Willapa Bay. Nearshore Habitat Program, Washington State Department of Natural Resources, Olympia WA. 39 pp. plus appendices.

Cohen, A.N. 2005. Guide to the Ex otic Species of San Francisco Bay

. San Francisco Estuary Institute, Oakland, CA ( www.exoticsguide.org )

Cohen, A.N. and Carlton, J.T. 1995. Nonindige nous Aquatic Species a Un ited States Estuary: A Case Study of the Biological I nvasions of San Francisco Bay a nd Delta. Report to U.S. Fish and Wildlife Service. 246 pp. plus appendices. ( http://nsgl.gso.uri.edu/conn/ connt95002/connt95002full.pdf )

Cohen, A.N. and Carlton, J.T. 1998. Acceleratin g invasion rate in a high ly invaded estuary.

Science 279:555-558.

Collin, R. 2003. Phylogenetic relationships am ong calyptraeid gastropods and their implications for the biogeography of marine speci ation. Systematic Biology 52:618–640.

Colautti, R.I., Grigorovich, I.A. and MacIsaac, H.J. 2006. Propagule pr essure: a null model for biological invasions. Biologi cal Invasions 8:1023–1037.

Cordell, J.R., Lawrence, D.J., Ferm, N.C., T ear, L.M., Smith, S.S., and Herwig, R.P. 2009. Factors influencing densities of non-indigenous species in the ba llast water of ships arriving at ports in Puget Sound, Washington, United States. Aquatic Cons ervation: Marine and Freshwater Ecosystems 19:322-343.

Costello, C.J. and Solow, A.R. 2003. On th e pattern of discovery of introduced species. Proceedings of the National Academy of Sciences 100:3321–3323.

Coulson, T., Mace, G.M., Hudson, E., and Possi ngham, H. 2001. The use and abuse of population viability analysis. Trends in Ecology and Evolution 16:219-221.

Courchamp, F., Clutton-Brock, T., and Grenfell, B. 1999. Inverse density dependence and the

Allee effect. Trends in Ec ology and Evolution 14:405-410.

Daniels, R.A. and Peteet, D. 1998. Fish scale evidence for rapid post-glacial colonization of an Atlantic coastal pond. Global Ecolog y and Biogeography Letters 7:467-476.

de Queiroz, A. 2005. The resurrection of oceanic dispersal in historical biogeography. Trends in Ecology and Evolution 20:68-73.

Dennis, B., Munholland, P.L., and Scott, J.M. 1991. Estimation of growth and extinction parameters for endangered species. Ecological Monographs 61:115-143.

93deRivera, C.E., Ruiz, G.M., Crooks, J.A., Wasson, K ., Longhart, S.I., Fofonoff, P., Steves, B.P., Rumrill, S.S., Brancato, M.S., Pegau, W.S., Bu lthuis, D.A., Preisler, R.K., Schoch, G.C., Bowlby, E., DeVogelaere, A., Crawford, M.K ., Gittings, S.R., Hines, A.H., Takata, L., Larson, K., Huber, T., Leyman, A.M., Collinetti, E., Pasco, T., Shull, S., Anderson, M., and Powell, S. 2005. Broad-scale nonindigenous species monitoring along the West Coast in

national marine sanctuaries and na tional estuarine research reserves. Report to the National Fish & Wildlife Foundation. 72 pp. plus appendices. ( http://cain.nbii.gov/portal/community/Communities/Geographic_Perspectives/Pacific_Nort hwest/Regional_Planning_Documents/Invasive_Species/).

Desmond, J.S., Deutschman, D.H., and Zedler, J.B. 2002. Spatial and temporal variation in estuarine fish and invertebrate assemblages: an alysis of an 11-year data set. Estuaries

25:552-569.

Dobbs, F.C. and Rogerson, A. 2005. Ridding ships’ ballast water of microorganisms.

Environmental Science a nd Technology 39: 259A-264A.

Dobroski, N., Scianni, C., Gehringer, D., a nd Falkner, M. 2009a. 2009 Assessment of the Efficacy, Availability and Environmental Imp acts of Ballast Water Treatment Systems for

Use in California Waters. Produced for the Ca lifornia State Legisl ature. 76 pp. plus appendices ( http://www.slc.ca.gov/Spec_Pub/MFD/Balla st_Water/Documents/2009CSLCTechReportFi nal.pdf)

Dobroski, N., Scianni, C., Takata, L., and Fal kner, M. 2009b. October 2009 Update: Ballast Water Treatment Technologies for Use in Calif ornia Waters. Produced for the California State Legislature. 19 pp. ( http://www.slc.ca.gov/Spec_Pub/MFD/Balla st_Water/Documents/2009CSLC_TechUpdate

_ final.pdf)

Downing, J.A., Perusse, M., and Frenette, Y. 19 87. Effect of interreplicate variance on zooplankton sampling design and data anal ysis. Limnology and Oceanography 32:673-680.

Drake, J.M. 2004. Allee effects and the risk of biological invasion. Risk Analysis 24:795-802.

Drake, J.M. 2006. Extinction times in experimental populations. Ecology 87:2215–2220.

Drake, J.M. and Bossenbroek, J.M. 2004. The pot ential distribution of zebra mussels in the

United States. Bioscience 54:931-941.

Drake, J.M. and Griffen, B.D. 2009. Speed of expansion and extinction in experimental populations. Ecology Letters 12:772-778.

Drake, J.M. and Lodge, D.M. 2004. Effects of environmental variation on extinction and establishment. Ecology Letters 7:26–30.

Drake, J.M., Costello, C., and Lodge, D.M. 2005. When did the discovery rate for invasive species in the North American Great Lakes accelerate? Bioscience 55:4.

94Drake, J.M., Lodge, D.M., and Lewis, M. 2005. Theory and preliminary analysis of species

invasions from ballast water: C ontrolling discharge volume and location. American Midland

Naturalist 154:459–470.

Drake, L.A., Doblin, M.A., and Dobbs, F. 2007. Potential microbial bioinvasions via ships’ ballast water, sediment, and biofilm. Marine Pollution Bulletin 55:333-341.

Drury, K.L.S., Drake, J.M., Lodge, D.M. and Dwyer, G. 2007. Immigration events dispersed in space and time: Factors affecting invasion success. Ecological Modelling 206:63-78.

Duggan, I.C., Bailey, S.A., Colautti, R.I., Gray, D.K., Makarewicz, J.C., and MacIsaac, H.J. 2003. Biological invasions in La ke Ontario: past, present and future. In: Munawar, M. (ed.) State of Lake Ontario: Past, Present and Future. Ecovision World Monograph Series, Aquatic Ecosystem Health & Management Society, New Delhi. pp. 541-558.

Eckert, G.L. 2003. Effects of planktonic pe riod on marine population fluctuations. Ecology 84:372-383. (Supplemental data available in Ecological Archives E084-009-A1 at http://esapubs.org/arc hive/archive_E.htm).

Eckert, G.L. 2009. A synthesis of variabili ty in nearshore Alaskan marine populations. Environmental Monitoring and Assessment 155:593-606.

Eldridge, L.G. 2006. Numbers of Hawaiian Species for 2003 – 2005. Bishop Museum Occasional Papers 88:62-79.

Elliot, J.M. 1971. Some methods for the statistical analysis of samples of benthic invertebrates. Freshwater Biological Association Scientific Publication No. 25.

Falkner, M., Takata, L., and Gilmore, S. 2006. California State Lands Commission Report on

Performance Standards for Ballast Water Discha rges in California Waters. Report produced for California State Legislature. Appendix 5 (Memo on a Natural Invasion Rate Standard) and Appendix 6 (Addendum to the Memo on a Na tural Invasion Rate Standard) in Appendix A (Majority Report and Recommend ations [sic] of the Californi a Advisory Panel on Ballast

Water Performance Standards. ( http://www.slc.ca.gov/Spec_Pub/MFD/Ba llast_Water/Documents/Appendix_A.pdf )

Faria, J.C. 2009. Resources of Tinn-R GUI/E ditor for R Environment. UESC, Ilheus, Brazil.

Fenchel, T. 2005. Cosmopolitan microbes and their ‘cryptic’ species . Aquatic Microbial Ecology 41:49-54.

Fieberg, J. and Ellner, S.P. 2000. When is it meaningful to estimate an extinction probability? Ecology 81:2040-2047.

Finlay, B.J. 2002. Global di spersal of free-living microbial eukaryote speci es. Science

296:1061-1063.

95Fofonoff, P.W., Ruiz, G.M., Steves, B., and Carl ton, J.T. 2003a. In ships or on ships?

Mechanisms of transfer and invasion for non-native species to the coasts of North America. In: Ruiz, G.M. and Carlton, J.T (eds.) Invasive Species: Vectors and Management Strategies

. .Island Press, Washi ngton, DC. pp. 152-182

Fofonoff, P.W., Ruiz, G.M., Steves, B., Hines, A.H ., and Carlton, J.T. 2003b. National Exotic Marine and Estuarine Species In formation System (NEMESIS). ( http://invasions.si.edu/nemesis/overview.html )

Galil, B.S. and Zenetos, A. 2002. A sea cha nge: Exotics in the eastern Mediterranean Sea. In:Leppäkoski, E., Gollasch, S., and Olenin, S. (eds.) Invasive Aquatic Species of Europe: Distribution, Impacts and Management . Kluwer Academic Publishers, Dordrecht, The Netherlands. pp. 325-336.

Gascoigne, J. and Lipcius, R.N. 2004. All ee effects in marine systems. Marine Ecology Progress Series 269:49-59.

Gollasch, S. 2006. A new ballast water sa mpling device for sampling organisms above 50 micron. Aquatic Invasions 1:46-50.

Gollasch, S., David, M., Voigt, M., Dragsund, E., Hewitt, C., and Fukuyo, Y. 2007. Critical review of the IMO international convention on the management of ships’ ballast water and sediments. Harmful Algae 6: 585–600.

Gray, D.K., Johengen, T.H., Reid, D.F., and M acIsaac, H.J. 2007. Efficacy of open-ocean ballast water exchange as a means of preventi ng invertebrate invasions between freshwater ports. Limnology and Oceanography 52:2386-2397.

Gregg, M., Rigby, G., and Hallegraeff, G.M. 2009. Review of two decades of progress in the development of management options for reduc ing or eradicating phytoplankton, zooplankton and bacteria in ship's ballast wa ter. Aquatic Invasions 4:521-565.

Griffen, B.D. and Drake, J.M. 2008. A review of extinction in experimental populations. Journal of Animal Ecology 77:1274-1287.

Grosholz, E. D. 1996. Contrasting rates of sp read for introduced species in terrestrial and marine systems. Ecology 77:1680-1686.

Herborg, L.M., Jerde, C.L., Lodge, D.M., Ruiz, G.M., and MacIsacc, H.J. 2007. Predicting invasion risk using measures of introduction effort and environmental niche models. Ecological Applicat ions 17: 663-674.

Hewitt, C.L, Gollasch, S., and Minchin, D. 2009. The Vessel as a Vector – Biofouling, Ballast Water, and Sediments. In: Ril ov, G. and Crooks, J.A. (eds.) Biological Invasions in Marine Ecosystems: Ecologial, Manage ment, and Geographic Perspectives (Ecological Studies)

. Springer-Verlag, Berlin. pp: 117-131.

96Hickey, B.M., Pietrafesa, L.J., Jay, D.A., and Boicourt, W.C. 1998. The Columbia River Plume Study: Subtidal variability in the velocity and salinity fields. Journal of Geophysical Research 103:10,339-10,368.

Holeck, K.T., Mills, E.L., MacIsaac, H.J., Dochoda , M.R., Colautti, R.I., and Ricciardi, A. 2004. Bridging troubled waters: Biol ogical invasions, transoceanic sh ipping, and the Laurentian

Great Lakes. BioScience 54:919-929.

Holmes, E.E. 2004. Beyond theory to applica tion and evaluation: Diffusion approximations for population viability analysis. Ecol ogical Applications 14:1272–1293.

Holmes, E.E., Fagan, W.F., Rango, J.J., Folarin, A., Sorensen, J.A., Lippe, J.E., and McIntyre,

N.E. 2005. Cross Validation of Quasi-extin ction Risks from Real Time Series: An Examination of Diffusion Approximation Methods. NOAA Technical Memorandum NMFS-NWFSC-67. 37 pp. ( www.nwfsc.noaa.gov/assets/25/6256_08092005_121845_C rossValidationTM 67Final.pdf )

Hoof, R. 2008. Oregon Task Force Report on Sh ipping Transport of Aqua tic Invasive Species.

Hutchinson, G.E. 1965. The Ecological Theater and the Evolutionary Play . Yale University Press, New Haven, CT. 139 pp.

IMO. 2004a. Adoption of the Final Act a nd Any Instruments, Recommendations and Resolutions Resulting from the Work of the Conference. BWM/CONF /36, International Maritime Organization, London. ( http:// www.epa.gov/owow/invasive_species/BWM

Treaty_36.pdf)

IMO. 2004b. Consideration of the Draft In ternational Convention for the Control and Management of Ships' Ballast Water and Sedi ments. Ballast Water Discharge Standards - Regulation D-2. BWM/CONF/14. Intern ational Maritime Orga nization, London.

Jarvis, B. 2000. Sampling for microbiological analysis. In Lund, B.M., Baird-Parker, T.C., and Gould, G.W. (eds.) The Microbiological Safety and Quality of Food Vol. 1. Aspen Publishers, Gaithersburg, MD. pp. 1691-1732.

Johnston, E.L., Piola, R.F., and Clark, G.F. 2008. Chapter 7. The Role of Propagule Pressure in Invasion Success. In: Rilov, G. and Crooks, J.A. (eds.) Biological Invasions in Marine Ecosystems: Ecological, M anagement, and Geographic Perspectives (Ecological Studies)

. Springer-Verlag, Berlin. pp:133-151.

Jossi, J.W., John, A.W.G., and Sameoto, D. 2003. Continuous plankton recorder sampling off the east coast of North America: history a nd status. Progress in Oceanography 58:313–325.

Kinlan, B.P. and Hastings, A. 2005. Rates of population spread and geographic range expansion: What exotic species tell us. In: Sax, D.F., Stachowicz, J.J., and Gaines, S.D. (eds.) Species Invasions: In sights into Ecology, Ev olution, and Biogeography . Sinauer Associates, Sunderland, MA. pp. 381-419.

97Knowlton, N. 1993. Sibling species in the s ea. Annual Review of Ecology and Systematics

24:189-216.

Kolar, C.S. and Lodge, D.M. 2001. Progress in invasion biology: predicting invaders. Trends in Ecology and Evolution 16:199-204.

Kramer, A.M., Dennis, B., Liebhold, A.M., and Drake, J.M. 2009. The evidence for Allee effects. Population Ecology 51:341-354.

Kuhnert, P.M., Hayes, K., Martin, T.G., and McBrid e, M.F. 2009. Expert opinion in statistical models. In: Anderssen, R.S., Braddock, R. D., and Newham L.T.H. (eds.) 18th World IMACS Congress and MODSIM09 International Congress on Modelling and Simulation. Modelling and Simulation Society of Aust ralia and New Zealand and International

Association for Mathematics and Computers in Simulation, July 2009. pp. 4262-4268. ( http://www.mssanz.org.au/m odsim09/J2/kuhnert_J2.pdf )

Lavoie, D.M., Smith, L.D., and Ruiz, G.M. 1999. The potential for intracoastal transfer of nonindigenous species in the ballast water of sh ips. Estuarine, Coastal and Shelf Science

48:551–564.

Lee II, H. and Chapman, J.W. 2001. Nonindi genous Species - An Emerging Issue For The EPA. Volume 2: A Landscape In Transi tion: Effects Of Invasive Species On Ecosystems,Human Health, and EPA Goals. U.S. EPA report by the ORD Regional Science Program. 54 pp. (http://www.epa.gov/owow /invasive_species/workshop/nisvol2.pdf)

Lee II, H., Thompson, B., and Lowe, S. 2003. Estu arine and scalar patterns of invasion in the

soft-bottom benthic communities of the San Fr ancisco Estuary. Biological Invasions 5:85­

102.

Lee II, H. and Reusser, D.A. 2006. Pacific Coast Ecosystem Information System ( PCEIS ) V.

1.0. United States Environmental Protection Agency and United States Geological Survey (Microsoft Access 2003 database).

Lee II, H., Reusser, D.A., Lamberson, J.O. a nd Nelson, W.G. 2006. Off the beaten track: Invasion of minimally exposed estuaries in the Columbian Biogeogr aphic Province. 14th Intern. Conf. Aquatic Invasive Sp ecies. Key Biscayne, FL, May 14-19 ( http://www.icais.org/ pdf/Abstracts_2006.pdf )

Lemieux, E.J., Robbins, S., Burns, K., Ratcli ff, S., and Herring, P. 2008. Evaluation of representative sampling for rare populations using microbeads. U.S. Coast Guard Research and Development Center. Report No. CG-D-03-09.

Leslie, H.M. 2005. Positive intraspecific effects trump negative effects in high-density barnacle aggregations. Ecology 86:2716–2725.

Lessios, H.A., and Robertson, D.R. 2006. Cro ssing the impassable: genetic connections in 20

reef fishes across the eastern Pacific barrier. Proceedings of the Royal Society, Series B

273:2201–2208.

98Lessios, H.A., Kessing, B.D. and Robertson, D.R. 1998. Massive gene flow across the world’s most potent marine biogeographic barrier. Pr oceedings of the Royal Society, Series B

265:583-588.

Levings, C.D., Cordell, J.R., Ong, S., and Piercey, G.E. 2004. The origin and identity of invertebrate organisms being transported to Canada’s Paci fic coast by ballast water.

Canadian Journal of Fisherie s and Aquatic Sciences 61:1–11.

Lewis, M.A. and Kareiva, P. 1993. Allee dynami cs and the spread of invading organisms. Theoretical Population Biology 43:141–158.

Locke, A., Reid, D.M., van Leeuwen, H.C., Sprule s, W.G., and Carlton, J.T. 1993. Ballast water exchange as a means of controlling disp ersal of freshwater organisms by ships.

Canadian Journal of Fisheries and Aquatic Sciences 50:2086-2093.

Lockwood, J.L., Cassey, P., and Blackburn, T. 2005. The role of propagule pressure in explaining species invasions . Trends in Ecology and Evolution 20:223-228.

Lodge, D.M., Williams, S., MacIsaac, H.J., Hayes, K.R., Leung, B., Reichard, S., Mack, R.N., Moyle, P.B., Smith, M., Andow, D.A., Carlton, J.T., and McMichael, A. 2006. Biological invasions: Recommendations for U.S. policy and management. Ecological Applications

16:2035-2054.

Ludwig, D. 1999. Is it meaningful to estimat e a probability of extinction? Ecology 80:298-310.

Lloyd’s Register. 2008. Ballast Water Treatment Technol ogy – Current Status. 32 pp. ( http://www.lr.org/NR/rdonlyr es/6B8B67B8-C135-4E55-B5B1

­ 4BB6A4A10632/85364/BWT021009.pdf)

McMichael, A.J. and Bouma, M.J. 2000. Global Changes, Invasive Species, and Human Health. In: Mooney, H.A. and Hobbs, R.J. (eds.) Invasive Species in a Changing World . Island Press, Washington, DC. pp. 191-210.

MEPC. 2003a. Harmful Aquatic organisms in Ballast Water: Summary of an International Workshop on Ballast Water Discharge Standard s. MEPC 49/INF.31 , Marine Environment Protection Committee, Internationa l Maritime Organization, London. ( http://www.sjofartsverket.se/upload/5290/49-INF31.pdf )

MEPC. 2003b. Comments on Draf t Regulation E-2 Concentrations of Organisms Delivered in Ships’ Ballast Water in the Absence of Any Treatment: Establishing a Baseline for Consideration of Treatment Efficacy. MEPC 49/2/21, Marine Environment Protection Committee, International Ma ritime Organization, London.

MEPC. 2003c. Harmful Aquatic Organisms in Ballast Water. MEPC 49/2/14, Marine

Environment Protecti on Committee, International Ma ritime Organization, London. ( http://www.sjofartsverket. se/upload/5290/49-2-14.pdf )

99MEPC. 2008a. Resolution MEPC.174(58). Gu idelines for Approval of Ballast Water Management Systems (G8). MEPC 58/23. Annex 4. Marine Environment Protection Committee, International Mari time Organization, London. ( http://www.bsh.de/de/Meeresdaten/Umwe ltschutz/Ballastwasser/MEPC_125_%2853%29.p df)

MEPC. 2008b. Resolution MEPC.169(57). Procedure for Approval of Ballast Water Management Systems That Make Use of Activ e Substances (G9). Marine Environment Protection Committee, Internationa l Maritime Organization, London.

MEPC. 2008c. Guidelines For Ballast Water Sampling (G2). Annex 3. Resolution MEPC.173(58). MEPC 58/23. Adopted on 10 October 2008. Marine Environment Protection Committee, Internationa l Maritime Organization, London.

McCollin, T., Shanks, A.M., and Dunn, J. 2007. The efficiency of regional ballast water exchange: Changes in phytoplankton abundance and diversity. Harm ful Algae 6:531-546.

Miller, A.W., Lion, K., Minton, M.S., and Ruiz, G .M. 2007. Status and Trends of Ballast Water Management in the United States. Third Bien nial Report of the National Ballast Information Clearinghouse. (January 2004 to December 2005). Smithsonian Environmental Research Center. Report Submitted to the United States Coast Guard. 62 pp. ( http://invasions.si.edu/nbic/reports/NBIC_Biennial_Report3_2004-05.pdf )

Minton, M.S., Verling, E., Miller, A.W., and Ruiz, G.M. 2005. Reducing propagule supply and coastal invasions via ships: effects of emer ging strategies. Frontie rs in Ecology and the

Environment 3:304-308.

Morris, W.F. and Doak, D.F. 2002. Quantitative Conservation Biol ogy: Theory and Practice of Population Viability Analysis . Sinauer Associates, Sunderland, MA. 480 pp.

Murphy, K.R., Ritz, D., and Hewitt, C.L. 2002. Heterogeneous zooplankton distribution in a ship’s ballast tanks. Journal of Plankton Research 24:729-734.

National Research Council. 1996. Stemming the Tide: Contro lling Introductions of Nonindigenous Species by Ships’ Ballast Water . National Research Council. National Academic Press, Washington, DC. 141 pp.

Nilsson, P.A., Turesson, H., and Brönmark, C. 2006. Friends and foes in foraging: intraspecific interactions act on foraging-cycl e stages. Behaviour 143:733-745.

Okubo, A. and Levin, S.A. 2002. Diffusion and Ecological Problems: Modern Perspectives

. Springer-Verlag, New York, NY. 492 pp.

Pershing, A.J., Greene, C.H., Planque, B., and Fr omentin, J-M. 2004. The influences of climate variability on North Atlantic zooplankton populations. In: Stenseth, N.C., Ottersen, G., Hurrell, J.W., and Belgrano, A. (eds.) Marine Ecosystems and Clim ate Variation: The North Atlantic: A Comparative Perspective. Oxford University Press, Oxford. pp. 59-69.

100Peterson, A.T. and Vieglais, D.A. 2001. Pred icting species invasions using ecological niche modeling: New approaches from bioinforma tics attack a pressing problem. Bioscience

51:363-371.

Phillips, S. 2005 (updated 2006). Ballast Water Issue Paper. Report for the Pacific States Marine Fisheries Commission. Portland, OR. 34 pp. ( http://www.aquaticnuisa nce.org/wordpress/wp

content/uploads/2009/01/balla st_water_issue_paper.pdf)

Pimentel, D., Zuniga, R., and Morrison, D. 2005. Update on the environmental and economic

costs associated with alien-i nvasive species in the United States. Ecological Economics

52:273-288.

Piola, R.F. and Johnston, E.L. 2009. Comp aring differential tolera nce of native and nonindigenous marine species to metal pollution using novel assay techni ques. Environmental

Pollution 157:2853–2864.

Price, J.P. and Clague, D.A. 2002. How old is the Hawaiian biota? Geology and phylogeny suggest recent divergence. Proceedings of the Royal Society, Series B 269:2429-2435.

R Development Core Team. 2008. R: A language and environment for statistical computing . R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, ( http://www.R-project.org ).

Raaymakers, S. 2002. 1st International Ball ast Water Treatment Standards Workshop, IMO London, 28-30 March 2001: Workshop Report. Gl oBallast Monograph Series No. 4. IMO London. ( http://globallast.imo.org/monograph%204%20standards%20workshop.pdf )

Reid, D.M. and Carlton, J.T. 1997. Shipping Study 1-A: A Study of the Introduction of Aquatic Nuisance Species by Vessels Entering the Great Lakes and Canadian Waters Adjacent to the United States. Final Report to U.S. Dept. of Transportation and U.S. Coast Guard. Report No. CG-D-17-97. 86 pp.

Reusser, D.A. and Lee II, H. 2008. Predictions for an invaded world: a strategy to predict the

distribution of native and non-indi genous species at multiple scales. ICES Journal of Marine

Science 65:742–745.

Ricciardi, A. 2006. Patterns of invasion in the Laurentian Great Lakes in relation to changes in vector activity. Diversity and Distributions 12:425-433.

Robertson, D.R., Grove, J.S. and McCosker, J.E. 2004. Tropical transpacific shore fishes.

Pacific Science 58:507-565.

Ruiz, G.M. and Carton, J.T. 2003. Chapter 18: Invasion Vectors: A Conceptual Framework for Management. In: Ruiz, G.M. and J.T. Carlton (eds.) Invasive Species: Vectors and Management Strategies. Island Press, Washi ngton, DC. pp. 459-504.

101Ruiz, G.M. and Reid, D.F. 2007. Current stat e of understanding about the effectiveness of ballast water exchange (BWE) in reduc ing aquatic nonindigenous species (ANS)

introductions to the Great Lakes Basin and Ches apeake Bay, USA: synthesis and analysis of existing information. NOAA Technical Memorandum GLERL-142. NOAA Great Lakes

Environmental Research Laborat ory, Ann Arbor, MI. 127 pp. ftp://ftp.glerl.noaa.gov/publications /tech_reports/glerl-142/tm-142.pdf

Ruiz, G.M., Fofonoff, P.W., Carlton, J.T., Wonh am, M.J., and Hines, A.H. 2000. Invasion of coastal marine communities in North America: Apparent patterns, processes, and biases. Annual Review of Ecology and Systematics 31:481-531.

Ruiz, G.M., Carlton, J.T., Groshol z, E.D. and Hines, A.H. 1997. Global invasions of marine and estuarine habitats by nonindigenous speci es: Mechanisms, extent, and consequences. American Zoologist, 37:621-632.

Sakai, A.K., Allendorf, F.W., Holt, J.S., Lodge , D.M., Molofsky, J., With, K.A., Baughman, S., Cabin, R.J., Cohen, J.E., Ellstrand, N.C ., McCauley, D.E., O’Neil, P., Parker, I.M., Thompson, J.N., and Weller, S.G. 2001. Th e population biology of invasive species. Annual Review of Ecology and Systematics 32:305–332.

Sandin, S.A., Smith, J.E., DeMartini, E.E., Di nsdale, E.A., Donner, S.D.,Friedlander, A.M., Konotchick, T., Malay, M., Maragos, J.E., O bura, D., Pantos, O.,Paulay, G., Richie, M., Rohwer, F., Schroeder, R.E., Walsh, S., Jacks on, J.B.C., Knowlton, N., and Sala, E. 2008. Baselines and degradation of co ral reefs in the northern Line Islands. PLoS ONE 3: e1548. doi:10.1371/journal.pone.0001548. ( http://www.plosone.org/a rticle/info%3Adoi%2F10. 1371%2Fjournal.pone.0001548 )

Scheltema, R.S. 1986. Long-distance dispersal by planktonic larvae of shoal-water benthic invertebrates among central P acific islands. Bulletin of Marine Science 39:241-256.

Scheltema, R.S. 1988. Initial evidence for th e transport of teleplanic larvae of benthic

invertebrates across the east Pacific barri er. Biological Bulletin 174:145-152.

Scheltema, R. S., and I. P. Williams. 1983. L ong-distance dispersal of planktonic larvae and biogeography and evolution of some Polynesian and western Pacific mollusks. Bulletin of

Marine Science 33:545–565.

Simberloff, D. 1989. Which Insect Introducti ons Succeed and Which Fail? In: Drake, J.A., Mooney, H.A., di Castri, F., Groves, R.H., Kruger, F.J., Rejmanek, M., and Williamson, M. (eds.) Biological Invasions: a Global Perspective . John Wiley and Sons, NewYork, NY. pp.

61-75.

Simberloff, D. 2009. The role of propagule pressu re in biological invasi ons. Annual Review of Ecology Evolution and Systematics 40:81–102.

Simkanin, C., Davidson, I., Falkner, M., Sytsma, M., and Ruiz, G. 2009. Intra-coastal ballast water flux and the potential for secondary spread of non-native species on the US West

Coast. Marine Pollution Bulletin 58:366–374.

102Sexton, J.P., McIntyre, P.J., Angert, A.L., and Rice, K.J. 2009. Evolution and ecology of species range limits. Annual Review of Ecology Evolution and Systematics 40:415–36.

Stephens, P.A. and Sutherland, W.J. 1999. C onsequences of the Alle e effect for behaviour, ecology and conservation. Trends in Ecology and Evolution 14:401–405.

Taylor, L. R. 1961. Aggregation, vari ance and the mean. Nature 189: 732-735.

Taylor, C.M. and Hastings, A. 2005. Allee e ffects in biological inva sions. Ecology Letters

8:895-908.

Taylor,W.D. and Shuter, B.J. 1981. Body size, ge nome size, and intrinsic rate of increase in ciliated protozoa. Ameri can Naturalist 118:160-172.

Thiel, M. and Gutow, L. 2005. The ecology of raf ting in the marine enviro nment. II. The rafting organisms and community. Oceanography and Marine Biology-An Annual Review 43:279­

418.

USCG. 2002a. Ballast water treatment standa rds – East Coast and West Coast workshop summaries. Produced by Battelle for U.S. Depart ment of Transportation/U.S. Coast Guard, Final Report on Contract No. DTCG39-00- D-R00019, March 2002. [From “Report and Recommendation of the California Advisory Pa nel on Ballast Water Performance Standard”]

USCG. 2002b. Standards for Livi ng Organisms in Ship’s Ballast Water Discharged in U. S. Waters. U.S. Federal Register 67(42):9632 (March 4, 2002). ( http://frwebgate.access. gpo.gov/cgi-bin/getdoc.cgi?dbname=2002_register&docid=02

­ 5187-filed.pdf)

USCG. 2008. Ballast Water Di scharge Standard - Draft Programmatic Environmental Impact Statement. Prepared by the United St ates Coast Guard, USCG-2001-10486. 221 pp.

USCG. 2009. Proposed Ballast Water Discharg e Standard Rulemaking. Fact sheet produced for U.S. Coast Guard Office of Opera ting and Environmental Standards. ( http://www.safinah.co.uk/uploads/assets//PDF s/Ballast_Water_Discharge_Standard.pdf ). The proposed rulemaking can be found at: http ://www.regulations.gov . Enter docket number

USCG-2001-10486 in the Search box.

U.S. EPA. no date. Water Permitting 101. Office of Wastewater Management - Water Permitting. ( http://www.epa.gov/npdes/pubs/101pape.pdf )

U.S. EPA. 1986. Ambient Water Quality Criter ia for Bacteria – 1986. U.S. Environmental Protection Agency, Office of Wate r. EPA440/5-84-002. 18 pp. ( http://www.epa.gov/waterscience/beaches/files/1986crit.pdf )

U.S. EPA. 1996. U.S. EPA’s NPDES Permit Wr iters’ Manual. U.S. Environmental Protection Agency, Office of Water. EPA-833-B-96-003. 292 pp. ( http://www.epa.gov/npdes/pubs/owm0243.pdf )

103U.S. EPA. 1999. Appendix A, Clean Ballast: Natu re of Discharge in “Phase I Final Rule and Technical Development Document of Unifor m National Discharge Standards (UNDS)”.

EPA-842-R-99-001.

U.S. EPA. 2003. Bacterial Water Quality Stan dards for Recreational Waters (Freshwater and Marine Waters) - Status Report. U.S. Envir onmental Protection Agency, Office of Water. EPA-823-R-03-008. 9 pp. plus appendix.

U.S. EPA. 2004a. An Examination Of EPA Risk Assessment Principles and Practices. Staff Paper Prepared for the U.S. Environmental Protection Agency by members of the Risk

Assessment Task Force. EPA/100/B-04/001. 180 pp. ( http://www. epa.gov/osa/pdfs/ratf

final.pdf)

U.S. EPA. 2004b. Overview of the Ecologica l Risk Assessment Process in the Office of Pesticide Programs, U.S. Environmental Prot ection Agency - Endangered and Threatened Species Effects Determinations. Office of Pr evention, Pesticides and Toxic Substances Office of Pesticide Programs Washington, DC. 92 pp. ( http://www.epa.gov/espp/consultation/ecorisk-overview.pdf )

U.S. EPA. 2008a. 2008 Final issuance of Natio nal Pollutant Discharge Elimination System (NPDES) Vessel General Permit (VGP) for Discha rges Incidental to the Normal Operation of Vessels Fact Sheet. ( www.epa.gov/npdes/vessels )

U.S. EPA. 2008b. Vessel General Permit. Finalized December 19, 2008. ( www.epa.gov/npdes/vessels )

Verling, E., Ruiz, G.M., Smith, L.D., Galil, B., Miller, A.W., and Murphy, K.R. 2005. Supplyside invasion ecology: characterizing propagule pressure in coastal ecosystems. Proceedings of the Royal Society, Series B 272:1249–1257.

Vermeij, G.J. 1991. When biotas meet: Unde rstanding biotic interchange. Science 253:1099­

1104.

Vermeij, G.J. 2005. From Europe to America: Pliocene to recent trans- Atlantic expansion of

cold-water North Atlantic mollu scs. Proceedings of the Royal Society, Series B 272:2545–

2550.

Wares, J.P. 2001. Biogeography of Asterias: No rth Atlantic climate change and speciation. Biological Bulletin 201: 95–103.

Wonham, M.J. and Carlton, J.T. 2005. Trends in marine biological invasions at local and regional scales: the Northeast Pacific Ocean as a model system. Bi ological Invasions 7:369–

392.

Wright, D.A. 2007. Logistics of shipboard a nd dockside testing of ballast water treatment systems in the United States. In: Gherardi, F. (ed.) Biological Invaders in Inland Waters: Profiles, Distribution, and Threats. Springer, The Netherlands. pp. 657-668.

104Zongguo, H. 2001. Marine Species and Their Di stribution in China's Seas . Krieger Publishing Co., Malabar, FL. 599 pp.

105

### Appendix A: Overview of Huma n Health Microbial Standards

Henry Lee II

Overview: It is beyond the scope of this document and the expe rtise of the author to critically review the microbial human health discharge standards pro posed by IMO or other en tities (see Table 1), and the reader is referred to water quality criteria documents and websites for additional information (e.g., U.S. EPA, 1986, 2003; http://www.epa.gov/b eaches /) as well as to reviews on microbes in ballast water (e.g., Dobbs and Rogerson, 2005; Dr ake et al., 2007). One approach taken by the IMO and the USCG is to use indicator organisms, specifically Escherichia coli and intestinal enterococci (Table 1). E. coli is usually non-pathogenic but is c onsidered an indicator of fecal

contamination. Enterococcus is a genus of bacteria that is a sub-group of fecal streptococci, and

is also an indicator of fecal contamination. EPA’s 1986 guidance (U.S. EPA, 1986) listed both

E. coli and enterococci as indicators in freshwater but only enterococci for marine waters since it survives longer than E. coli in marine waters. The IMO and USCG, however, do not

differentiate between fresh and marine waters in their standards.

The genesis of the proposed IMO and USCG Phase I microbial standards is not well defined. They are both set at about twice the criteria for steady state geometric mean densities for “Bathing (Full Body Contact) Recr eational Waters” in the 1986 “A mbient Water Quality Criteria

for Bacteria” document. These values are based on multiple samples: “generally not less than 5 samples equally spaced over a 30-day period”. Th e USCG Phase II standards and the Wisconsin and interim California standards are equal to the freshwater standards in the 1986 criterion

document.

Both the IMO and the USCG also list standards for Vibrio cholerae (serotypes O1 and O139) as does California in its interim standards (Table 1). Vibrio cholerae is the pathogen causing cholera, and as noted by the MEPC (2003c), “Som e cholera epidemics appear to be directly associated with ballast water. One example is an epidemic that began simultaneously at three separate ports in Peru in 1991, sweeping across South America, affecting more than a million people and killing more than ten thousand by 1994. Th is strain had previously been reported only in Bangladesh.” It is not clear to the current authors how the particular standards were derived by the IMO or USCG. It is interesting to not e that in a presentation by Professor Rob Bragg (“Understanding Cholera - A Review”; http://www.ufs.ac.za/apps/congress/documents/ 05/Presentations/107-Pr of%20R%20Bragg.ppt )

he stated that it took about one million bacteria to start an infection in a healthy person. However, it is not possible to compare this valu e with the ballast sta ndards because they are given in colony forming units” (cfu). It is also interesting to note that the U.S. EPA recently

removed Vibrio cholerae from its final Contaminant Candidate List 3 (CCL 3) for drinking water ( http://www.epa.gov/ogwdw/ccl/pdfs/ccl3_docs/fs_ cc3_final.pdf ) because of the low incidence

of cholera in the United States.

Recommendation/Conclusions: As a first step, we suggest that a clearer rationale for the microbial standards be developed. Is the purpose of the standards to protect bathers or is it to protect drinking water? Or are the

106standards considered surrogates to help protect against the transport of animal diseases, such as viral hemorrhagic septicemia virus (VHS; see ht tp://biology.usgs.gov/faer/vhs.html )? These are all laudable objectives but the st andards, and the indicators, ar e likely to differ depending upon the most important objective(s).

Consideration should be given to the design of sampling protoc ols both during land/ship based verification testing and during compliance monitori ng. As detailed in the 1986 “Ambient Water Quality Criteria for Bacteria”, there are differe nt standards for long-term means and individual samples.

107

### Appendix B: Calculation of Coasta l Per Capita Invasion Probabilities

Deborah A. Reusser

Statistical Analysis Using R: Analysis was done using the statistical program R (R Development Core Team 2008) because it is widely available and free. The scripts were developed in the text editor Tinn-R (Faria 2009). The R script below reads foreign ballast water disc harge values for ship discharges for each coast

in the United States. The calcPCIP function runs a simulation 10,000 times. For each run, a random organism concentration is selected for each ship based on estimates of Minton et al. (2005) sample data. The function then calculate s the high, median and low quantiles of PCIP values for each coast. A histogram of the PCIP values is generated for each coast and written to a png file. Code is also provided that uses the PCIP values to generate contour plots indicating the number of invaders per year given organism concentrations and total amount of ballast water discharged. The code to generate contour plots is given, based on a safety factor of 1. If the safety factor is changed, the text locations will need to be modified to plot correctly on the contour plot. Ballast water disc harge data are required, along with an organism density file and

historical invasion rate to run this code.

Load the library files needed >library(Hmisc) >library(MASS) > library(RColorBrewer) >library(fields)

Identify the column definitions for reading in the file >col.defs<-c(rep("numeric",2))

Read in the density Values from the Minton graph >ballastDF <- read.csv("DensityVa ls.csv", colClasses=col.defs)

Create the MeanData table from the density values (N=354) >MeanData <- rep(ballastDF$Density, ballastDF$NumShips)

The density values data is a table of the numbe r of ships with organism concentrations of a

certain value. The MeanData table contai ns 354 values with approximate organism

concentrations extracted from th e table in Minton et al. (2005).

Indentify the columns and read the ballast water file >col.defs <- c(rep("character", 5),"numeri c", rep("character",2), rep("numeric",2)) >allBallast<-read.csv("coastforiegnballast.csv", colClasses = col.defs)

Identify the columns and read the number of invaders per coast in >col.defs <- c("character", "numeric") >ballastInvaders<-read.csv("Ballast_I nvaders.csv", colClasses = col.defs)

108Create a summary table containing the sums for each coast >ballastSums<-tapply(allBallast$DISCHARGE, allBallast$Coast, sum) >bwSumsdf <- data.frame(ballastSums) >bwSumsdf$coast<-row.names(bwSumsdf) >bwSumsdf$annualForeign <- bwSumsdf$ballastSums/3

Function CalcPCIP runs 10,000 simulations random ly assigning an organism concentration to each discharge event, summing the total organism concentrations for the run and calculating the

PCIP for each run. After all runs are completed, a histogram of th e PCIP values is written to a png file and the 2.5, .5, 97.5 quantile values are ca lculated for the set of PCIP values generated.

>calcPCIP <-function(bInfo, bData) {

#Define a dataframe to contain the calculated values >RandRun=data.frame(MeanConc=rep(NA,10000), TotalProp=rep(NA, 10000), PCIP=rep(NA,10000))

#Run the calculations 10,000 times to get a no rmal distribution of per capita probabilities

>for (i in 1:10000) { # Get a random array of concentrations for all >Conc <- sample(MeanData, size=bInfo$shipCount, replace=TRUE)

# Calculate the mean concentration for this run and store it >RandRun$MeanConc[i] <- mean(Conc) # Calculate the number of organisms for each ship for this run >Prop<- round(Conc*bData$DISCHARGE,0) # Calculate the total organism inoc ulation from all ships for this run and store it >RandRun$TotalProp [i] <- sum(Prop,na.rm=TRUE) # Calcuate the annual per capita probability >RandRun$PCIP[i] <- bInf o$TotBWInvaders/(RandRun$TotalProp[i]/3) >}

# Create a file name and write out th e data generated by the Random Run > csvFile <- paste(bInfo$Coast, "RanRun", ".csv", sep="") >write.csv(RandRun, file = csvFile, append = FALSE, na = "NA", row.names = TRUE)

#Calculate the lower, median and upper bound of the annual per capita invasion probability >tmp <- quantile(RandRun$PCIP, probs=c(0.025,.5, 0.975)) >bInfo$medianPCIP <- tmp[2] >bInfo$hbPCIP <- tmp[3] >bInfo$lbPCIP <- tmp[1]

# Create a histogram of all calculated annua l PCIPs, write the graphic to a png file

# Create the name of the file to be written >pngFile <- paste(bInf o$Coast, ".png",sep="") # Open the png file for writing >png(pngFile)

109# Create a title for the Historgram based on the name of the coast being processed >hTitle <- paste("Histogram of", bInf o$Coast, "Coast Annual\nPer Capita Invasion Probabilities") >hist(RandRun$PCIP, font=2, font.lab=2,main=hT itle, xlab="Per Capita Invasion Probabilites") # add lines for the lower, median and uppe r quantile PCIP values on the histogram >abline(v=bInfo$lbPCIP, col="red") >abline(v=bInfo$hbPCIP, col="red") >abline(v=bInfo$medianPCIP, col="blue") # Close the png file >dev.off()

# Return the dataframe of information fo r the coast to the calling routine >return(bInfo) }

## END FUNCTION Create a unique list of Coasts in allBallast >coastlst<-unique(allBallast$Coast) >allBallastLst <- unique(allBallast$Coast) >recCount <- length(coastlst)

Create a dataframe to hold the in formation calculated for each coast >CoastInfo=data.frame(CoastName=rep(NA, recCount), shipCount=rep(NA, recCount), TotFB=rep(NA,recCount),TotAnnFB=rep(NA,r ecCount),TotBWInvaders=rep(NA,recCount),lb PCIP=rep(NA,recCount), medianPCIP=rep( NA,recCount), hbPCIP=rep(NA,recCount))

Loop through all the coasts calling the PCIP function >for(j in 1: length(coastlst)){

## Get the name of the current coast ## >CoastInfo$CoastName[j] <- coastlst[j]

## Get the records for the current coast ## >CoastData <- allBallast[allBallast$Coast %in% CoastInfo$CoastName[j],]

## Get the count of the numbe r of records for the current coast ## >CoastInfo$shipCount [j] <-length(CoastData$Coast) ## Get only the records that have foreign ba llast discharge ## >FBCoastData <- CoastData[CoastData$DISCHARGE > 0,] ## Calculate the total foreign ballast >CoastInfo$TotFB[j] <- sum(FBCoastData$DISCHARGE)

## Calculate the total annual foreign ballast >CoastInfo$TotAnnFB[j] <- sum(FBCoastData$DISCHARGE)/3

## Store the ballast wate r invaders per year for a coast
>CoastInfo$TotBWInva ders[j] <- ballastInvaders$invpy r[ballastInvaders$Coast %in% CoastInfo$CoastName[j]]

## Calculate the PCIP values for the Coast >CoastInfo[j,] <- calcPCIP(CoastInfo[j,], CoastData)

>}

110Write out the results for each coast to a CSV file >write.csv(CoastInfo, file = "RegionalPCIP.cs v", append = FALSE, na = "NA", row.names = TRUE)

# Build a vector of values for 3D pl ot- Organism Concentrations 0 - 1000 >conc<-c(seq(0.0001, 0.001, by = 0.00001), seq(0.0011, 0.01, by = 0.0001), seq(0.011, 0.1, by=0.001), seq(0.11, 1, by = 0.01), seq(1.1, 100, by = .1), seq(101, 1000, by=1))

# Build a vector of discharge values from 0 to 30,000,000 >discharge<-seq(0,30000000, length=6001)

# Get the stored value for the upper quantile for West Coast >probinv<- CoastInf o$hbPCIP[3]

# Set the safety factor >safetyFactor<- 1

#Create a matrix to contain the number of i nvaders given a concentration and discharge >num_invaders=matrix(data=NA, nrow=6001, ncol=2251, byrow="T", dimnames=NULL)

# Fill the matrix looping through each concentration and discharge value >for (i in 1:6001) {

>for (j in 1:2251) { >num_invaders[i,j]=probinv*discharge[i]*c onc[j]*safetyFactor > } >}

# Make a plot of the probabillity Matrix

# Set the Breaks for the Plot >brk <- c(0,0.0001, 0.001, 0.01, 0.1,1, 10)

#Create a color pallette of Red Yellow Green with six different colors >myPal<-brewer.pal(6,"RdYlGn")

# Identify the png the plot will be written to >png("WCRegionalPCIPJan2010.png") >par(xaxs="i", family="serif") >iTitle <- paste("Predicted Number of Inva ders Per Year \n Give n Per Capita Invasion Probability of", format(pr obinv,scientific = TRUE, digits=4), " \n West Coast")

# Make the plot

111>image.plot(x=discharge, y=log(conc,10),z= num_invaders, axes=F, breaks=brk, font.lab=2, col=rev(myPal),lab.breaks=names(brk), xlab="Foreign Ballast Water Discharge in Million m3 Per Year", ylab="Concentration (organism/m3)", main=iTitle, add=FALSE, legend.shrink=100)

#label the axes >axis(1, at=c(0, 1000000, 5000000,10000000,15000000,20000000,25000000, 30000000), labels = c(0, '1', '5','10','15','20','25','30'),font=2, las=1) >axis (2, at = c(-4,-3, -2, -1, 0, 1, 2, 3), labels = c('0.0001','0.001', '0.01' , '0.1', '1', '10', '100', '1000'), font=2, las=1)

# Label the plot with the number of NIS per year for each color >text(27900000,-2.3, "# NIS < 1 per 10,000 years" , cex=1, col="black", font=2, adj=c(1,0)) >text(27900000,-.4, "# NIS < 1 per 1000 years", cex=1, col="black", font=2, adj=c(1,0.5))

> text(27900000,.55 , "# NIS < 1 per 100 years", cex=1, col="black", font=2,adj=c(1,0.5)) >text(27900000,1.5, "# NIS < 1 per 10 years", cex=1, col="black", font=2, adj=c(1,0))

> text(27900000,2.50 , "# NIS < 1 per year", cex=1, col="black", font=2, adj=c(1,0)) >dev.off()

112

### Appendix C: R Statistical Tools to De velop/Evaluate Ballast Water Sampling

Protocols

Melanie Frazier

Statistical Tools Using R:

Here we describe some tools that can be used to develop and evaluate sampling protocols. For these examples we use the statistical program R (R Development Core Team 2008) because it is widely available, free, and the preferred program for analysis of many researchers. We also suggest working with a data editor such as Tinn- R (Faria 2009). We do not attempt to provide an overview of R; however, some excellent intro ductory materials can be found at http://cran.rproject.org by following the “Contributed” link. Input and output from R are represented with

courier font, and input is preceded by “>”. The symbol “ <-“ indicates the assignment of a

variable name to a variable. R will not r ead input preceded by “#”, which is for user

documentation.

Random distributions

To calculate the confidence interval around a con centration based on the results from sampling,

the ci.poisson function from the epicalc package (Chonsuvivatwong 2008) can be used. This function calculates the possible range of concentr ations based on the desired confidence interval (alpha = significance level = 1 – CI/100), the total number of obs erved organisms (events), and the total sample volume (person.time). For ex ample, if 0 organisms are observed in a 0.1 m 3
sample volume, the true concentration may be as high as 36.89 organisms m -3 based on the twotailed 95% confidence interval:

> ci.poisson(0, 0.1, alpha=0.05 )

events person.time incidence se exact.lower95ci exact.upper95ci

0 0.1 0 0 0 36.89

If 10 organisms are observed in a 1m 3 sample volume, the concentration is estimated to be between 4.8 and 18.4 organisms based on the 95% confidence interval:

> ci.poisson(10, 1, alpha=0.05 )

events person.time incidence se exact.lower95ci exact.upper95ci

10 1 10 3.162 4.79 18.4

The Poisson distribution can be further explored using dpois, ppoi s, qpois, and rpois functions. These functions allow lots of flexibility for evaluating and developing sampling protocols.

Poisson distributions are desc ribed by a single parameter, λ , which equals both the mean and the variance ( λ = μ = σ 2 ). As the mean of a Poisson dist ribution increases, the variance also increases. For ballast water analyses, λ represents the concentration of organisms in the ballast

water. For more information about these func tions, type the function name preceded by a “?” (i.e., ?dpois) into the R console. For the follo wing examples, we assume a sample volume of 1

3 m

.

113The dpois function is the probability density function for a Poisson distribution. It calculates the probability of obtaining a specific number of organisms in a sample unit based on λ . For example, if a ballast tank contains 1 organism m -3 the probability of a 1 m 3 sample volume containing zero organisms is 36.8%:

> dpois(0, lambda=1)

0.3678794

A plot of the probability distribut ion can be created (see Fig. 9): > counts <- c(0,1,2,3,4,5,6) > poissonDist <- dpois(counts, lambda=1) > barplot(poissonDist, ylab="Probability", xlab="Count of organisms in sample", names.arg=counts)

The ppois function is the cumulative distribution function. This is used to calculate the probability of a sample containing ≤ a specified number of organism s. The probability of a 1 m 3
sample volume containing ≤ 3 organisms when the concentration is 1 organism m -3 is 98.1%:

> ppois(3, lambda=1)

0.9810118

The probability that a sample will contain >3 organisms is 1.9%: > 1 - ppois(3, lambda=1)

0.01898816

or, alternatively: > ppois(3, lambda=1, lower.tail=FALSE)

0.01898816

The qpois function is the quantile function and returns the number of organisms predicted to be in a sample for a given quantile of data (the i nverse of ppois). For example, if the concentration of organisms in ballast is 10 m -3 , about 95% of 1 m 3 samples will contain 15 or fewer organisms.

> qpois(0.950, lambda=10)

15

The rpois function generates random values from a Poisson distribution wi th a specified lambda.

To obtain ten 1 m 3 random samples from a population with concentration 1 organism m 3 :

> rpois(10, lambda=1)

1 0 3 1 2 1 0 0 3 2

Aggregated distributions

One way to determine whether a pop ulation is aggregated is to compare the observed distribution of sample data with an expect ed distribution derived from the mean and variance of the sample data. A chi-square test can then be used to compare the observed and expected values (this and other methods are described in Jarvis, 2000). Ne gative binomial distributions are described by two parameters, μ (mean) and θ (dispersion factor, referred to as “size” in R). These parameters can be estimated with maximum likelihood technique s using the fitdistr f unction from the MASS

114package from replicate samples taken from a population. Once the parameters have been estimated, the probability distribut ion for the negative binomial can be used to develop sampling protocols for aggregated populations. The nega tive binomial functions in R are: dnbinom, pnbinom, qnbinom, and rnbinom.

115