Density Matters: 
 Review of Approaches to Setting 


Organism-Based Ballast Water Discharge Standards 


U.S Environmental Protection Agency Henry Lee II1

Office of Research and Development Deborah A. Reusser2

EPA/600/R-10/031 Melanie Frazier1

April 2010 (revised August 2010) 

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Greg Ruiz3

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. 

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2: U.S. Geological Survey, 

Western Fisheries Research Center, 

2111 SE Marine Science Drive, 

Newport, OR 97365, U.S.A. 

3: Marine Invasion Research Laboratory, 

Smithsonian Environmental Research Center, 

 647 Contees Wharf Road, P.O. Box 28, 

Edgewater, MD 21037, U.S.A. 

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0123456 01 2 
Disclaimer: The information in this document has 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 Research 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 publication 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 the exclusion of others that may be suitable. 

Acknowledgements: 

The authors wish to thank the following for their contributions to this report: M.S. Minton, P.W. 

Fofonoff, and A.W. Miller provided data on ballast water discharge and historical invasion rates 

and insights into their interpretation. Richard Everett, John Lishman, and Ryan Albert provided 

guidance through the intricacies of IMO, national, and state regulations; Cheryl A. Brown 

provided advice on mathematical issues; John Van Sickle provided advice on statistical issues. 

Richard Everett, John Lishman, Ryan Albert, John 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 Setting Organism-Based Ballast Water Discharge Standards. U.S. 

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

Research Laboratory, Western Ecology Division. EPA/600/R-10/031. 

ii 
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 Proposed USCG Standards Background: .................................. 3
 

U.S. EPA Regulatory Background: ............................................................................................ 5
 

Challenges in Setting Organism-Based Discharge Standards: ................................................... 6
 

II. PROPAGULE SUPPLY DOSE-RESPONSE 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 Based on Natural Invasion Rates: ..................................... 25
 

Estimate of Natural Invasion Rate on Pacific Coast: ................................................................ 26
 

Discharge Standards Derived from Natural Invasion Rates: .................................................... 29
 

Evaluation of Natural Invasion Rates and Adjustment Factors: ............................................... 29
 

Adjustment of Ballast Water Organisms Concentrations to IMO Mean .............................. 29
 

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

Biogeographic Analysis of Potential Species Pool for Invasion .......................................... 30
 

Evidence for Transoceanic Interchange:................................................................................... 31
 

Assumptions and Limitations: .................................................................................................. 32
 

Recommendations/Conclusions:............................................................................................... 34
 

VI. REACTION-DIFFUSION MODELS .................................................................................... 35
 

Overview:.................................................................................................................................. 35
 

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

Parameter Estimation: ............................................................................................................... 37
 

Assumptions and Limitations: .................................................................................................. 39
 

Recommendations/Conclusions:............................................................................................... 40
 

VII. POPULATION VIABILITY ANALYSIS (PVA) MODELS ............................................... 42
 

iii 
Overview:.................................................................................................................................. 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 Coastal Waterbodies and the Great Lakes: .......... 56
 

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

Estimates of Historical Invasion Rates: .................................................................................... 59
 

Uncertainties in Historical Invasion 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 Per Capita Invasion Probabilities ..................................... 108
 

Appendix C: R Statistical Tools to Develop/Evaluate Ballast Water Sampling Protocols ........ 113
 

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

Random distributions .......................................................................................................... 113
 

Aggregated distributions..................................................................................................... 114
 

iv 
 LIST OF FIGURES 

Figure 1: Illustrations of Allee effects on per capita population growth ........................................ 9 

Figure 2: Hypothetical propagule supply dose-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 and after theoretical ballast water exchange ........................................................ 14 

Figure 4: Example of relative population growth 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 Kareiva (1993) with and without 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 Coast illustrating the effect of three different 

safety factors (1, 10, and 20)..................................................................................................... 66 

Figure 8: Risk diagrams for the Pacific 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 

aggregated distributions (B and C) ........................................................................................... 74

Figure 10: Probability distributions for random samples of 1 m2

 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 m3

 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 probabilities from a randomly distributed (Poisson) 

 population vs. an aggregated population with a dispersion parameter of 0.1 (negative 

 binomial) for a sample volume of 1 m3 and concentration of 1 organism m-3. ........................ 84 

Figure 14: Theoretical example of how the apparent aggregation in the population differ 

 based on the scale of aggregation relative to the size of the sample unit. ................................ 85 

v
 

 

 

 

LIST OF TABLES
 

Table 1: Existing or proposed international and national ballast water discharge 

 standards applicable to the 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 standard for >50 micron organisms ......................................................... 21 

Table 4: Estimates of natural invasion rates, resulting discharge 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 range of population sizes 

in Alternative 1 used by the DPEIS .......................................................................................... 46 

Table 7: Probability of extinction (pe) expressed 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 organism concentrations 

 in ballast water and the “biological 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 introductions for treatment alternatives 

 relative to Alternative 1 ........................................................................................................... 50 

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

 invades from a ballast discharge compared to unexchanged 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: PCIPCI 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 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 m3

) and ballast water concentrations (0, 100 organisms m-3) ........................................ 80 

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

vi 
 

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 international ballast water treaty was negotiated 

through the International Maritime Organization (IMO). The IMO has proposed organism-based 

ballast water discharge standards for different size classes of organisms (Table ES-1). While this 

represents a major accomplishment, there is concern that the IMO standards are not sufficiently 

protective. Accordingly, the United States Coast 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 (Table ES-1). Additionally, 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 obtain 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 general 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 Water currently is undertaking development of 

organism-based 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, the Office of 

Water is seeking an objective and independent scientific opinion on approaches for deriving 

these standards and has requested that a National Academy of Sciences (NAS) expert panel 

evaluate the technical merits of approaches to generating the standards. 

To assist the NAS technical review, this report evaluates the potential approaches to generating 

national organism-based discharge standards. Because of data available, we focus on the >50 

micron organism class in our review. On the basis 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 per se, sampling issues need to be considered 

when assessing the practicality of verifying that a discharge standard has been met either in test 

facilities for purposes of regulatory approval of a treatment system or as part of compliance 

monitoring of vessel discharges. Additionally, the sampling protocol, particularly the volume of 

vii 
Table ES-1: Existing or proposed international and national ballast water discharge standards applicable to the w

States and examples of state standards. All organism dimensions are for the “minimum dimension”. Standards f

and >10 - <50 micron classes are for “viable” or “living” organisms. Note that Phase II of the Coast Guard standimplemented incrementally. The date for the implementation of the final California standard is 2020. The Califoinstantaneous standards while those for Wisconsin are daily averages. NPRM = Notice of proposed rule makingMaritime Organization. cfu = “colony forming units” 

Organism Class IMO D-2 Standard USCG NPRM Phase I USCG NPRM Phase II WI State Standard CA Interim Standard

Organisms >50 

microns <10 per m3 <10 per m3 <1 per 100 m3 (< 0.01 per m3) <1 per 10 m3 (<0.1 per m3) “No detectable living 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) 

Organisms <10 

microns No standard No standard <103 bacteria/100 ml <104 viruses/100 ml No standard < 103 bacteria/10

ml < 104 viruses/100 

Escherichia coli <250 cfu per 100 ml <250 cfu per 100 ml <126 cfu per 100 ml <126 cfu per 100 ml <126 cfu per 100 ml 

Intestinal 

enterococci 

<100 cfu per 

100 ml 

<100 cfu per 

100 ml 

<33 cfu per 

100 ml 

<33 cfu per 100 

ml 

<33 cfu per 

100 ml 

Toxicogenic 

Vibrio cholerae 

(serotypes O1 and 

O139) 

<1 cfu per 100 ml 

or 

1 cfu per g wet wt. 

zooplankton 

<1 cfu per 

100 ml 

<1 cfu per 

100 ml No standard 

<1 cfu per 100 m

or 

<1 cfu per g wet 

zoological sampl

viii 
water sampled, defines the actual risk level associated 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 below and summarized in Table ES-2. 

Reduction in Propagule Supply Based on Expert Opinion/Management Consensus: Several of 

the proposed discharge standards, including the IMO standards, were based on a combination of 

expert opinion and management consensus. As used 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 explicit use of a quantitative invasion model. 

“Management consensus” is used to capture decisions made utilizing this 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 consensus 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 models, which then can be evaluated in a risk 

management context. Expert opinion/management consensus was successful in generating the 

IMO organism-based standards despite the uncertainties 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 discharges. The question remains, 

however, as to whether the IMO standards are sufficiently protective. In part, this question arises 

because the expert opinion/managerial consensus 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 scientific understanding, we recommend that future development of 

standards rely more heavily on quantitative models than qualitative expert opinion. If expert 

opinion is used as a major input into the development 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 diverse range of biological, shipping, and engineering fields be 

consulted. 

Zero Detectable Living Organisms: California and other states have adopted or proposed 

standards with the goal of “zero detectable living organisms” in ballast water discharges. 

California’s standards will be adopted in two phases, with an interim standard of “no detectable 

living organisms” >50 microns in ballast discharged 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 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 potentially result from the 

discharge of a small number of individual organisms — in some cases as few as a single mated 

ix 
Table ES-2: Comparison of approaches to generate national, organism-based discharge standards for >50 micron 

discharges. Assessment is based on current implementation; potential modifications are identified when appropris used to denote that the approach could be used to help evaluate whether predictions from other approaches fall 

range. “Recommend for national standard development” is our assessment of whether the approach should be co

generating quantitative organism-based discharge standards at the national level. 

Approach / 

Attribute 

Expert Opinion / 

Management 

Consensuses 

Zero Detectable 

Organisms 

Natural 

Invasion 

Rate 

Reaction – 

Diffusion 

Population 

Viability 

Analysis 

Per Ca

Invas

Probab

Current 

implementation 

generates quant. 

standards 

Yes Yes 

Yes 

(prelim. for 

CA) 

No 

(volume 

based) 

No 

(relative 

comparison) 

Yes 

Apparent range of 

uncertainty in 

standard 

10,000 fold 

(range of conc. 

proposed in IMO 

negotiations – 

0.01 to 100 org m-3) 

 10,000 fold 

( upper possible 

conc. w/1L vs. 

10 m3 sample) 

100-fold 

(3 experts) 

or 

10,000-fold 

(our analysis) 

About 200 fold 

(approx. range 

in “max. safe 

release 

volumes”) 

<2 fold (w/12 spp. 

in ballast) to 

10,000 fold 

(multiple voyages 

– our analysis) 

6-fold (a

coast

or 

12-fold (w

Lake

Key data needs for 

generation of quant. 

standards 

Unknown since 

decision process not 

transparent 

Development of 

statistically 

rigorous 

sampling 

protocol 

Natural 

invasion rates 

in range of 

ecoregions 

Instantaneous 

population 

growth rates 

for a range of 

taxa 

Instantaneous 

population growth 

rates & 

instantaneous 

variance of the 

population growth 

rate for a range of 

taxa 

Non

Assumes linear dose 

response 

Unknown since 

decision process not 

transparent 

NA 

(does not assume 

a dose response) 

Yes No No Yes 

Incorporates invasion 

risk from multiple 

species in a discharge 

Yes? Yes Yes No? Yes Yes 

Incorporates invasion 

risk from multiple 

ship discharges 

Yes? Yes Yes No 

No 

(modify to 

incorporate 

multiple ships?) 

Yes 

Based on historical 

invasion rates No No Yes No No Yes 

Based on population 

dynamics No No No Yes Yes No 

x 
Approach / 

Attribute 

Expert Opinion / 

Management 

Consensuses 

Zero Detectable 

Organisms 

Natural 

Invasion 

Rate 

Reaction – 

Diffusion 

Population 

Viability 

Analysis 

Per Ca

Invas

Probab

Applicable to all taxa 

and guilds Yes? Yes 

Yes? 

(depends on 

taxa included 

in analysis) 

No 

(limited to 

short-lived 

holoplanktonic 

species) 

Yes? 

(depends upon 

which species the 

pop. data can be 

obtained) 

All 

Separates risk 

assessment from risk 

management 

No No? Yes Yes Yes Yes 

Published in peerreviewed scientific 

literature 

No No No 

Yes 

(extensive 

literature on 

reactiondiffusion 

models) 

No 

(extensive 

literature on PVA 

models) 

No 

(in proc

Recommended for 

national standard 

development 

No 

(use as “reality 

check”) 

No 

No 

(possible use 

as “reality 

check”) 

No 

(use as “reality 

check” for 

holoplanktonic 

species) 

Yes 

(if sufficient pop. 

data available for 

predictions of 

actual vs. relative 

risk) 

Yes 

xi 
pair, or in the case of asexually-reproducing species, a single individual.” From this perspective, 

the only biologically safe standard is no discharge of exotic organisms. 

While it sounds protective, the zero detectable organism standards suffer from several technical 

limitations. The first is that unless the entire ballast water discharge is sampled, it has to rely on 

samples of the discharge, and the degree of protection depends directly on the sampling protocol. 

If a small volume is used to evaluate whether the discharge meets the standard, 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 standard paired with a poor sampling protocol 

than a more lenient standard paired with a stringent sampling protocol. 

The second limitation is the feasibility of developing 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 treatment systems; however, we did assess California’s 

review of existing treatment systems. They rated a system as having “potential” if no organisms 

were detected in a laboratory, land-based, or ship-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 with 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-based, and shipboard testing). While 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 treating ballast water under the 

Federal Insecticide, Fungicide, and Rodenticide Act (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 the 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 Commission, “this approach is based on numerous 

assumptions that create a high level of uncertainty 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 standards. Nonetheless, the natural invasion rate 

approach is worth examining since it addresses generating ballast water discharge standards in a 

novel way. 

xii 
The rationale for the natural invasion rate approach is that marine/estuarine ecosystems are 

subject to a very small natural rate of invasion from rare events when species drift or raft across 

oceans and then become established in new locations. 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 range of variation, and thus would be reasonably 

protective of the environment.” To generate a discharge standard from natural invasion rates, 

four parameters are needed: 1) natural invasion rate; 2) historical invasion rate from ballast 

discharges; 3) organism concentrations 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 suggests that the full range of uncertainty could be as 

much as 10,000 fold in the standards depending upon estimates of ballast water organism 

concentrations, whether additional 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 indicated a much greater genetic exchange 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 invasion approach is suitable for the development of 

national ballast water discharge standards. 

Reaction-Diffusion Models: Reaction-diffusion models predict the concentration of a 

“substance” that is simultaneously influenced by diffusion which dilutes it and by some type of 

reaction affecting its concentration. The basic assumptions of this family of models in terms of 

invasions are: 1) they model continuous time and space; 2) there is local random movement of 

individuals; and 3) population dynamics are deterministic. When applied to ballast water, the 

two competing processes are the dilution of the ballast water containing the introduced 

organisms, which rarefies the populations, and the population growth rate of the organisms in the 

ballast discharge. If the dilution 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 invasion spread of terrestrial invaders. The only published example of 

a reaction-diffusion model applied to ballast water is that of Drake et al. (2005). Using changes 

in relative population densities, Drake et al. (2005) predicted 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 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, such pelagic copepods. Because of this limitation, diffusion models 

do not appear to be suitable for generating concentration-based discharge standards applicable to 

the wide range of taxa found in ballast water. 

xiii 
Population Viability Analysis (PVA) Models: Population viability analysis (PVA) models are a 

family of population growth models commonly used to predict the extinction 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 greater the probability of extinction. 

When used with nonindigenous species, the objective is to predict either the time to extinction or 

the probability of extinction for an invader, where extinction is the converse of establishment of 

a new invader. 

A PVA model was used in the USCG Draft Programmatic 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. The 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 population growth rate, and the critical population density (the 

threshold at which the population is considered “extinct”). The strategy taken in the DPEIS was 

to evaluate different discharge standards by predicting the relative increase in the probability of 

extinction based on the fractional reductions in the number of organisms per cubic meter of 

ballast discharge among the different standards. This 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 discharge, though we contend that the latter, which 

predicts the risk of any invasion occurring from a discharge, is the more ecologically relevant 

analysis. 

A potentially confusing strategy in the DPEIS was to compare relative decreases in organism 

concentrations resulting from different standards to the full range of organism concentrations 

found in unmanaged ballast water and ballast water after exchange. In several cases, the use of 

these extreme ranges obscured the long-term benefits from reducing organism concentrations. 

Our reanalysis suggests that the relative 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 reasons, 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, versions of PVA models that predict actual (vs. relative) risk of 

invasion may be a viable approach to generating organism-based standards. The limitation to 

developing such models is the lack of instantaneous 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 comprehensive sensitivity analysis should be conducted. In particular, a 

range of instantaneous growth rates and instantaneous variances in growth rate should be 

explored, with the ranges based on an extensive review of population dynamics. 

xiv 
Per Capita Invasion Probability: During the process of generating this synthesis, the authors 

developed a new method of generating ballast water discharge standards that appears to resolve 

many of the limitations associated with the other approaches. Based on the general consensus 

that an increase in propagule 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 calculated ballast-associated propagule pressure. 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 specified 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 rate of new ballast-associated invasions 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 Ballast Information Clearinghouse for 2005 to 2007, 

which represent the most complete records after mandatory ballast water reporting was 

instituted. A distribution of organism concentrations in unmanaged ballast water was obtained 

from published estimates and a simulation conducted 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 coastal estuaries. In 

addition, a preliminary analysis was carried out for the Great Lakes. Predictions across 

individual estuaries showed high variation, possibly due to secondary invasions from other 

estuaries or ports. The three coast-wide estimates, which eliminate the uncertainty with 

secondary invasions, showed only a 6-fold variation even with the large differences in 

environments, donor regions for invaders, and intensity of nonindigenous species surveys. Risk 

diagrams were then constructed that illustrate the relationship of the likelihood of invasion to 

organism concentrations and ballast water discharge volumes, which allow risk managers to 

assess the risk with different discharge 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 invasibility of a specific 

waterbody over time. These types of uncertainties 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 organism-based standards, we recommend that the 

per capita invasion probability be considered for the development of national standards. 

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

of invasion under controlled environmental conditions and dosing scenarios. Over the last 

decade both the number and sophistication of such experiments have increased using both 

freshwater and marine organisms. However, we conclude that it is impractical to derive 

discharge standards from laboratory or field experiments because of the: 1) impracticality of 

xv 
adequate replication to quantify rare events; 2) limitation in the number and types of species than 

can be experimentally manipulated; and 3) artificiality and simplification of laboratory 

experiments and, to a lesser extent, field experiments. The real power of these experiments is to 

advance the theory of propagule supply and to evaluate and parameterize different types of 

population models. 

Statistical Considerations in Estimating Concentrations 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 begin to estimate the actual concentration. To 

assess the requirements for a statistically rigorous sampling protocol, we assumed a random 

(Poisson) distribution of organisms in a set of samples. We then calculated the upper possible 

concentration (UPC) of organisms based on one-tailed 95% confidence intervals when zero 

organisms are detected in a range of sample volumes. For a 1 L sample with no organisms, the 

UPC was almost 3000 organisms m-3 while for a 10 m3

 sample the UPC was 0.3 organisms m-3. 

Thus, even if no organisms are detected in a very large sample (10 m3

), the actual concentration 

could be 30 times greater than the USCG Phase II standard of 0.01 m-3. As large as these 

volumes are, they likely underestimate the volumes 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 possible strategy is to require the 

large sample sizes required for high statistical power 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 violations, 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 standards is to directly regulate the concentration of 

organisms in ballast discharges using “average based sampling”. However, if “maximum 

instantaneous” discharge standards are used, then additional statistical factors must be considered 

because the results will be very sensitive 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 standards 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) summarize 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) expert panel to evaluate the technical merits of 

approaches to generating effluent limits for living 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 benthic organisms. We 

focus on this size class because most of the theoretical, empirical, and experimental studies have 

focused on these larger organisms. To the extent possible, we assess whether an approach is 

potentially applicable to organisms in the 10-50 micron size class, such as phytoplankton and 

protozoa. The human health endpoints for microbes 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 elsewhere (e.g., Lloyd’s Register, 

2008; Gregg et al., 2009). 

On the basis of ecological principles, we identified 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 per se, sampling issues need to be considered 

when assessing the practicality of verifying that a discharge standard has been met either in test 

facilities for purposes of regulatory approval of a treatment system or as part of compliance 

monitoring of vessel discharges. As discussed in Section IV, the sampling protocols define the 

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

1
 
 

 

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. 

Niche or species distribution models that predict the potential distribution 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; Reusser 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 freshwater and 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 Bossenbroek, 2004) and the European green crab (Carcinus 

maenas) on both the Atlantic and Pacific coasts (Carlton 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 large number of invaders found 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 nonindigenous species on aquatic 

systems, and the reader is referred to previous reviews on the ecological, human health, and 

economic impacts of invasive species (e.g., McMichal 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 aquatic systems through a variety of mechanisms 

(Ruiz and Carlton, 2003). Of these potential routes, shipping, including both ballast water 

discharges and hull fouling, is the primary vector for biological invasions 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 Mediterranean where Lessepsian invasions through 

the Suez canal is the major invasion 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 nonindigenous species arriving in new environments 

around the world (Ruiz et al., 1997). This increasing propagule supply appears to have increased 

the rates of invasions in a number of aquatic ecosystems (e.g., Cohen and Carlton, 1998; Holeck 

et al., 2004; but see Costello and Solow, 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 marine/estuarine environments (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 specific connotation of ecological, human health, or economic 

impacts. “Invasive species” is used to denote a nonindigenous 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). 

2
 
 

take on ballast water to compensate for changes in load, vast assemblages of aquatic organisms 

are collected and then discharged into subsequent ports. This international transfer of organisms 

is massive – untreated ballast discharges can contain thousands of organisms per cubic meter 

(Minton et al., 2005) and the total foreign ballast 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://invasions.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 number 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 the risk of invasion, a number of studies have 

shown that ballast water exchange was not sufficiently effective or consistent in reducing 

organism concentrations in ballast water especially 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 water exchange, given constraints of design and 

construction. 

In response to this concern, national and international efforts began to evaluate other options for 

managing ballast water discharges. Ultimately, a key decision was made to base ballast water 

discharge standards on the concentration of organisms in discharged ballast water, rather than on 

the percentage of ballast water exchanged during mid-ocean exchanges. Through the Marine 

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

an international ballast water treaty (“The International Convention for the Control and 

Management of Ships' Ballast Water and Sediments, 2004”) was initiated to reduce the spread of 

nonindigenous species through ballast water transport (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 standards for the maximum concentrations of organisms allowed in 

discharged ballast water based on different size groups of organisms (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 IMO standards were not sufficiently protective, a number of states, 

such as California and Wisconsin, have initiated or passed more stringent discharge limits for 

ballast water. 

The United States Coast Guard (USCG) responded 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 discharge 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, California and some other states have proposed 

alternative standards with the ultimate goal of “no detectable” discharges of organisms in ballast 

water (Table 1). 

3
 
Table 1: Existing or proposed international and national ballast water discharge standards applicable to the water

and examples of state standards. All organism dimensions are for the “minimum dimension”. Standards for the <50 micron classes are for “viable” or “living” organisms. Note that Phase II of the Coast Guard standard can be 

incrementally. The date for the implementation of the final California standard is 2020. The California standard

California State Lands Commission (2009). The Wisconsin standards are from the Wisconsin Department of Na(2010). The California standards are instantaneous standards while those for Wisconsin are daily averages. NPRproposed rule making. IMO = International Maritime Organization. cfu = “colony forming units” 

Organism Class IMO D-2 Standard USCG NPRM Phase I USCG NPRM Phase II WI State Standard CA Interim Standard

Organisms >50 

microns <10 per m3 <10 per m3 <1 per 100 m3 (< 0.01 per m3) <1 per 10 m3 (<0.1 per m3) “No detectable living 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) 

Organisms <10 

microns No standard No standard <103 bacteria/100 ml <104 viruses/100 ml No standard < 103 bacteria/10

ml < 104 viruses/100 

Escherichia coli <250 cfu per 100 ml <250 cfu per 100 ml <126 cfu per 100 ml <126 cfu per 100 ml <126 cfu per 100 ml 

Intestinal 

enterococci 

<100 cfu per 

100 ml 

<100 cfu per 

100 ml 

<33 cfu per 

100 ml 

<33 cfu per 100 

ml 

<33 cfu per 

100 ml 

Toxicogenic 

Vibrio cholerae 

(serotypes O1 and 

O139) 

<1 cfu per 100 ml 

or 

1 cfu per g wet wt. 

zooplankton 

<1 cfu per 

100 ml 

<1 cfu per 

100 ml No standard 

<1 cfu per 100 m

or 

<1 cfu per g wet 

zoological sampl

4
U.S. EPA Regulatory Background: 

Under the Clean Water Act (CWA), the U.S. EPA has the responsibility for managing the 

National Pollutant Discharge Elimination System (NPDES) Program (see 

http://cfpub.epa.gov/npdes/home.cfm?program_id=45). Under the NPDES Program, 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. EPA, 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)) had excluded discharges 

incidental to the normal operation of vessels (including ballast water) 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 other 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 incidental to the normal operation of vessels 

operating in a capacity as a means of transportation. The VGP includes general effluent limits 

applicable to all discharges; general effluent limits applicable to 26 specific discharge streams; 

narrative water-quality based effluent limits; inspection, monitoring, recordkeeping, and 

reporting requirements; and additional requirements applicable to certain vessel types. 

Recreational vessels as defined in section 502(25) of the Clean Water Act are not subject to this 

permit. In addition, with the exception of ballast water discharges, non-recreational vessels less 

than 79 feet (24.08 meters) in length, and all commercial fishing vessels, regardless of length, are 

not subject to this permit.” (U.S. EPA, 2008b) 

EPA currently is undertaking development of organism-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 deriving these standards. As part of the effort 

to achieve that objective, this document synthesizes 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 Advisor, “The primary purpose of a risk assessment 

is to inform the risk manager’s decision making process. The primary purpose of a risk 

assessment is not to make or recommend any particular decisions; rather, it gives the risk 

manager information to consider along with other pertinent information.” (U.S. EPA, 2004a). 

Accordingly, it is not the purpose of this document to propose specific discharge standards, 

which is a risk management decision that incorporates additional factors potentially including 

existing laws, social factors, economics, and feasibility. 

5
 
Challenges in Setting Organism-Based Discharge Standards: 

Predicting the rate of invasion into specific water 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 from the initial entrainment of a 

potential invader in its native environment to its establishment and spread 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 examples listed in Table 2 (also see Ruiz et al., 

2000). The purpose of listing these complexities/uncertainties is not to imply that the problem is 

insurmountable but rather to help set reasonable expectations about what is possible in the nearterm given the nature of the problem and the state of the science. Realistically, development of 

discharge standards will require a number of simplifying assumptions, and the 1000 fold range in 

quantitative standards for the >50 micron class (Table 1) reflects, to a large part, differences in 

the assumptions made. Therefore, one of the objectives 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 protective of the environment under most situations by making “conservative” 

assumptions, using safety factors similar to those 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 technological feasibility and economic viability. 

6
 
 

Table 2: Examples of complexities and uncertainties confounding the prediction 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 routes are modified in response to changes in the 

economies at regional, national, and global scales. 

● Ship voyages that span multiple foreign and domestic ports and biogeographic regions. 

● Mixing of ballast water from multiple waterbodies 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 concentrations 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-response relationship for any particular species at any 

place or time. 

● Secondary invasions into a waterbody 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 invasibility within a waterbody due to environmental trends (e.g., increase in 

nutrient loading). 

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

● Differences in invasibility among different 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 population dynamics at low densities 

● Competitive interactions with existing flora and fauna. 

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

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

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

Taxonomy and Sampling Biases 

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

identification of new invaders. 

● Differences in extent of invasion among waterbodies or regions because of different sampling efforts 

and/or taxonomic expertise. 

7
 
 

II. PROPAGULE SUPPLY DOSE-RESPONSE AND ALLEE EFFECTS 

Henry Lee II and Deborah A. Reusser 

Two major factors driving the likelihood of invasion are the nature of the propagule supply doseresponse relationship and Allee effects on population dynamics. We first discuss Allee effects 

and then propagule dose-response relationships before addressing specific approaches to setting 

ballast water standards. 

Allee Effects: 

Allee effects are reductions in the per capita population growth rate in sparse populations. Such 

depressions in individual growth rates in rarefied populations may occur due to several 

potentially interacting mechanisms (see Stephens 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 and loss of heterozygosity. 

3) Demographic stochasticity of a small population, which may result from random

 fluctuations in sex ratios and/or birth rates or environmental perturbations. 

4) Increased predation due to less effective or lack of predator swamping. 

5) Increased predation due to less effective cooperative defense against predators. 

6) Absence or reduction of cooperation in social species, including cooperative feeding. 

7) Absence or reduction in habitat alteration that increases fitness of recruits. 

8) Increased dispersal away from areas of low density. 

A distinction is made between “weak” and “strong” Allee effects (Taylor and Hastings, 2005; 

Kramer et al., 2009) (Figure 1). A weak Allee effect depresses the per capita growth rate at low 

densities, but the per capita growth rate remains positive. In comparison, a strong Allee effect 

results in a negative per capita growth rate below a threshold density, referred to as the “critical 

density”. With deterministic population growth models, the population will go extinct after it 

falls below its critical density unless there is immigration of new individuals. 

Allee effects are predicted to have 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 regarding the role of Allee 

effects in natural populations, or the 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 did find “suggestive observations” 

with exploited fish and shellfish populations, as well as with broadcast spawners, a common 

breeding type among marine/estuarine 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 chordates (including three classes of vertebrates). 

They also concluded that there was evidence that these effects occurred through at least six of the 

mechanisms listed above. 

8
 
In assessing the likelihood of Allee effects in populations of non-native species introduced via 

ballast water discharges, it is important to recognize that the density of any individual species 

will be very low given the proposed discharge standards (Table 1). This density will be further 

reduced by dilution of the ballast water in the receiving water. As an upper case example 

assume: 1) total discharge concentration of zooplankton equal to the 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 discharged 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 constitutes 10% of the discharged 

individuals; and 3) a 50-fold dilution 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 standard concentrations and dilution in the receiving waters would 

also result in low densities of benthic organisms. 

B. Weak Allee Effect 

0 

Density Density 

C. Strong Allee Effect 

Per 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 population densities in all three scenarios due to intraspecific interactions such 

as competition. Scenario A illustrates the case where there is no Allee effect and the per capita 

rate increases at lower densities. Scenario B illustrates a weak Allee effect where there is a 

decline in the per capita growth rate at lower population densities but the growth rate does not 

became negative. Scenario C illustrates a strong Allee effect where the per capita growth rate 

declines below 0 at population levels below the “critical density”. (Modified from Taylor and 

Hastings, 2005) 

Propagule Supply Dose-Response: 

The concept that invasion risk decreases with decreasing propagule supply is the fundamental 

assumption behind the IMO and USCG ballast water performance standards. This assumption is 

supported by a wide body of empirical, theoretical, and experimental evidence showing that 

invasion success increases with an increase in propagule 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; Kolar 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 corresponding change in 

invasion success in terms of either the type (general shape) of the response or the specific 

magnitude (slope) of the response” (Ruiz and Carlton, 2003). 

9
 
While it is not possible to predict the exact shape 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 organisms 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 response 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 linear 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 freshwater and marine/estuarine 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 result in invasion probabilities substantially greater than the linear 

model. 

There are, however, important exceptions to the generalization that establishment is unlikely at 

very low densities. In experimental studies with freshwater cladocerns, Bailey et al. (2009) 

found that the probability 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 Carlton - 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 probabilistically (and invasion biology is largely a probabilistic 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 establishment.” In terms of setting ballast water discharge 

standards, the possibility that a single mated female or parthenogenic individual may result in a 

successful invasion needs to be acknowledged. However, the only standard that would 

completely eliminate this possibility is the discharge 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 concentration 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/m3

Increasing probability

Allee effect

Propagule Supply Propagule Supply 

Probability of Invasion Success 

Increasing number of organisms 

Allee effect 

Figure 2: Hypothetical propagule supply dose-response curves. Potential responses include; a) 

exponential; b) sigmoid; c) linear; and d) logarithmic or hyperbolic. The triangles denote the 

range in invasion probabilities predicted at a single propagule dose (X) for different response 

models. The exponential and sigmoid models demonstrate the possible influence of Allee effects 

on invasion dynamics, and the double-headed arrow shows the reduction in invasion probability, 

relative to the linear model, due to Allee effects. The box on the left illustrates that the 

propagule doses associated with the proposed discharge standards (Table 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 discharge standards were based on a combination of expert opinion and 

management consensus. As used 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 explicit use of a quantitative invasion model. “Management consensus” is 

used to capture decisions made utilizing this expert opinion as well as inputs from experts in 

other disciplines, such as shipping and engineering, risk managers, as well as state, national, nongovernmental organization (NGO), and industry representatives. Thus, management consensus 

decisions incorporate components of risk assessment, risk management, and lobbying. With 

homage to G. E. Hutchinson (1965), the consensus process can be characterized as a scientific 

opera staged by experts in a political theater. 

Perhaps the apogee of a consensus driven process 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 health criteria and thus had a different origin.) As discussed 

below, there were several meetings of national and international invasion experts prior to and 

during the IMO convention evaluating the scientific merits of possible standards. At the treaty 

convention itself, however, the vast majority of the delegates were not invasion experts and, as is 

true of any international 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 concentrations of the standards. 

It is beyond the scope of this document to attempt 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 regulations. 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 opinion 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 difficult or currently impossible to quantify in a 

model. Finally, decisions generated using expert opinion inputs provide a focus for guiding 

future research and management strategies. Because of all the complexities associated with 

12
 
generating ballast water standards (see Table 2), expert opinion has been a key type of scientific 

input into the generation of ballast water standards to date. 

One of the authors (HL) participated in several technical workshops and IMO meetings where 

much of the discussion focused on estimating organism concentrations in unexchanged ballast 

water (see Figure 3 and MEPC, 2003a) and what reduction in these concentrations would be 

ecologically protective. The basic premise driving the expert decision process was that “less is 

better” and the greater the reductions in propagule supply, the lower the risk of invasion. No 

quantitative invasion models were used, though the expert consensus was that the discharge 

standard needed to be substantially below that normally achieved through ballast water 

exchange. Additionally, in the U.S.-sponsored workshops, the practicability of achieving the 

expert-derived concentrations was not explicitly considered. Thus some of the values generated 

via expert opinion should be viewed as conceptual end-points rather than achievable near-term 

goals. 

To document the expert opinion decision making 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 groups ... (GLOBALLAST 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, juveniles, and adults). Remove 95% of all 

photosynthetic organisms ... (COAST GUARD WORKSHOP PROPOSAL ‘‘A’’.) 

S4. Discharge no organisms greater than 50 microns in size, and treat to meet federal criteria 

for contact recreation ... (COAST GUARD WORKSHOP PROPOSAL ‘‘B’’.)” 

In 2003, an International Workshop on Ballast Water Discharge Standards was hosted by the 

State Department and the USCG in cooperation with the National Science Foundation (NSF) 

in Washington, DC. Workshop participants included IMO representatives and technical experts 

from seven countries (MEPC, 2003a). The synthesis suggestion from this workshop was a 

standard of <1 organism m-3 by 2006 for the >50 micron size 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 

13
 
Une

b

Exchanged Expert ballast

Opinion 

USCG 

Phase II

Relative Density 

Figure 3: Relative density distributions of zooplankton (>80 micron) in unexchanged ballast water (blue line) anballast water exchange (red line). The dashed line indicates the IMO standard of <10 organisms m-3 for >50 mic

gray area indicates concentrations that meet the IMO standard. The “Expert Opinion” arrow pointing to the left i

assumption that lower organism concentrations would reduce invasion risk. The “USCG Phase II” arrow points 

standard of 0.01 organisms m-3 for organisms >50 microns. (Modified from Minton et al., 2005). 

14
 based on the large number of organisms that would be discharged even at these low 

concentrations and the additive densities from multiple 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 m3 of 

ballast water would discharge 46,000,000 zooplankton. This vessel would actually be carrying 

4,600 zooplankton/m3, and in the absence of treatment would discharge a total of 46,000,000 

zooplankton. Even if treated to reduce the concentration by 4 orders of magnitude [= 0.46 

organisms m-3], this single vessel would still potentially 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 weeks, the cumulative number of organisms introduced 

will be quite a bit larger. For these reasons the United States urges the Conference to adopt less 

than 0.01/m3 as the concentration standard for zooplankton.” 

In February of 2004, the IMO adopted by consensus “The International Convention for the 

Control and Management of Ships’ Ballast Water and Sediments, 2004” (IMO, 2004a) with the 

specific standards given in Annex D-2 of the Convention as listed in Table 1. There is no 

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

as to how these values were settled upon. The reality is that the final IMO standards represent a 

negotiated compromise between the more stringent standards proposed by the U.S. and some 

other countries and the less protective standards (100 organisms m-3) proposed by several other 

countries. Note that the standards in the Convention will enter into force 12 months after 

ratification by 30 nations, representing 35% of the world shipping tonnage. As of October 2, 

2009, 18 countries representing 15.36% of the world’s shipping have ratified the treaty. The 

United States has not yet 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 the many countries with differing views that 

participated in the Diplomatic Conference negotiations. This is not uncommon, as in general, 

decisions generated through an expert opinion/management 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 what 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 provides detailed documentation of their process 

(http://www.slc.ca.gov/Spec_Pub/MFD/Ballast_Water/Ballast_Water_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 decision making process. A related limitation is 

that one, or a few, outspoken experts may drive the decision making 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. 

15
A group of experts restricted to a narrow field of specialization tend to look to at problems 

through the “lenses” of their particular expertise. Such differences not only reflect differences in 

the knowledge base of the individuals, but also their values. While such specialization is both 

appropriate and required, the reality is that additional factors, including economics, feasibility, 

and timeliness, are likely going to be important considerations when making risk management 

decisions. Accordingly, we suggest that the best approach would be for experts to provide a 

range of suggested standards accompanied with details on the ecological risks associated with 

the different standards. This would allow the risk managers to weight better all the cost-benefits 

of different standards. 

With the exception of certain structured approaches (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 validity 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 the 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 their final estimate from this value irrespective 

of the initial estimates’ accuracy.” These authors present several methods to minimize such 

biases that are summarized below. 

Recommendations/Conclusions: 

Expert opinion/management consensus was successful 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 via ballast discharges. The question remains, however, as to 

whether the IMO standards are sufficiently protective. In part, this question arises because the 

expert opinion/managerial consensus 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 scientific understanding, 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 revise their opinions as well as comparing their 

assumptions of the methodology with their beliefs; 5) utilize a methodology that allows the 

16
 
experts to respond in a non-threatening 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 add that experts in a diverse 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 adopted or have proposed standards with the goal of 

“zero detectable living organisms” in ballast water discharges. In this assessment 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 two-phases, with an interim standard 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 detectable discharge” of zooplankton, phytoplankton, 

protists, bacteria, or viruses for 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 “no 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 the 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 throughout 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 detectable discharge standard given by the “Report and 

Recommendation of the California Advisory Panel on Ballast Water Performance Standards” 

(www.slc.ca.gov/Spec_Pub/MFD/Ballast_Water/Documents/Appendix_A.doc) was, “The scientific 

basis for a standard of discharging no exotic organisms 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 potentially result from the 

discharge of a small number of individual organisms—in some cases as few as a single mated pair, 

or in the case of asexually-reproducing species, a single individual. From this perspective, the only 

biologically safe standard is no discharge of exotic organisms.” This rationale was also discussed 

by Cohen (2005 in Appendix 3 of the California Panel Report). 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 regulation, which is entirely dependent upon the 

sampling regime used. 

Another rationale for setting stringent standards is to “force” technology development. In a letter to 

California Lt. Governor Bustamante and the California State Lands Commission, The Ocean 

Conservancy (TOC) stated, “During the [Ballast Water] Committee’s work, TOC sought higher 

18
 
standards 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/Ballast_Water/Documents/Appendix_C.pdf). 

California states that their ballast water standards should be interpreted 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 would be grounds for finding non-compliance and it is 

unnecessary to show non-compliance in multiple samples 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., November, 2009). It is worth noting that while 

California cites the earlier G2 guidelines as a justification, any zero based standard is inherently an 

instantaneous standard since once any sample contains an organism 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 theoretically, impossible, particularly for microbiological organisms unless ballast 

water is discharged into a land-based treatment facility 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 mentioned 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 detectable” 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 other standards. For example, as 

discussed in Section X, when zero 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 m3

 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 actual concentration could be as much as 300-fold higher than the 

IMO standard, while for a 10,000-fold larger sample the actual concentration could be 30-fold 

higher than the proposed USCG Phase II standard. Without a statistically-robust sampling protocol 

to quantify the detection limits during both testing of treatment systems and compliance monitoring, 

it is impossible to conclude that the zero detectable discharge standard is actually any more 

stringent than the other standards. 

These problems with a zero detectable discharge standard for ballast water have been previously 

identified by various expert panels. For example, the summary of the 2003 “International 

Workshop on Ballast Water Discharge Standards” (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 specified in the testing protocol guidelines.” 

Other major challenges are whether the putative low concentration associated with the “zero 

detectable” standard is economically viable and/or technologically feasible 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 m3

 of ballast and the 

rates of ballasting and deballasting can be as high as 20,000 m3 hr-1 (NRC, 1996; Wright, 2007). 

Treatment systems must fit within the confined spaces 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 the crew or environment. As pointed out by Gregg et al. (2009), 

“Effectively eliminating the risk of ballast water mediated invasions still 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 information (Dobroski et al., 2009a, b) in 

terms of whether they presently meet the California standards or showed the 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 viruses, but concluded that there 

was no widely accepted technique or proxy for enumerating 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 methodologies, 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 review by an independent scientific organization. 

Based on the January 2009 review (Dobroski 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 that California listed a system as 

having the “potential” to meet their 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 systems 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-based testing facility but failing on a ship), or 

statistical variation in the results 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 Protection Committee (MEPC) of the IMO. The G8 

MEPC Guidelines for Approval of Ballast Water Management Systems provide that to obtain typeapproval, a system needs to satisfy the IMO Regulation D-2 standards in three consecutive valid 

shipboard test cycles and five consecutive valid land-based cycles (MEPC, 2008a). 

20
 
 

To gain a better insight into the performance of these treatment systems, we analyzed their failure 

rates among replicate trials as presented in Appendix B1 of Dobroski et al. (2009a) (Table 3). It 

was not possible to conduct this analysis 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 the replicates and/or they were 

not tested in all three modes (laboratory, 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 minimum G8 requirements mentioned above. Additionally, 

there are concerns over residual toxicity from SeaKleen®, as well as its effectiveness against 

bacteria, resistant resting stages, and sediment-dwelling organisms (Gregg et al., 2009). SeaKleen® 

has not been registered by EPA for use in treating ballast water under the 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 substance. 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 failure as reported in 

Dobroski et al. (2009a); it would take a detailed statistical review of the sampling protocols used in 

testing these systems to ascertain the statistical confidence of detecting a zero discharge (see 

Section X) and thus what level of confidence to place in the reported system successes. 

Dobroski et al. (2009a) concluded based on their review that “at least two treatment systems have 

demonstrated the potential to comply with California’s performance standards. Many additional 

systems are close to completing system performance verification testing and will soon have data 

available for review. Commission staff expects that before 2010 several 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 been approved by IMO. While predictions about 

technology development are littered with embarrassing 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 treatment system will approach an actual zero discharge 

of organisms, defined here as concentrations substantially less than the USCG Phase II standards, in 

the near term, in particular for microbes and viruses. Of course it is possible 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 protocols with adequate 

sample volumes and replication to quantitatively assess these systems. 

Recommendations/Conclusions: 

As discussed above, “zero detectable” discharge standards are undefined in the absence of a 

quantitative sampling protocol, and depending on the sampling protocol, the actual risk may be 

considerable higher than that associated with other standards. Therefore, we recommend that it not 

be used at the national level as an approach for deriving environmentally protective limits on 

concentrations of living organisms in ballast water. 

If zero detectable discharge standards are considered as a possible approach for national standards, 

part of the technical analysis should include an assessment of the relative risk associated with the 

zero detectable discharge standards versus risk associated with the USCG Phase II standards 

21
 
Table 3: Failure rates of the systems listed as having the “potential” to achieve the California 

discharge standard for >50 micron organisms (Dobroski et al., 2009a). Failure is defined as 

detection of organisms in a test sample. The failure rate was calculated as the percent of the 

replicate tests that failed the criterion using the data in Appendix B1 of Dobroski et al. (2009a). 

The Hitachi system was listed as achieving 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 status of the type and active substance approval are 

from Dobroski et al., 2009a, Dobroski 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 Dobroski et al. (2009a, b). 

System 

Failure Rate 

for Laboratory 

Testing 

(# Tests) 

Failure Rate 

for Landbased Testing 

(# Tests) 

Failure Rate 

for Shipboard 

Testing 

(# Tests) 

Type 

Approval1 

Active 

Substance 

Approval2 

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 

22
 
System 

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 granted by Flags states following successful equipment 

performance during land based and ship board testing in accordance with the IMO G8 Guidelines to 

verify treatment system efficacy, safety, design, construction, operation, and function (MEPC, 

2008a). 

2) Active Substance Approval: Active Substance Approval is granted by MEPC, not the Flag state, 

and is required by Convention Regulation D-3 for those treatment systems that make use of Active 

Substances (biocides) to comply with the Convention’s Regulation D-2 standards. Active 

Substance Approval relates to the environmental and safety aspects of the system's use of biocides 

and is conducted in accordance with the IMO G9 Guidelines (MEPC, 2008b). Approval typically is 

given in 2 stages, first “basic” approval, and then “final” approval. Systems subject to Active 

Substance Approval also must undergo type-approval testing by Flag states under the IMO G8 

Guidelines. 

*: Harmann Ag ceased work on its ballast water treatment 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 the 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 parthenogenic invaders, in comparison to the likelihood that the zero 

detectable standards would have prevented their introduction, assuming some practical sampling 

protocol for the zero detectable standards. 

If zero detectable standards are considered at the national level, it is critical to define all aspects 

of the sampling protocols for verification of ballast water treatment systems and for compliance 

monitoring. (see Section X). 

24
 
 

V. NATURAL INVASION RATES 

Henry Lee II 

Overview: 

The natural invasion rate approach 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 corrected 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 regulatory 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 addresses generating ballast water discharge standards 

in a novel way. 

Rationale: 

The rationale for the natural invasion rate approach is that marine/estuarine ecosystems are 

subject to a very small natural rate of invasion from rare events when species drift or raft across 

oceans and then become established in new locations. A ballast water discharge standard that 

resulted in an invasion rate approximately 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 reasonably protective of the environment” (Cohen, 

2005 in Falkner et al., 2006). Cohen further assumed that such a standard would be “reasonably 

protective of the various environmental, recreational 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 Falkner et al. (2006), development of a discharge 

standard (= concentration standard) resulting in a ballast water invasion rate approximately equal 

to the natural rate requires that the concentration of organisms in ballast discharges needs to be 

reduced “by the ratio between the natural invasion rate and the invasion rate due to the discharge 

of untreated and unexchanged ballast water.” This ratio is referred to as the Reduction Factor: 

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

and unexchanged BW 

Where: 

BW = ballast water
 

25
 
 

Cohen 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 standard, 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 invasion rate. For organism concentrations, Cohen 

assumes concentrations in untreated ballast water to be on the order of 102-103 per m3 for 

organisms >50 microns, 10-102 per mL for organisms between 10 and 50 microns, and 108-109 

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 experience (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 estimated the rate of invasion as 3.7 species per 

year, with an increase to 5.2 species per year 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 numbers underestimate the actual rate of invasion 

because of: 1) new invaders that have not yet been 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 uncertain (cryptogenic species). Cohen estimates that 

these factors could increase the invasion rate by 50 to 100%. Cohen 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 underestimation is not known, increasing the 

observed invasion rate by 50% to 100% does not seem unreasonable. 

These rates only capture invasions 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 rest 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/about/science/misp.html) to determine 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 all 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 Invasion Rate on Pacific Coast: 

The third input value needed is the natural invasion 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 and rare transport mechanism and becomes 

established initially as a disjunct, isolated population in waters on the other side” (Falkner et al., 

26
 
 

2006). In assessing the prevalence of natural invasion rates, Cohen excluded several groups of 

organisms that would “inflate” the natural invasion rate. Pelagic organisms that have “regular, 

natural genetic exchange between populations on opposite sides 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 British Columbia) were excluded. Another group 

that was excluded was species that 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 consist 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 would 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 result from natural invasion 

The length of time it takes for isolated 

populations to become morphologically distinct 

The natural invasion rate as defined by this formula 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 “common to both sides of the ocean” because they 

evolved into a new species. For example, given 100 species in common and a speciation rate of 

0.75 million years, the adjusted natural invasion rate (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 relevant data”, Cohen 

estimated that the number of fish and invertebrates 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 given 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 species per million years (corrected value from Appendix 6 of 

Falkner et al., 2006). The assumptions inherent in these estimates are discussed below. 

27
 
Table 4: Estimates of natural invasion rates, resulting discharge limits, and adjusted discharge limits. Adjustme

extent to which the discharge limit would be increased because of the identified factor. The first three estimates experts who participated in the CA Advisory Panel on Ballast Water Performance Standards (Falkner et al., 2006are adjusted based on the mean IMO organism concentrations for zooplankton compared to that used by Cohen. to adjusting the discharge rates is to adjust the natural invasion rate from Vermeij (1991) for gastropods from the invaded the Northeast Pacific. The reduction factors for Vermeij’s natural invasion rate are derived from Equatio

range in the estimate of yearly ballast water invaders in California. The taxonomic adjustment increases Vermeij

estimated relative proportion of gastropods to total number of invertebrate and fish species. The two species pooincrease Vermeij’s rate based on the presumed increase in the number of natural invaders when considering the ePolynesia Province or all the ecoregions within the Northwest Pacific and Indo-West Pacific. For reference, the 

micron size class is organisms is 10 organisms per m3 while the USCG Phase II is 0.01 organisms per m3. 

Expert / 

Type of Adjustment 

Number of one-way natural 

invasions per 106 years / 

Extent of adjustment 

Reduction 

Factor 

Discharge limits per m3 for 

organisms >50 microns 

Discharge limit

ml for organism

50 microns 

J. Carlton ≤10 10-6 10-4 to 10-3 10-5 to 10-4 

A. Cohen ≤100 10-5 10-3 to 10-2 10-4 to 10-3 

G. Ruiz ≤1,000 10-4 10-2 to 10-1 10-3 to 10-2 

Ballast water conc. 

adjustment to mean 

IMO conc. 

4.6 to 46 fold increase NA 4.6 10-4 to 4.6 100 

(0.00046 - 4.6 org. m-3) NA 

Vermeij (1991) 5.5 4.2 - 28 x 10-7 4.2 10-5 to 2.8 10-4 (0.00004 – 0.0003 org. m-3) NA 

Taxonomic adjustment 

for all inverts & fish 10.6 fold increase NA 4.45 10-4 to 2.97 10-3 (0.00045 - 0.003 org. m-3) NA 

Species pool within

Central Polynesia

Province 

2 fold increase NA 8.90 10-4 to 5.94 10-3 

(0.00089 - 0.0059 org. m-3) NA 

Species pool within

Western Pacific & 

Indo-West Pacific 

10 fold increase NA 8.9 10-3 to 5.94 10-2 

(0.0089 - 0.059 org. m-3 NA 

28
 

As mentioned, the only quantitative estimate of a natural invasion rate was for gastropods from 

the Line Islands to the Eastern Pacific (U.S. Pacific coast). The Line Islands are located 2,500 

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

between the Line Islands and the Clipperton Islands off western Mexico constitute the “East 

Pacific Barrier” (EPB), the single largest oceanic barrier in the world (e.g., Scheltema, 1988; 

Collin, 2003). Thus a natural invasion rate derived 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 subtropical/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 calculated 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 invasion rate for the >50 micron size class reported in Falkner et 

al. (2006) ranged from 0.1 to 0.0001 organisms per m3 (Table 4). Natural invasion rates for 

smaller organisms were not addressed in Falkner et al. (2006) but the reduction factors for the 

>50 micron invaders were applied to 10-50 micron 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 size classes, respectively (Table 4). 

Evaluation of Natural Invasion Rates and Adjustment Factors: 

In this section we evaluate several of the assumptions 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 the expert estimates and second to derive a new 

discharge limit based on modifying the invasion rate from Vermeij (1991) (Table 4). 

Adjustment of Ballast Water Organisms Concentrations to IMO Mean 

Cohen uses ballast water organism concentrations in untreated ballast water of 102-103 per m3 

for organisms >50 microns. In comparison, the 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), the estimates of 102-103 per m3

 potentially underestimate 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 total number of species available 

for invasion (i.e., the species pool). The natural invasion rate from Vermeij’s (1991) work is 

based solely on gastropods, and thus substantially underestimates 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 number 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 

29
 
preface (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 species inventory for the Line Islands, a total of 281 

coastal fishes have been estimated from Kiritimati, one of the Line Islands (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. Accordingly, 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 million years. Adding the number of fishes 

estimated from Kiritimati to the total species count results in gastropods constituting 9.4% of the 

total fauna. In turn, this results in an upward 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 invasion rate by about 10-fold, assuming all taxa have approximately 

equal probability of natural invasion. These are approximate corrections as ideally the 

invertebrate ratio would be based 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 Potential Species Pool for Invasion 

The size of the potential species pool available for natural invasions depends not only on the taxa 

included in the analysis but also the geographical area considered 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 Western Pacific, it is possible to 

use the number of distinct biogeographic regions as a relative indicator 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 breakout 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 Polynesia Province”. The Central 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 gastropod 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 Line Islands Ecoregion alone, as indicated by the 

50% greater number of gastropods 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 total number of potential invaders in the entire 

Central Polynesia Province is at least 100% greater than the Line Islands alone. 

30
 
In addition to these tropical island ecoregions, there have likely been natural invasions to the 

U.S. Pacific Coast from the subtropical/tropical ecoregions of Asia and the Indo-West Pacific as 

well as the temperate/boreal ecoregions of the Cold Temperate Northwest Pacific Province 

(northern China, Korea, Japan, and Russia). It is beyond the scope of this document to attempt a 

biogeographic synthesis of these areas, but it is suffice to say that 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 species 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 species from the six ecoregion making 

up the Cold Temperate Northwest Pacific Province 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 underestimate the total number of natural invasions 

and thus result in artificially low discharge standards. The extent of this underestimate is not 

known, but given the small size of the Line Island Ecoregion compared to all the potential donor 

ecoregions, it is possible that it is at least 10-fold. 

Evidence for Transoceanic Interchange: 

Independent of the adjustments to the natural invasion rates, there are several lines of evidence 

indicating that transoceanic migrations are not as rare as originally 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 because of environmental mismatches rather 

than an absence of dispersal. Additionally, in a review of tropical 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 likely migrated westward from the tropical Eastern 

Pacific. 

Another line of evidence for transoceanic transport 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 genetic 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 the Pacific. Additionally, these authors had 

previously found “massive breaching of the EPB” in two species of sea urchins (Lessios et al. 

1998, 2003). Thus Lessios and Robertson (2006) concluded 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 shells) (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 that there is periodic 

mixing of populations across the Eastern Pacific Barrier, and that such transport is not as 

“irregular and rare” as assumed in generating the natural invasion rates in Table 4. 

A final line of support for the potential for transoceanic dispersal is the increasing appreciation 

of ocean dispersal as an important factor in determining organism distributions (de Queiroz, 

31
 
2005) and the importance of rafting as a transport mechanism in particular (e.g., Thiel and 

Gutow, 2005). As stated by de Queiroz (2005), “If vicariance biogeography 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 Committee. 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 populations, what constitutes a 

continuous range on both sides of the ocean, the larval duration defining a species as teleplanic, 

or documentation for assuming a speciation rate of 1 million years. 

An inherent assumption of the natural invasion rate approach is that a doubling of this rate would 

be sufficiently protective. This is a central 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 effects of invasive species to the effects of a two-fold increase 

in atmospheric CO2) provides no real scientific support for the adequacy/inadequacy of a ballast 

water standard equivalent to the natural invasion rate. Furthermore, 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 could decide that an invasion rate equal to the 

natural rate constitutes too great a risk and set a standard based 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 approach, and all the science-based 

models reviewed in this document, is to provide risk managers with scientifically-sound and 

transparent estimates of the rate and/or effects of invasion based on different ballast water 

concentrations. 

Our review suggests that the analysis by Cohen underestimated the rate of natural invasions, 

which then results in an artificially low discharge standard. Specifically, the following would all 

result in higher natural invasion rates: 1) including taxonomic groups in addition to gastropods; 

2) including the additional potential invaders (species pool) from other ecoregions within the 

Western Pacific; and 3) using higher mean organism concentrations in ballast water. Our 

conclusion that natural invasion rates were underestimated 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 invasions per million years from Falkner et al. (2006) 

(Table 4) is the most defensible rate for natural invasions, and potentially may still underestimate 

the rate. 

Estimating natural invasion rates is likely to have high uncertainty as indicated by the 100-fold 

difference among just three invasion experts (Table 4). With the available evidence, it appears 

that this approach will not generate discharge standards with 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 these reduction factors to the 10-50 and <10 micron 

32
 
groups, which primarily consist of phytoplankton and protozoa, introduces additional uncertainty 

especially given the differences in rates and vectors 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 approach 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 invasion rate in both directions across the Pacific 

(the 0.5 multiplier in Equation 3). This assumption 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 traveling propagule would encounter the Pacific Coast of the United 

States compared to the probability that a westward traveling propagule would encounter the Line 

Islands, or other islands in the central Pacific. 

The calculated natural invasion rate will vary inversely with the speciation rate (Equation 3). 

Thus, the speciation rate is a key 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) should be consulted to generate a range of 

scientifically-defensible rates. 

The calculation of the natural invasion 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 extinct invaders artificially lowers the natural invasion rate, and 

thus results in a lower discharge standard. 

As with all the approaches that rely on historic invasion rates, the possibility that a 

nonindigenous species may have invaded via secondary vectors and/or hull fouling or another 

vector instead of ballast water potentially inflates the ballast-water invasion rate. Incorrectly 

assigning invaders to ballast water reduces the reduction factor (Equation 1) which in turn 

reduces the discharge standard. 

The geographic scope of the current analysis is the state of California, which is a political entity 

and is not defined by any specific set of biological or environmental conditions. By the MEOW 

biogeographic schema, California encompasses two coastal provinces and three ecoregions. 

Thus the current analysis mixes a number of different areas which likely have different natural 

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

Before the Wisconsin glacier, natural invasions into 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 population of at least some lakes and ponds (e.g., 

Daniels and Peteet, 1998), though it is not clear whether this would be considered “natural 

33
 
invasions” or a re-colonization process. Thus, it is not clear that ecologically relevant natural 

invasion rates could be generated for the Great Lakes or whether the 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 review, high level of uncertainty and number of 

unsupported assumptions, the current range of values based on the natural invasion approach 

should not be used to generate discharge standards. Furthermore, given the inherent 

uncertainties with the approach, we do not believe that even a revised analysis should be used to 

generate national discharge standards. It is worth noting, however, that after adjusting for IMO 

ballast discharge rate, the upper estimate of the ballast water discharge standard derived from the 

natural invasion approach is about 50-fold greater than the USCG Phase II standard. 

Because the natural invasion rate approach is the only technique that attempts to define an 

ecologically acceptable invasion rate other than 0, values from a revised analysis could be used 

as an informal benchmark for comparisons with values generated by other methods. The 

purpose of such comparisons would be to put results from other methods in context with our 

current understanding of natural invasion rates. Such a comparison would require that all the 

techniques use similar assumptions regarding ballast water discharge volumes and organism 

concentrations. 

If the natural invasion rate approach is to be considered either as a formal approach to 

developing discharge standards or as an informal benchmark for other approaches, it is critical 

that it be further developed and reviewed not only by invasion biologists but also paleontologists, 

biogeographers, and geneticists working on connectivity among transoceanic populations. Any 

future development should address the limitations mentioned above, especially those that are 

likely to reduce the discharge standards artificially. Such an analysis should develop estimates 

of uncertainty around the predictions. 

Any further development should expand the geographic range considered. Instead of assessing 

invasion rates across a political entity (California) it would be more ecologically relevant to 

generate estimates by the biogeographic ecoregions making up the U.S. Pacific Coast. If each 

ecoregion was evaluated independently, it would then be possible to generate confidence 

intervals around the suite of estimates. Within the north Pacific, Hawaii provides a “natural 

experiment” on rates of colonization and speciation, and such an analysis could draw on the 

efforts to document the biodiversity of the Hawaiian Islands (Eldridge, 2006) as well as their 

evolutionary history (Price and Clague, 2002). Additionally, natural invasion rates should be 

evaluated on the East Coast of the 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-diffusion models in invasion biology has been the 

theoretical analysis of the pattern of invasion spread of terrestrial 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 Discharges 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 the volume of ballast water released. Note that 

this approach predicts “acceptable volumes” of ballast water and does not directly use or predict 

concentrations of organisms in the 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 population density scaled by carrying capacity (i.e., between 0 and 1) 

t = time
 

D = diffusivity of discharged ballast water (m2

s

-1) 

 = Laplace operator defining the spatial gradient over two dimensions 

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

In Equation 4, the first set of terms is the “diffusion” 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 “reaction” component. By normalizing population 

35
 
 

size to carrying capacity, the model does not predict a population concentration but rather 

changes in relative population size 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 population growth (Lewis and Kareiva, 1993). As can be seen in 

Figure 4, inclusion of a mild Allee effect has a minor effect on population growth over most 

densities. It is only at very low relative densities (Figure 5) that 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 negative intraspecific interactions. 

Assuming a mild Allee effect and an initial population density substantially above the critical 

density (a), the necessary and sufficient conditions for the establishment of a population of an 

introduced species in terms of area occupied is: 

1 D Equation 6: Rmin  1/ 2  a 2r 

Where: 

Rmin = 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 this 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 establishment 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 and population growth rate (r) (their equation not given). They 

then estimated the maximum per capita population growth rate, rmax , using the upper 0.01, 0.001, 

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

36
 
 

 

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

would become established. Based on Lewis and Kareiva (1993), they then set rmax as 

approximately equal to 4  r or r  rmax 4 . Substituting rmax for r in Equation 6 results in: 

2 D Equation 7: Rmin  1/ 2  a 2rmax 

Based on the rmax 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 discharged at a specified risk level (from the 

confidence level of the r): 

2 Equation 8: Vmax   Rmin d Vmax = π Rmin2 d 

Where: 

Vmax = maximum volume of ballast water discharge for specified risk level (m3

) 

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 growth 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 discharge standards that have been 

proposed (e.g., 0.01 to 10 organisms > 50 microns per m3

). 

As mentioned, a single depth (d) of 10 m was assumed for all ballast water discharges. Vmax 

scales linearly with depth so the “exact value is not hugely important”. The authors used two 

horizontal diffusivity values in their calculations, 0.02 m2 s

-1 and 0.3 m2 s-1, the minimum and 

maximum values reported from a study of lakes. These values are substantially lower than those 

found in many estuarine/marine systems, which can have diffusivities over 1000 m2 s

-1 (e.g., 

Banas et al., 2004; also see Figure 5 of Drake et al., 2005). Because the 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 harbors which physically restrict diffusion (see their Figure 5). 

Note that the diffusivity values in m2 s

-1 need to be multiplied by 86,400 to convert them to m2 

day-1 so that the units are consistent with the intrinsic rate of growth (day-1) when used in 

Equations 6 and 7. 

37
 
Mild Allee Effect 

0 

No Allee Effect 

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 

Population 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 population 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 relation 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 Size 

Population Growth Rate

Mild Allee Effect 

No Allee Effect 

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

model from Lewis and Kareiva (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. 

38 
Drake et al. (2005) use risk tolerance values of p = 0.01, p = 0.001, and p= 0.0001 to represent 

the “chance of establishment per introduction” to bracket different levels of protection. These 

risk tolerance values are derived 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 acceptable 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 this would require, at the minimum, estimates of carrying capacities 

for the species in the ballast discharge, which 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 predict changes in organism concentrations resulting from dilution. 

A general limitation of using reaction-diffusion models to develop ballast water discharge 

standards is that they only apply to small holoplanktonic species (such as calanoid copepods), 

that spend their entire adult life span in the water column and that are 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 model assumptions including: 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 through 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 holoplanktonic species make up a relatively small 

fraction of the total marine/estuarine 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 constitutes 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 “acceptable” ballast water volumes for “invasion risk 

tolerances” of 0.01, 0.001, and 0.0001. The risk 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 environmental question is not whether any particular 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 100th 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 

39
 
value used by these authors results in a high risk of invasion when considering 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 generated 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, they used the intrinsic rate of 

growth equal to the upper 0.0001 confidence level for the particular size of organism in Equation 

7. While an innovative approach, the problem is that the intrinsic growth rates associated with 

the upper 0.001 and 0.0001 upper confidence levels are unrealistically high. For example, backcalculating from their equations using 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 protection levels is limited to risk tolerance levels 

around 0.01, a very high, and presumably unacceptable, invasion risk. 

The authors state that the derivation of Equation 6 assumes that the original release density u0 is 

“considerably above the Allee threshold a”. Given the low proposed discharge standards (0.01 – 

10 organisms m-3) it is possible that ballast water concentrations 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 Lewis and Kareiva (1993) relies on the assumption 

that population dynamics are relatively fast compared 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 (= species with slower population growth rates). 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 organism-based discharge standards 

since it is based on “relative densities” to predict acceptable volumes of ballast discharge. 

However, it should be possible to generate reaction-diffusion models addressing ballast water 

discharges that utilize actual densities rather than relative densities, though this would require 

estimates of species specific population vital rates. Alternatively, it may be possible to link 

population growth models with models simulating 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 “turned on their head” and the ballast discharge would occur at the 

surface rather than from depth. These simulation models are “mature” and allow for inclusion of 

40
 
real 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 models would have to be modified to model ballast discharges. 

The more germane question is how much effort should 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 substantial 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 standards applicable to the wide range of taxa found in ballast 

water. 

While not suitable as a general approach to generating discharge standards, results from diffusion 

models with holoplanktonic organisms can be used to help elucidate the role of population 

dilution in initial establishment. Such an analysis may help explain why there are relatively few 

copepod invaders in marine/estuarine systems even though they make up a substantial portion of 

the fauna in ballast water (e.g., Lavoie et al., 1999; Levings et al., 2004). 

41
 
VII. POPULATION VIABILITY ANALYSIS (PVA) MODELS 

Henry Lee II 

Overview: 

Population viability analysis (PVA) models are a family of population growth models commonly 

used in the conservation field to predict the extinction probability of endangered species 

(Beissinger and McCullough, 2002; Morris and Doak, 2002). 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 

greater the probability of extinction. There are three general types of PVA models: 1) countbased PVA; 2) demographic PVA; and 3) spatially explicit PVA. The count based PVA is the 

simplest, and utilizes historical census data to estimate population growth rate and variation 

assuming all individuals are identical. The diffusion approximation of Dennis et al. (1991) is the 

simplest of the count-based PVA models and is based on two parameters -- the instantaneous 

population growth rate and instantaneous variation 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 projection 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 complex 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 extinction or the probability of extinction for an 

invader, where extinction is the converse of establishment. Recently, PVA models have also 

been evaluated in laboratory experiments on population dynamics to gain insights into the 

invasion process (see Section IX). In this section, we examine the PVA analysis conducted in 

the USCG Draft Programmatic Environmental Impact Statement (DPEIS; USCG, 2008). We 

detail this analysis both because it is part of the technical analysis used by the USCG in setting 

their proposed rules (USCG, 2009) and because it is the only study that we are aware of that used 

PVA models to directly address ballast water standards. However, as discussed below, the 

formulation used in the DPEIS is not the only possible PVA methodology to addressing the risks 

associated with ballast discharges. 

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

The DPEIS used the diffusion approximation model (Dennis et al., 1991). The strategy taken in 

the DPEIS was to evaluate different discharge standards by predicting the relative increase in the 

probability of extinction based on the fractional reductions 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. 

42
 
 

 In 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 option if vessels can conduct it). 

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

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

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

Alternative 5: 0 organisms (= sterilization) 

Alternative 1 (No Action) was taken as the baseline against which the other treatments were 

compared. Ranges in organism concentrations for both unexchanged and exchanged ballast 

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

invasions would occur with sterilization. The DPEIS did not analyze the USCG Phase II 

standards (= 1/1000th IMO standard), but when possible we include such an analysis for the >50 

micron organisms. 

The remainder of this sub-section will detail the diffusion model and input parameters used in 

the DPEIS for a single species analysis, which implicitly assumes that all the individuals in a 

ballast discharge are of single species. The parameters 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 for a more detailed derivation of the equations. 

The simplest model of population dynamics incorporating stochastic variation is: 

Equation 9: dX(t) = μdt + σdW(t) 

In this model, dW(t) is a normal random variable 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 size, and the more likely that the population 

will drop to the critical population threshold (ne). Populations with negative growth (μ < 0) will 

go extinct regardless of initial population size (N(0)) and are not further considered. For 

populations with positive growth (μ > 0), the probability that a population with an initial size of 

N(0) will go extinct (i.e., reach the critical population threshold) is: 

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

[Note: Equation 10 is a direct reproduction of Equation 3 in the DPEIS (App. 4, p. A-25); we 

assume this represents a typographical error and that the authors meant to write: 

pe = exp(-2 μ ‘d’ / σ

2

) 

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

43
Table 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 deviation of the population growth rate 

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

dynamics)
 

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

critical threshold is assumed to be 1 individual in the DPEIS for the single species scenario, which is the 

smallest possible value. 

xe = log ne
 

pe = probability that a population with initial size N(0) will go extinct 

‘d’ = X(0) – xe = log (N(0)/ne) Log of the ratio of the initial population size to the critical population 

threshold. (Note that we put quotes around d to differentiate it from “delta” in the rate equations) 

c = 2 μ / σ

2

 = “biological parameter” (ratio of instantaneous 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). 

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

fe = fractional effect on extinction probability (pe) 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 (= pe(f) / pe). 

fr = the proportion of the mean rate of successful introductions relative to that under Alternative 1 (No 

Action option) 

DE = number of discharge events when calculating joint probabilities of no establishment of a single 

species from multiple identical discharge events 

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

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

Equation 11: pe = (ne / N(0))c

 Where N(0) > ne 

This equation predicts the probability of extinction (i.e., an invader not becoming established) 

based on the initial propagule supply (N(0) = organism concentration in ballast * volume of 

ballast discharged). However, these predictions require quantitative estimates of instantaneous 

population growth and variance for the specific species. As discussed in the DPEIS, such values 

are not available for most marine/estuarine or freshwater 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 fractional decreases (f) in the initial population size resulting from 

different levels of ballast water treatment. 

To calculate the relative fractional reductions in initial population size (f) by treatment type, the 

DPEIS first estimated the range of organism concentrations in unexchanged ballast water and the 

range that these concentrations would be reduced by ballast water exchange. The range in 

concentrations in unexchanged ballast water includes concentrations below the IMO limit, thus 

the range in the percent removal from ballast exchange 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 fractional decreases in initial population size in the other treatment 

alternatives (Table 6). 

Because the DPEIS used the lower and upper bounds of organism concentrations in their 

analyses, there is a wide spread in the fractional decreases for the ballast water treatment 

alternatives, including 1 (= no reduction). We believe more representative fractional decreases 

for the >50 micron size group can be calculated from the relative decrease in median propagule 

doses from ships undergoing ballast water exchange (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 slightly 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 the USCG Phase II standards each 

by an order of magnitude, representative of the changes in their ballast water concentrations 

(Table 6). 

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

6 to fe , the factor by which the reduction in initial population size increases 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 DPEIS, 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 give a detailed justification for these values. A 

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

45
 
 

Table 6: Ranges in the fractional decreases (f) in initial ballast water population size generated 

by treatment Alternatives 2 - 4 relative to the range of population sizes in Alternative 1 used by 

the DPEIS. A value of 0.1 signifies that the initial population size was reduced to 1/10th of the 

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

Alternative 1. The bolded value for the >50 micron size class for Alternative 2 is a recalculated 

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

standard versus that associated with exchanged 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 

(1/10th IMO) 

0.01 – 1 

0.0001 – 0.1 

(0.01) 

Alternative 4 

(1/100th IMO) 

0.001 – 1 

0.00001 – 0.01 

(0.001) 

USCG Phase II 

(1/1000th 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 dynamics it is unclear whether variances on the order of 1000 fold 

greater than the mean growth rate 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 critical population threshold (ne). 

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: pe(f) = f -c pe = f -c (ne / 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 fe, the ratio of the extinction 

probability with and without the fractional decrease in initial population size resulting from the 

treatment alternative: 

Equation 13: fe = f -c = pe(f)/pe 

46
 
 

The DPEIS used these formulas to evaluate the sensitivity 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 organisms in the ballast. We have recalculated the 

probabilities (Table 7) and believe that the apparent insensitivity to initial densities needs to be 

re-examined. In this recalculation we used the assumptions in the DPEIS of a critical population 

threshold of 1 organism and a ballast discharge volume (used to calculate N(0)) of 10,000 m3

. 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 decreasing 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%) with 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 extinction probabilities become important 

when considering the joint extinction probabilities of multiple species (discussed below) or with 

discharges from multiple ships. To explore the risk associated with multiple ship discharges, we 

calculated the probability that a species would not become established assuming 10 independent, 

identical ballast water discharges of 10,000 m3

. 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 (pe) 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 calculated from Equation 11 based on a single discharge 

event of 10,000 m3 with a critical population threshold of 1 organism. The probability that the 

species becomes established is 1 minus the probability of extinction given in the table, thus the 

higher the value, the lower the risk of invasion. While the probabilities of extinction are given as 

actual values, the data are most appropriately analyzed as relative differences among organism 

concentrations or values of c. Modified from Table 5-2 of the DPEIS, including adding the 

organism concentration for the USCG Phase II standard. 

Initial Organism Concentration (>50 microns) in Ballast Water (organisms m-3) 

c 

10-2 

(USCG 

Phase II) 

10-1 

(1/100th 

IMO) 

100 

(1/10th 

IMO) 

101 

(IMO) 102 103 104 106 108 

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 approach 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 established from multiple, identical discharges 

= 1 - pe

DE
 

Where: 

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

47
 
 

 

Results 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 concentrations. 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 risk with the more stringent standard. A similar 

two-fold difference in invasion risk was also seen with these standards with a c value of 0.01. 

The key point from results given in Tables 7 and 8 is that reductions in the organism 

concentrations in ballast water result in ecologically 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 (pe) 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 probabilities are calculated from Equation 11 based on 10 discharge 

events each of 10,000 m3

 with a critical population threshold of 1 organism. The probability that 

the species becomes established is 1 minus the probability of extinction given in the table, thus 

the higher the value, the lower the risk of invasion. While the probabilities of extinction are 

given as actual values, the data are most appropriately analyzed as relative differences among 

organism concentrations or values of c. 

Initial Organism Concentration (>50 microns) in Ballast Water (organisms m-3) 

c 

10-2 

(USCG 

Phase II) 

10-1 

(1/100th 

IMO) 

100 

(1/10th 

IMO) 

101 102 103 104 106 108 

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 Alternative 1 (versus the absolute values in Table 7). 

This extinction probability factor (fe) was calculated from Equation 13 for Alternatives 2-4. 

Their ranges in fe for the >50 micron size class are replicated in Table 9 along with our analysis 

for multiple voyages. For the multiple ship voyages, we calculated fe from pe(f)/pe (see Equation 

13). We first calculated pe for a single voyage based on the assumptions of an organism 

concentration of 1,000 m-3 after ballast water exchange, a discharge volume of 10,000 m3

 per 

voyage, and a critical population threshold of 1 organism. The pe(f) were calculated using the 

same assumptions and the organism concentration associated with each treatment. Then both 

extinction probabilities for a single voyage were raised to the 10th power and the ratio calculated. 

The results in Table 9 from a single voyage show that for the lowest c (high variance compared 

to growth rate), the treatment alternatives do not increase the probability of invasion. As 

discussed above, this is a consequence, 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 additional reduction of organism concentrations in the 

ballast. 

48
 
 

Table 9: Factor by which the probability of extinction would be increased compared to 

Alternative 1 (fe) for >50 micron organisms. The values in Column I represent the fe for the 

range in fractional decrease values (f) and in c for a single voyage calculated in the DPEIS. 

Column II is our calculations of fe for 10 independent voyages using only the range in c. 

Modified from Table 5-3 of the DPEIS. 

Alternative c f 

I. Single Voyage 

fe 

(range in f & c) 

II. Multiple Voyages 

fe

 (range of c) 

Alternative 2 

(IMO) 

0.001 – 

0.1 

0.001 – 

1.0 1.0 – 2.0 1.047 – 100 

Alternative 3 

(1/10th IMO) 

0.001 – 

0.1 

0.0001 – 

1.0 1.0 – 2.51 1.072 – 1000 

Alternative 4 

(1/100th IMO) 

0.001 – 

0.1 

0.00001 – 

1.0 1.0 – 3.16 1.097 – 10,000 

Phase II USCG 

(1/1000th IMO) 

0.001 – 

0.1 - - 1.122 – 100,00 

With multiple voyages using the median reduction in concentration, there is a relatively small 

increase in the extinction rate, about 5% to 12%, with the low values of c. However, with the 

high values of c, the extinction 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 concentrations in the ballast becomes increasingly 

important when there is a likelihood 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 analysis of the risk of invasion from 

multiple voyages is warranted. 

The final analysis in the DPEIS for single species was to calculate fr, the mean rate of successful 

introductions for a treatment relative to Alternative 1. Recalling that the probability of 

introduction is 1- probability of extinction, fr is calculated as: 

Equation 15: fr = 1- pe(f)

 1- pe 

The numerator in this equation is the probability that invaders will become established with the 

organism concentration associated with the treatment alternative while the denominator is the 

extinction probability under Alternative 1. As before, the extinction probabilities were 

calculated assuming a critical population threshold (ne) of 1 organism, a ballast discharge of 

10,000 m3

, and range of values for c and organism concentrations. The ranges in fr for the two 

size fractions from the DPEIS are given in Table 10. We also analyze the ratio of successful 

invaders using the pe calculated using a concentration of 1000 m-3, the approximate modal 

organism concentration after ballast water exchange (from Figure 2 in Minton et al., 2005). 

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

1. The ranges in the first two columns are from 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 organism concentration of 1000 m-3 for ballast water exchange (BWE) 

and a range of value for c. The smaller the value, 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 

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

Alternative 4 

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

Phase II USCG 

(1/1000th 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 complement of the ranges 

of values presented above. As a result, the reduction in the mean rate of successful 

introductions, as compared to the No Action Alternative under: 

• Alternative 2 is expected to range between 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 between 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 between 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 median 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 alternatives. 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 standard, the predicted relative reduction in invasion 

rate is 54% to 71%. 

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

The analysis detailed above predicts the relative effects of the alternative treatment options on 

the invasion probability of a single species discharged in ballast water. The DPEIS also 

50
 
conducted a multiple species scenario, which addressed 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 successfully invade?” Similar to the 

calculation of the probability of establishment for a single species with multiple discharges 

(Equation 14), the simplest equation to predict the probability that at least one of the multiple 

species discharged from a single ballast event is introduced is: 

Equation 16: probability that at least one species becomes established = 1 - pe

n 

Where: 

n = number of species introduced in a single ballast water discharge that are not already 

successfully established 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 would 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 successfully introduced (= becomes established)
 

pj(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 densities 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 critical population threshold, they compared the probability of extinction with ne
 

= 1 and ne = 100. Finally, in this section they also considered different organism population 

sizes resulting from unexchanged 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 Environmental Impact Statement (USCG, 

2008). Rather we will present the final relative treatment efficiencies for Alternatives 2-4 

compared to initial organism populations equivalent to unexchanged and exchanged ballast water 

discharges. From these population sizes and the assumption of 12 different species within the 

ballast discharge, they calculated the probability (qm) of at least one successful introduction of a 

species from the ballast discharge. Probabilities 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). 

51
 
 

Table 11: Relative efficiencies of Alternatives 2, 3 and 4 that no species 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 (ne) is equal to 1 or 100 organisms. Modified from Table 5-9 in the DPEIS. 

ne = 1 ne = 100 

Alternative Unexchanged BWE Unexchanged BWE 

2 

(IMO) 52% 37% 78% 63% 

3 

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

4 

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

The conclusion that the DPEIS draws from this analysis is, “The specific reduction depends upon 

the alternative selected and the size class of the organism considered, 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 evaluating the total risk for the multiple species in 

ballast discharges. Finally, the reduced risk at the higher critical population threshold value 

illustrates the importance of this value in driving the results from PVA models, at least at the 

very low population densities that will be associated with the proposed ballast water standards. 

Assumptions and Limitations: 

Use of PVA models are not without their critics (e.g., Ludwig, 1999; Fieberg and Ellner, 2000; 

Coulson et al., 2001). Coulson et al. (2001) “doubt the general claim that they can be accurate in 

their ability to predict the future status of wild populations.” More optimistically, in a review of 

271 time series representing 46 taxa, Holmes et al. (2005) concluded that diffusion 

approximations did a reasonably good job at predicting proportional and severe population 

declines. They were not as good at predicting true extinction. Some of the 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 precludes the use of the 

models to directly develop organism-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 the DPEIS seems low given the diversity of 

phytoplankton and zooplankton found in ballast water (e.g., Choi et al., 2005; Cordell et al., 

2009). 

52
 
In several cases, the use of extreme ranges for input 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 concentrations of Alternative 1 bracketed the treatment 

concentrations, resulting in the erroneous conclusion 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), and on the average ballast water treatment will 

substantially reduce organism concentrations, 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 PVA models for marine/estuarine organisms is 

deriving high quality values for the instantaneous 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 monitoring. Such long-term population data for the 

marine/estuarine organisms likely to be discharged in ballast water (e.g., phytoplankton, 

holoplanktonic zooplankton, and benthic species with pelagic larvae) are rare. Even when longterm monitoring data are available, population estimates for marine/estuarine organisms may 

display a higher sampling variability than found with birds and mammals, which can affect 

parameter estimation (Holmes et al., 2005; Holmes, 2004). 

Recommendations and Conclusions: 

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

tools to estimate the relative effectiveness of different ballast water treatment alternatives. While 

recognizing the substantial insights into relative treatment efficiencies provided by the DPEIS 

(USCG, 2008), we recommend that any new efforts 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 alternatives. Additionally, an independent assessment 

may suggest a modified approach. 

The use of PVA models to generate quantitative predictions of invasion success (versus relative 

treatment efficiencies) is less clear. The advantage of such models is that they would provide 

quantitative invasion risks for proposed discharge standards. The greatest limitation is the 

current lack of quantitative population vital rates. Accordingly, before initiating any quantitative 

PVA modeling study, we recommend that a dedicated effort be undertaken to extract estimates 

of population growth rates and variances from long-term studies of marine/estuarine species. 

One obvious source are the commercial catch statistics, but this would require separating 

population variability from variability due to fishing related mortality and/or changes in fishing 

effort. There are, however, other data that would not have these confounding effects. Eckert 

(2003) synthesized 570 population time series for 170 invertebrate species, with the durations 

ranging from one to 39 years while Eckert (2009) collected 786 population time series greater 

than 2 years for 226 species in the Gulf of Alaska. Desmond et al. (2002) report on an eleven 

year record of fish and invertebrates in Southern California. We are less familiar with 

zooplankton, but even a cursory scan of the literature suggested that long-term records exist for 

several estuarine and marine copepod species (Jossi et al., 2003; Pershing et al., 2004). Not all 

53
 
these 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 variability 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 scenarios rather than modeling a single species. 

That is, the analysis should address the question “what is the likelihood of any species from a 

ballast discharge becoming established?” rather than “what is the likelihood of any particular 

species becoming established?” The former is the critical ecological and regulatory issue. 

A comprehensive sensitivity analyses should be part of any new PVA modeling. In particular, a 

range of instantaneous growth rates and instantaneous variances in growth rate (the “c” 

parameter as used in the DPEIS formulation) should be explored, with the ranges based on the 

review of population vital rates mentioned above. Another important factor that should be 

evaluated is the critical population density. While a full range of values should be used for all 

the input parameters, it is critical that the interpretation of the results explicitly consider the 

likelihood of particular values so as not to obscure the general trends with rare events, such as 

ships with organism concentrations below the proposed standards. 

Any new PVA modeling should evaluate the full range of potential discharge standards including 

the proposed USCG Phase II standards. Since the USCG may implement more stringent 

standards in an incremental fashion, we suggest that standards equivalent to 1/10th and 1/100th of 

the IMO standards (e.g., standards of 1 and 0.1 organisms per m3

 for the >50 micron class) also 

be evaluated. 

54
 
VIII. PER CAPITA INVASION PROBABILITIES 

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

Overview: 

As discussed in Section 2, there is a general consensus that an increase in propagule supply 

increases the likelihood of invasion. Based on this premise, we developed a “per capita invasion 

probability” (PCIP) approach to estimating the 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 specified 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. 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 available. We calculate 

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

as well as individual PCIP values for 17 coastal estuaries. Additionally, we include a PCIP value 

for the Great Lakes as a preliminary assessment 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 quantitative discharge standards 

because it directly relates the risk of invasion to ballast water 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 objective was to “cut through” the 

complexities to develop an approach to allow risk 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 = Nh / (Dh * Ch) 

Where: 

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

Nh = historical annual invasion rate of potential ballast-associated invaders for a waterbody 

(new invading species * year-1) 

Dh = historic annual foreign ballast discharge rate into a waterbody (m3

 year-1) 

Ch = 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. 

55
 
For 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 ballast water organism concentrations and/or greater volumes of 

ballast water discharged. Accordingly, after calculating a PCIP from a historical 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: Np = PCIP * Dp* Cp 

Where: 

Np = predicted annual invasion rate of potential ballast-associated invaders for a waterbody 

(new invading species * year-1) 

Dp = predicted annual foreign ballast discharge rate into a waterbody (m3

 year-1) 

Cp = predicted concentration of organisms in ballast water discharged into a waterbody 

(organisms * m-3) 

Foreign Ballast Water Discharge Rates for Coastal Waterbodies and the Great Lakes: 

Historical average annual foreign ballast discharge rates (Dh in Equation 18) were used to 

calculate the total propagule supply. 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. The values in Table 12 are the average of the yearly rates for the 

period 2005 to 2007, which was chosen because it occurs after the implementation of mandatory 

ballast water reporting and represents the most complete discharge records available. Average 

annual foreign discharge rates were also calculated 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 for foreign ships that 

initially entered one port but did not discharge their ballast until they visited 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 Biological Invasion Shipping Study (Reid and Carlton, 

1997) reported a total annual foreign ballast water discharge into the Great Lakes of 1,395,461 

metric tons in 1991. This is before mandatory ballast water exchange, which was initiated in the 

Great Lakes in 1993. 

Estimates of Organism Concentrations in Ballast Water: 

Organism concentrations in ballast water discharged in coastal waters (Ch in Equation 18) were 

estimated from Minton et al. (2005), who reported zooplankton (> 80 microns) concentrations in 

56
 
Table 12: Historical number of invaders (Nh), foreign ballast discharge volumes (Dh), number of ships dischargi

per capita invasion probabilities (PCIP) for the East, Gulf, and Pacific coasts of the United States, 17 coastal port

Lakes. The number of coastal invasions is the number of non-native invertebrates and macroalgae >50 microns f

1981 to 2006 that were possibly introduced via ballast water and considered established. The total number of invports includes marine, brackish, and freshwater species, while the total without freshwater excludes the freshwateforeign ballast discharges for the coastal waterbodies are the annual averages of 2005 to 2007 and include marine

freshwater ports within the waterbody. Per capita invasion probabilities for the coastal waterbodies are given for 

values, including the lower quantile (0.025), median, and upper quantile (0.975), based on the simulation estimatconcentrations among the ships discharging into a waterbody. The number of invaders for the Great Lakes is givmacrofauna and phytoplankton for the period 1960 to 1988, while the ballast water discharge volume is for 1991discharge volumes and number of ships from the 17 ports is less than the coastal averages because all ports were coastal values. FW = freshwater. 

Waterbody 

Total # 

Invaders / 

Total # w/o 

FW species 

Average Annual 

Foreign Ballast 

Water Discharge 

Vol. 

(m3 year-1) 

# Ships with 

Foreign 

Ballast Water 

2005-2007 

PCIP 

(lower 0.025 

quantile) 

PCIP 

(median) 

East Coast 40 7,407,832 12,860 4.00E-11 4.31E-11 Charleston 13/12 281,160 563 3.05E-10 3.70E-10 

Chesapeake 17/14 3,011,982 1315 3.85E-11 4.51E-11 

Jacksonville 14/13 130,296 791 7.48E-10 8.58E-10 

Miami 4/4 578,482 2515 5.04E-11 5.51E-11 

Narragansett Bay 13/13 21,030 19 2.38E-09 5.41E-09 

Portsmouth 9/9 6,377 10 3.26E-09 1.54E-08 

Gulf Coast 18 19,605,340 11,821 6.98E-12 7.31E-12 Corpus Christi 5/5 1,254,845 621 2.65E-11 3.18E-11 

Galveston 4/4 748,136 778 3.53E-11 4.28E-11 

Pensacola 3/3 1,121 8 8.72E-09 2.45E-08 

 Tampa Bay 7/1 734,718 923 5.37E-11 6.54E-11 

Pacific Coast 67 14,788,369 5998 3.41E-11 3.61E-11  Columbia River 22/12 5,533,618 1759 2.89E-11 3.17E-11 

Coos Bay 22/22 583,517 87 2.18E-10 3.04E-10 

Humboldt Bay 29/29 5,539 10 1.42E-08 5.24E-08 

57
Waterbody 

Total # 

Invaders / 

Total # w/o 

FW species 

Average Annual 

Foreign Ballast 

Water Discharge 

Vol. 

(m3 year-1) 

# Ships with 

Foreign 

Ballast Water 

2005-2007 

Per Capita 

Invasion 

Probability 

(lower 0.025 

quantile) 

Per Capita 

Invasion 

Probability 

(median) 

Los Angeles / Long Beach 

31/31 2,676,874 1693 8.20E-11 9.23E-11 

Puget Sound 23/21 3,960,438 1167 4.12E-11 4.64E-11 

San Diego Bay 23/21 31,271 112 4.20E-09 5.92E-09 

San Francisco Estuary 

53/45 1,548,116 1015 2.33E-10 2.74E-10 

Great Lakes – Macrofauna 17 1,395,461 Unknown NA 9.10E-11 Great Lakes – Phytoplankton 14 1,395,461 Unknown NA NA 

58
unmanaged 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 magnitude among ships. For example, about 3.8% 

of the ships reported by Minton et al. (2005) had organism concentrations less then 10 m-3 while 

about 1.1% of the ships had concentrations greater than 50,000 m-3. Thus, the actual propagule 

dose a waterbody receives will depend on the distribution of organism concentrations among the 

ships discharging within the system. 

Because the distribution of organism concentrations in ballast water of is highly skewed, the 

mean concentration may over or underestimate the true propagule pressure depending upon the 

concentrations in the specific set 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 discharging 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 Table 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 generated with this method. Using a range of possible PCIP values 

allows us to make predictions that do not underestimate the risk of invasion, which might occur 

if only the mean concentration of organisms is used. (Note that with a fixed historical invasion 

rate, higher PCIP values result from lower discharge values since the same number of invaders 

occurred with a lower propagule pressure.) Because 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 concentration 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 between 1981 and 2006 were synthesized for the 

contiguous United States Pacific Coast, 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 for coastal waterbodies, allowing the use of the 

estimates of organism concentrations in unexchanged ballast. A 25 year time period was chosen 

to smooth out short term variations in invasion rates as well as variations in monitoring efforts. 

A longer time period also helps to mitigate effects of the lag between 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 macroalgae >50 microns; fishes 

and vascular plants were not included. Besides being reported in each coast or waterbody within 

the 25 year window, the species included in the analyses had to be considered established and 

potentially introduced via ballast water. The coastal invaders were classified into three salinity 

tolerance regimes: marine/estuarine (>20 psu), brackish (0.5-20 psu), and freshwater (<0.5 psu). 

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

59
 
versus nonindigenous phytoplankton 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 database (Fofonoff et al. 2003b) 

and the majority of the East, Gulf, and Pacific invaders and their vectors are listed in Appendix 

A of Ruiz et al. (2000). 

The 1960 to 1988 time period was chosen for the Great Lakes because it is before the 

implementation of mandatory ballast water exchange in 1993. During this interval, a total of 17 

macrofaunal ballast-associated invaders was reported 

(http://www.glerl.noaa.gov/res/Programs/ncrais/docs/great-lakes-list.xls, accessed September 26, 

2009), resulting in an invasion rate of 0.58 invaders per year. This rate is based on all shippingrelated invaders as well as three macrofaunal invaders with unknown vectors. The invasion rate 

for phytoplankton was similar (Table 12), resulting in a total 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 probabilities (PCIPs) for the Pacific Coast based on 

10,000 random simulations of organism concentrations among the 5998 ships discharging 

foreign ballast. The red lines indicate the lower 0.025 quantile and the upper 0.975 quantile 

while the blue line indicates the median. Approximately 95% of the values fall between the red 

lines. 

60
 
Uncertainties 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 worth exploring both the sources of this uncertainty and whether it 

tends to over or underestimate future invasion rates. One source of this uncertainty is that many 

coastal nonindigenous species can potentially invade 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, resulting 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 comparing 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 Pacific Coast consisting of 

approximately 54 naval ships. Ballast discharges 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 may 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 inflate estimates of historical ballast-associated invasion rates in 

individual waterbodies. After the primary invasion and establishment of a new NIS into a 

biogeographic region, the invader may spread within the biogeographic region via secondary 

invasions from the initially established population. Likely mechanisms for secondary invasions 

include ballast water discharges and hull fouling 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 uncertainty that could result in underestimating PCIP values is the 

underestimation of historical invasion rates. Carlton (2009) identified 12 sources of error leading 

to invader underestimation including unknown, unreported, misclassified, and rare invaders. In 

some parts of the world, such as Denmark, South Africa, and Chile where no invasions prior to 

mid-nineteenth century are recognized, the number of known invaders could be underestimated 

by as much as 5 to 10 times (Carlton 2009). For California, Cohen (in Falkner et al., 2006) 

suggested that unrecognized invaders could increase the invasion rate by 50% to 100%. A recent 

analysis of California invaders lists 457 cryptogenic species versus 358 nonindigenous species 

(California Dept. of Fish and Game, 2009); the California invasion 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., Knowlton, 1993), the high number of 

cryptogenic species in California suggests that 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 discharges: the relationship between propagule pressure and the 

61
 
probability of invasion could be steeper than the proportional relationship we assume, in 

particular at very low concentrations (curve d in Figure 2); survival in ballast tanks could 

improve if voyage durations decrease due to faster ships; and waterbodies may become 

increasingly susceptible to invasion 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 discharge standards (see Equations 20 and 21). We strongly suggest 

using a single safety factor rather than multiplying 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 individual 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 difference. We suspect these among-estuary differences 

are due to a suite of non-exclusive 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 lower 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 the smaller ports had more invaders than expected 

from the amount of foreign ballast water, which resulted 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 had 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 these smaller ports have a greater invasibility than 

larger systems, but we suggest secondary invasions 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 along the coast from San Francisco Estuary 

(particularly in El Niño years) may provide one mechanism of secondary invasion (Grosholz, 

1996; Behrens Yamada et al., 2005) in addition to intracoastal shipping. 

We evaluated the potential effect of polyvectic species and secondary invasions on the invasion 

rate in Humboldt by removing NIS from the Humboldt list if they: 1) had been observed in 

Pacific Coast estuaries that do not receive ballast water discharges; 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 Humboldt 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 invader list is only about 5% of 

the value when all potential invaders are included. 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 

62
 
based on small sample sizes. Consequently, ports with small amounts of ballast discharge will 

have high PCIP values even with the occurrence of a single ballast associated invader. 

Because of these factors, we believe the PCIP values for the moderate to large ports are more 

reliable, with moderate/large ports defined as those having an average annual foreign discharge 

volume of >100,000 m3

. This threshold was chosen because of a distinct break in ballast 

discharge volumes that occurs between 31,271 m3

 (San Diego) and 130,296 m3 (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 large 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 individual ports by rearranging Equation 19 to 

calculate the organism concentration in ballast water (Cp) associated with a projected ballast 

discharge volume (Dp), acceptable risk as represented by the number of new invaders per year 

(Np), PCIP value from Table 12 or otherwise calculated, and a safety factor: 

Equation 20: Cp = Np/(Dp * 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 concentration 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 standard on a specified confidence interval (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: Cp = Np/(Dp * PCIPCI * Safety Factor) 

PCIPCI = probability that a single propagule from ballast discharge will become established as a 

new invasive species; calculated for a given confidence interval estimate of PCIP for the 12 

moderate to large ports. 

PCIP values for 12 individual ports can be based 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 PCIPCI. Table 13 

gives the 90%, 95%, 99%, and 99.9% upper confidence 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 the 90% confidence interval values. 

63
 
 

 

Assuming a doubling of the annual ballast water discharge rate on the Pacific Coast to 30 million 

m3

 (see Table 12), an acceptable risk as represented by an invasion rate of one new invader per 

thousand years, the upper 99.9% confidence interval value for the 0.975 quantile PCIP for the 

Pacific Coast, and a 10-fold safety factor, the discharge standard becomes: 

Equation 22: Cp = (1x10-3 invader/yr) / (30x106

 m3 ballast water/yr * 5.90x10-10 

invader/organism * 10) = 0.006 organisms m-3 

The resulting discharge standard 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 current 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 way to visualize the “regulatory 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 rates for 1000 to 10,000 years in the future are best interpreted 

as indicating a very low probability of invasion rather than quantitative predictions.) Figure 7 

shows the risk diagrams for the Pacific Coast based on three different safety factors (1, 10, and 

20), using the PCIP value for the 99.9% confidence 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: PCIPCI 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 large 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 invasions, we believe the best alternative to 

developing discharge standards is to use Equation 20 with PCIP values derived from the 

aggregated data for an entire coast. The aggregated coastal data eliminate the uncertainty 

associated with secondary invaders as the historical invasion rate is based on the number of 

unique invaders to a coast so no invader is counted more than once. This approach is supported 

by the small variance in PCIP values 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 the 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. 

64
 
We focus our analysis on the Pacific Coast because the extensive research on the distribution of 

NIS in this region (e.g., Cohen and Carlton, 1995; Cohen et al., 2001; Lee et al., 2003: deRiveria 

et al., 2005; California Dept. Fish Game, 2009) produces the most complete historical invasion 

rate. Using the same inputs for an acceptable risk level, ballast water discharge volume, and 

safety factor as for the estuary calculation (Equation 22), and the upper 0.975 quantile PCIP 

value specific to the Pacific Coast, the discharge standard becomes: 

Equation 23: Cp = (1x10-3 invaders/yr) / (30x106

 m3 ballast water/yr * 3.83 10-11 

invaders/organism * 10) = 0.087 organisms m-3 

Based on this set of assumptions, the discharge 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 median 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 not 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 calculation of the PCIPs and the discharge standard 

derived from these probabilities. 

The PCIP values for the smaller ports are substantially 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 the presumed ballast-associated invasion rate. However, if the 

higher invasion rates are actually a result of the smaller ports having a greater invasibility, the 

standards generated from the coast values or the moderate/large ports would not be protective of 

these systems. Another way that the present analysis could underestimate risk is by failing to 

account for the introduction of species that can become 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 microns, though the PCIP approach is theoretically 

applicable to smaller size classes. The practical limitations, however, are the difficulty in 

distinguishing native from nonindigenous protozoa, phytoplankton, and microbes and the 

corresponding lack of data on historical invasion rates. As pointed out by Carlton (2009), “no 

introduced diatoms, dinoflagellates, or other phytoprotists 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 for the Great Lakes given 

the reported historical invasion rate for phytoplankton (Table 12) if an estimate for the historical 

ballast water phytoplankton concentrations can be obtained. 

65
 
Figure 7: Risk diagrams for the Pacific Coast illustrating the effect of three different safety factors (1, 10, and 20). C

99.9% confidence interval of the 0.975 quantile value of PCIP from the 12 moderate to large estuaries. A safety factor 

adjustment for the uncertainties. 

66
Figure 8: Risk diagrams for the Pacific Coast based on less protective (left diagram) and more 

protective (right diagram) assumptions. The risk 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 and 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 potential of any new invaders 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 measured population vital rates in PVA models) but the 

issue is more apparent when using historical rates. If the best colonizers tended to invade first, 

then the PCIPs derived from these historical data would over predict the number of new invaders 

for a given propagule pressure. However, the apparent 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 invasibility 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. Development 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 attempts to cut through the “Gordian Knot” of 

uncertainties associated with predicting ballast water invasions, and Equations 20 and 21 and the 

67
 
risk 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 approach that allows risk managers the option to develop discharge 

standards with different risk levels based on different sets of assumptions. Specifically, the 

following inputs can be set: 1) acceptable invasion risk as measured by an invasion rate; 2) 

ballast water discharge volume; 3) use of PCIPs based on median ballast water organism 

concentration or upper quantile values; 4) median or an upper confidence 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 invasion 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 population vital rates that are needed 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 modeling approaches. Finally, the data going into the per capita 

probability approach are readily understandable by managers and the public, which is beneficial 

in gaining acceptance for any ballast water discharge standard. 

Of the three approaches to setting discharge standards (PCIP from individual estuaries; values 

based on upper confidence intervals from distributions of PCIPs about individual estuaries; 

PCIP values based on aggregated coastal values), we suggest that the coastal approach has the 

lowest inherent uncertainty. Furthermore, since most invaders spread along the coast, analysis at 

this scale is ecologically appropriate. 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 likelihood of any individual propagule 

becoming established as a new invader in the Great Lakes. However, less complete data were 

available for ballast discharge volume and organism concentrations, and we consider the 

calculations for the Great Lakes a preliminary analysis. While there is the complicating factor of 

mandatory ballast water exchange after 1993, it may 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 also 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, future surveys for nonindigenous species should not only focus on 

the larger ports but should also include smaller ports and estuaries with no foreign ballast input. 

Additionally, further studies of the role of intracoastal shipping and ballast discharges are needed 

to help elucidate their role in spreading invaders into smaller ports with minimal foreign ballast 

water discharges. 

68
 
Table 14: Major assumptions of the per capita invasion probability (PCIP) approach to setting ballast water disch

Assumption Effect on Estimate of Per Capita Invasion Probability Effect on Discharge standard Miti

Linear dose-response 

Likely over estimates invasion 

probability for many sexual species due 

to Allee effects; potentially under 

estimates for asexual and parthenogenic 

species. 

Protective against most sexual 

invaders; possibly under protective 

for asexual and parthenogenic 

species. 

Use u

for 

safety 

cases 

Secondary invasions did not 

contribute to historical invasion 

rate. 

Inflates PCIP to the extent that invaders 

did not invade via foreign ballast water 

discharged into the waterbody. 

Erroneously results in too low 

discharge standard. 

Excl

ana

analy

Polyvectic invaders actually 

invaded via ballast water. 

Inflates PCIP to the extent that 

polyvectic invaders were introduced via 

some vector other than foreign ballast. 

Erroneously results in too low a 

discharge standard. 

Ana

wou

inva

a

Exclusion of small ports from 

across-port calculations. 

Generates more accurate PCIPs if 

invasions in small ports from secondary 

vectors. Artificially decreases PCIP if 

actual primary invasions into the small 

ports. 

Depends whether invasions in 

small ports are from primary or 

secondary vectors. 

Co

coasta

and 

No change in the invasion 

potential of new invaders over 

time. 

Decrease in viability of new invaders 

results in PCIPs based on historical rates 

over predicting new invasions. 

Erroneously results in too low a 

discharge standard. . 

No ad

data i

in 

No change in invasibility of 

waterbody over time. 

Either increases or decreases PCIP 

depending upon type & magnitude of 

environmental changes in waterbody. 

Protective or under protective 

depending upon the type & 

magnitude of changes. 

Use u

for 

safety 

chan

69
IX. EXPERIMENTAL APPROACHES 

Henry Lee II 

Overview: 

Laboratory and field experiments can be used to quantify the likelihood of invasion under 

controlled environmental conditions and dosing scenarios. Such experiments may represent the 

cutting edge in invasion science, at least in the Popperian sense, and the frequency of 

experiments has increased over the last decade (see review of extinction studies 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 with 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 parameterize and evaluate the diffusion approximation PVA model. 

Their results indicated that the proposed IMO standards for >50 micron organisms would reduce 

the probability of establishment of certain parthenogenic species by three fold. Examples of 

marine/estuarine field experiments include the studies on the recruitment of native and 

nonindigenous bryozoans (Clark and Johnston, 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 Pacific Coast after invading the East Coast (Carlton and 

Cohen, 2003). Quantifying the probability of such rare events is generally impractical using 

experiments. The main problem is that the number 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 carcinogenic potency of a compound using laboratory 

exposures. 

Some of the experiments have used high propagule doses, which biases 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 experiments to the aquatic “white rats” (e.g., use of 

Daphnia magna in Drake and Griffen, 2009). Such species are often “opportunistic” and thus 

are unlikely to be representative of the full breadth 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. 

70
 
The main advantage of experiments, the tightly controlled environmental 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 “dumbing 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 discharge standards using the experimental approach 

because of the: 1) impracticality of adequate replication to quantify rare events; 2) limitation in 

the number and types of species than can be experimentally manipulated; and 3) artificiality and 

simplification of laboratory experiments and, to a lesser extent, field experiments. 

The real power of the laboratory and field experiments is to advance the theory of propagule 

supply, test the assumptions of the various invasion models, and parameterize 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 CONSIDERATIONS IN ESTIMATING THE 

CONCENTRATION OF ORGANISMS IN BALLAST WATER 

DISCHARGES 

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

Overview: 

In the previous sections, we evaluated the potential utility and limitations of several approaches 

for generating ballast water discharge standards; here we address the statistical issues associated 

with monitoring organisms at very low concentrations. This is not an approach for setting 

standards; however these issues must be considered when assessing the practicality of verifying a 

discharge standard either in test facilities or as part of compliance 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. Furthermore, 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 sampling 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 Fed. Reg. 44632, August 28, 2009). 

Some states, such as New York and California, 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-approval 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 Lemieux et al. (2008) and Wright (2007). We also use 

a “best-case-scenario” approach: we limit our focus to organisms > 50 μm in size, which are the 

easiest to quantify; we assume no human or equipment 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 standard 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 adequate 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 protocol. If a small volume is used to evaluate 

whether the discharge meets a standard, the sample 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 

72
 
 

concentration, based on a 95% confidence interval, is about 3,000 organisms m-3. More 

information about these calculations is presented below. The general point is that more 

organisms may be released in ballast discharge using a stringent standard paired with a poor 

sampling protocol than a more lenient standard paired with a stringent sampling protocol. For 

these reasons, some researchers claim that “part of establishing the criteria is defining the 

required sampling plan” (Jarvis, 2000). 

The current lack of consistent sampling protocols makes it difficult to compare among existing 

and proposed standards. Even if a single discharge standard is adopted, without consistent 

sampling protocols the outcome of different ballast management programs will vary 

dramatically. Furthermore, the efficacy of different ballast treatment technologies cannot be 

compared without consistent sampling protocols (Phillips, 2005). In this chapter, we explore 

some of the statistical aspects of estimating the concentration 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 nature of sampling, multiple samples taken from the 

same population will have varying numbers of organisms due to random chance. However, if we 

know how organisms are distributed in their environment, 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, ships that do not violate the standard would be 

unfairly penalized. Conversely, a sample may have 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 that exceed the standard would 

not be detected. 

Two questions that must be answered to develop adequate sampling protocols, 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 violate the standard? The answers will depend on the 

size of the sample, the true concentration of organisms, the discharge standard, and the definition 

of “reasonable confidence”. 

The answer also depends on how organisms are distributed in the discharged ballast water. The 

best-case scenario, from a sampling perspective, is a random distribution (Figure 9A), meaning 

that 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 environment. There are several biological reasons for this phenomenon. 

Organisms may be responding to similar environmental cues, resources or physical forces, such 

as gravity (Figure 9B); they may be actively seeking conspecifics (Figures 9B and C); or, for 

73
 
 

organisms with fast population growth rates, reproduction may occur at a faster rate than 

diffusion or convection away from each other (Figure 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 abundance of zooplankton varies with depth in the 

ballast tanks, indicating that at least one type of aggregation in ballast discharges is likely. 

Random Aggregated 

A B C 

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

aggregated distributions (B and C). 

For most of the analyses in this report, we assume that organisms are randomly distributed in 

ballast tanks and the discharges. From a practical perspective, this was the only option because 

we do not possess data that can be used to estimate 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 null, hypothesis, and therefore, should be assumed 

until rejected by testing. Elliott also makes the point that for benthic organisms low density 

populations are effectively randomly distributed in regard to sampling, 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 concentrations discharged. Important aspects of developing sampling 

protocols may be determining the extent that organisms are aggregated in ballast discharges and 

whether samples of ballast water discharges are representative of the total 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 the statistical basis of 

sampling protocols for randomly distributed populations. A defining characteristic of the Poisson 

74
 
distribution is that it is defined by a single parameter, λ, which describes both the mean and 

variance of the expected counts per 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 distribution which has two parameters, the mean and 

variance, which can vary independently 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 m3

 samples do not provide more 

information than a single 10 m3

 sample when a population is randomly distributed. However, 

the first sampling scenario (i.e., ten 1 m3

 samples) provides the data for independently estimating 

variance, which can be used to determine whether a population is randomly distributed versus 

aggregated. If the population is randomly distributed, 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 m3

) 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 organisms in the ballast tank is 15 organisms m-3, there is a 

4.9% chance that a 1 m3

 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 events 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 unit. 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 population 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 organisms in the entire volume of a ship’s ballast 

discharge. 

Sample In this case, a random sample of a ship’s ballast discharge in which all >50 μm 

organisms are counted. 

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

Poisson A distribution that describes the probability of a given number of “events” 

(counts, individuals, arrivals, etc) occurring in a unit of time/space if the events 

are independent of each other. A defining characteristic of the Poisson is that the 

mean and variance of the expected sample counts are equal (λ = μ = σ

2

). If 

organisms in a ballast tank are randomly distributed, then sampling probabilities 

can be modeled using the Poisson. 

λ Lambda, the single parameter of the Poisson distribution, which is a rate 

describing the average number of events expected to occur per unit of time/space. 

In this case, it also describes the true concentration 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 distribution often used to model aggregated populations (σ

2

 > μ). 

θ Theta, dispersion parameter for the negative 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 binomial for modeling aggregated populations 

76
 
A 

0.12 10 org m-2 

0.10 

0.08 

0.06

ProbabilitProbability 0.04 

0.02 

0.00 

0 4 8 12 16 2 0 24 2 8 

B 1 m 

0.35 1 org m-2 

0.30 

0.25

ty 

0.20

abili

0.15 

Probabilityob

0.10 

0.05 

0.00 

0 1 2 3456 

C 

0.01 org m-2

0.8 

0.6 

0.4 

0.2 

0.0 

0 1 2 

Number of organisms in sample 

Figure 10: Probability distributions for random samples of 1 m2

 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 m2

, but the probabilities are the 

same for volumes. Plots on the right indicate the probability that a 1 m2

 sample will contain a 

given number of organisms. At low concentrations, the concentration of organisms is likely to 

be estimated as 0 organisms m-2, unless very large volumes are sampled. Probability 

77
 
From equations 23 or 24, probability distributions can be obtained that describe the probability 

of a sample containing a specific number of organisms given λ and the sample volume (Figure 

10). If 1 m3 of ballast is sampled from the discharge with a concentration of 10 organisms per 

m3

, 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 distribution, for a fixed sample volume, changes with λ. 

For a concentration of 10 organisms m-3 and a sample volume of 1 m3

, the probability 

distribution for the number of organisms in a random 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 distribution: 1) the model is bounded at 0, indicating 

there is zero probability of a negative 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 concentration decreases, the 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 m3

, the 

probability of a 1 m3

 sample volume containing 0 organisms is 36.8% (Figure 10B). For a 

concentration of 0.01 organisms per m3

, 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 from the theoretical probability 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 sampling protocols that meet the goals of regulatory 

agencies. For the following analyses, we use the conditions presented in Table 16. 

78
 
Table 16: Conditions for ballast water sampling scenarios (unless otherwise stated). 

1)	 We interpret the ballast performance standards 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-based sampling”). An alternative interpretation 

(Dobroski et al. 2009a) is that the standards are “instantaneous” and consequently, a ship 

is non-compliant if any samples exceed the discharge 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 using the Poisson distribution either because 

organisms are randomly distributed in ballast discharge, or alternatively, continuous 

integrated sampling is used to obtain the sample (method used by the land-based testing 

facilities of the U.S. Coast Guard). 

3)	 We assume ALL organisms in a sample are counted 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, the “sample volume” can be obscured by the 

steps required to collect and count the organisms. The sample volume must be calculated 

from the total volume of ballast that is filtered (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 quantity 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 number of organisms. If 100 m3

 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 m3

 (20 mL of aliquot /1000 mL filtrate × 100 

m3

 filtered ballast = 2 m3), not 100 m3. 

5)	 Sometimes we report organism counts and sample volumes rather than concentration. 

These can be converted to concentration by dividing 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 getting 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 concentrations and sample volumes (Table 

17). For a concentration of 0.01 organisms m-3 about 300 m3

 of ballast must be sampled to have 

a 95% probability of detecting at least one organism. 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. 

79
 
 

Table 17: Probability of detecting ≥ 1 organism for various sample volumes (100 mL to 100 m3

) 

and concentrations (0 to 100 organisms m-3). Gray boxes indicate probabilities of detection ≥

0.95. 

True concentration (organisms per m3) 

Sample volume, m3

 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 standard of “zero detectable organisms” may appear 

very protective; however, the true degree of protection depends on the sample volume. From the 

Poisson distribution, the upper possible concentration (UPC, upper 95% confidence 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 detected in sample volumes ranging from 100 mL 

to 100 m3

 (Table 18). In this report, we primarily 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, confidence intervals based on 1-tailed sampling 

probabilities may be preferred when there are zero detects. If zero organisms are detected in 1 

m3

 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 upper 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, m3 one-tailed two-tailed 

0.0001 m3 (100 mL) 29,960 36,890 

0.001 m3

 (1 L) 2,996 3,689 

0.01 m3

 (10 L) 299.6 368.9 

0.1 m3

 (100 L) 29.96 36.89 

0.5 m3

 (500 L) 5.992 7.378 

1 m3

 2.996 3.689 

10 m3

 0.300 0.369 

100 m3

 0.030 0.037 

80
 
 

0 25 

0 5 0.75

0.9 0.95

0.25

0.5 0.75 0.9 0.95

In an ideal world, we would always detect ballast water with concentrations of organisms that 

exceed the discharge standard. In reality, this is not possible with current 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 among these variables, we estimated the likelihood of detecting an 

exceedance for a discharge standard of <0.01 organism m-3 when the sample volume ranged 

from 1-50 m3

 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 percentage 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 concentration of organisms exceeds the discharge 

standard. However, as the concentration approaches the discharge standard, increasingly large 

volumes of ballast must be tested to confidently 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 m3

 of ballast water must be sampled to detect this exceedance 95% of the time 

(Figure 11A). When the true concentration of organisms is 0.1 m-3 (10x the standard) 

approximately 30 m3

 of ballast water must be sampled (Figure 11B). For perspective on the 

magnitude of these sample volumes, a Volkswagen Transporter bus has a volume of about 14 

3 m . 

50 

A B 0.95

0.9 

40 

0.75 

Sample volume, m3 

30 30

0.5 

20 

0.25 

10 

4 

1 0.25 0 5

0.75 

0.01 0.2 0.4 0.6 0.8 1.0 0.01 0.05 0.10 0.15 0.20 0.25 

True concentration, organisms m-3 

Figure 11: Probability of detecting an exceedance for sample volumes between 1 and 50 m3

 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 the exceedance. See text for information about 

specific examples identified by the blue lines. 

81
 

The examples thus far have been theoretical because we begin with a known 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 concentration 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 concentration likely 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 stochasticity 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 that exceeds the discharge standard, but the true 

concentration may actually be less 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 m3

 is 

sampled, about 17% of samples will have 10 or more 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-compliant with a discharge standard of either <0.01 or <10 

organisms m-3 (Figure 12). For a very stringent discharge 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-compliant with the standard. If a single organism is detected in a 

sample volume of ≤2 m3

 then we can be fairly confident that 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 discharge standard of <0.01 

organisms m-3, approximately 370 m3

 of ballast water must be sampled, with zero detects, before 

a ship’s discharge is statistically compliant with the standard (Figure 12A, green region). 

Another way to think about this is that the probability of detecting 0 organisms in a 370 m3 

sample must be <2.5% (based on two-tailed test). Of course, the discovery of a single organism 

in a 370 m3

 sample does not suggest the true concentration 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 within our desired confidence 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 discharge standard of <10 organisms m-3 (Figure 12B) nearly 0.4 m3 

of ballast discharge must be sampled before it’s possible for ballast discharge to be statistically 

compliant with the standard. 

82
 
 

Noncompliant

Compliant

Total observed organisms

Indeterminate

0

5

10

15

20

25

Log10 Sample volume, m3

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 10

Total observed organisms

0

5

10

15

20

25

Log10 Sample volume, m3

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 10

Total observed organisms 

0 

5 

10 

15 

20 

25 

Log10 Sample volume, m3 

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 discharge exceeds or meets a discharge standard of 

<0.01 (A) and <10 (B) organisms m-3 (note: axes have different scales). Red regions indicate 

total organism counts that would be statistically non-compliant with the standard. Green regions 

indicate total organism counts that would be statistically compliant with the standard. White 

regions indicate indeterminate results 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 populations. 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 because the number of organisms in a random 

sample becomes increasingly unpredictable. Consequently, aggregated populations must be 

sampled more intensively to estimate concentration confidently. 

Aggregation results from many different ecological and physical processes, making it difficult to 

apply a single probability distribution to the diverse array of possible patterns of aggregation. 

Although many distributions have been used to model aggregated populations, the negative 

binomial is probably the most useful of these 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 dispersion 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 estimate of this relationship is: θ = μ

2

/(σ

2

 - μ). 

83
 
0 1 2 3 4 5 6 7 8

Poisson

Aggregated

Number of organisms in sample

Probability

0.0

0.2

0.4

0.6

0 1 2 3 4 5 6 7 8 

Poisson 

Aggregated 

Number of organisms in sample 

Probability 

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 parameter of 0.1 (negative binomial) for a sample 

volume of 1 m3

 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 m3

 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 organisms (Figure 13). Conversely, the probability 

of obtaining samples with large numbers of organisms, 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 probability is 8.3%. If large 

sample volumes are not taken from aggregated populations, 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 population to estimate both parameters of the negative binomial 

distribution (see Elliott, 1971). This 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 aggregation 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 distributed or only slightly aggregated. As the volume 

of the sample unit increases, the variation in the number of organisms will increase relative to the 

mean, peaking at the point when the sample volume 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 several clusters. Given these and other issues, the 

84
 
Taylor 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

σ2 = μ

(Poisson)

σ2 < μ

(regular)

σ2 > μ

(aggregated)

variance / mean

Increasing aggregation

A 

B 

C 

A B C 

σ2 = μ

(Poisson) 

σ2 < μ

(regular) 

σ2 > μ

(aggregated) 

variance / mean 

Increasing aggregation 

Figure 14: Theoretical example of how the apparent aggregation in the population will differ 

based on the scale of aggregation relative 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 ballast testing may differ according to the situation. 

For stringent discharge standards, such as the <0.01 standard proposed 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 discharge 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 certainty is important when testing the performance of ballast treatment 

systems; however, it may be less critical during compliance 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 organism 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 classified as acceptable or marginally acceptable it 

is critical to ensure that the upper possible concentration 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 quite high depending on the sample volume. This 

can be true even if zero organisms are detected during sampling (Tables 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% confidence interval. Given this, for 

85
 
ballast 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 testing and the stringency of the current and proposed 

discharge standards, it will be difficult to sample large enough volumes of ballast discharge to 

detect ballast discharges that do not meet the standard, even if the concentration of organisms is 

1-3 orders of magnitude greater than the discharge standard. Consequently, 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 rigorous type-approval of ballast 

water treatment systems in controlled testing facilities, rather than 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. This type of testing can detect 

gross exceedences of the discharge standard, which can be used to identify treatment system 

failures and problematic ships. Until new sampling technologies are developed, however, ship 

board testing using existing sampling methods are likely to be inadequate 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 test results for individual ships 

through the IMO in order to increase the probability of detecting troublesome patterns. For a 

discharge standard of <10 organisms m-3, a single 1 m3

 sample containing 15 organisms does not 

necessarily indicate a ship’s treatment 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 subsequent discharge 

events, there is mounting evidence that the treatment 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 aspect 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 approach is currently not 

practical for ship-board testing. 

In these analyses, we assume the goal of discharge standards is to directly regulate the 

concentration of organisms in ballast discharges using “average based sampling”. However, if 

“maximum instantaneous” discharge 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 discharge standard of <10 organisms m-3 is enforced using instantaneous 

sampling, then a ship discharging ballast with a true concentration of 5 organisms m-3 will fail 

about 3.2% of the time based on a single sample of 1 m3

. However, as the number of samples 

increases the probability of a false failure increases, assuming failure is defined as one or more 

of the 1 m3

 samples having a concentration of ≥10 organisms m-3. If five 1 m3 samples are taken 

from a ballast discharge event, about 15% of the ships will have at least one sample with ≥10 

organisms m-3. 

86
 
XI. COMPARISON OF APPROACHES 

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

It is difficult to compare the approaches that have been used to determine the risk of ballastassociated invasions because they do not use a consistent 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 scientific rigor of the approaches and to their applicability to risk 

management decisions, in particular as they relate to the development of a national discharge 

standard. A table can not capture all the nuances 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 generates 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 implemented, because it is 

not based on organism concentrations, because the 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 the standard itself, and does not attempt to capture 

all the potential sources of uncertainty of the input parameters going into the approach. Because 

the actual organism concentration generated from the zero detectable organism approach is 

dependent upon the sampling protocol, we compared the upper possible organism concentration 

from the 95% confidence interval (one-tailed test) for 1 liter sample to a 10 m3

 sample (Table 

18). Note that this type of uncertainty would also apply to other approaches. 

Key data needs for generation of quantitative standards: These are the most important types of 

data required to generate a national 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 invasion rate from ballast discharges is 

directly proportional to the propagule supply? Note that approaches based on historical invasion 

rates may actually incorporate Allee effects if the invasion success of historical invaders was 

dependent upon them exceeding some critical population threshold. 

Incorporates invasion risk from multiple species in a discharge: Does the approach assess the risk 

of invasion from all the species contained within a ballast discharge or does it inherently assume 

that all the discharged individuals 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? 

87
 
Based 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 holoplanktonic 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 management decisions, or are the two intermingled? 

Intermingling the two makes it difficult to evaluate the decision making process rigorously or to 

determine what new information is required 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 peer-reviewed literature indicates 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 studies 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 development of national discharge standards. It is meant 

to promote further technical review, and we recognize 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 approach, or some foreseeable modification, could 

generate organism-based standards. We also considered whether the approach applies to the full 

suite of taxa and guilds and can address the combined risk from discharges from multiple ships. 

88
 
Table 19: Comparison of approaches to generate national organism-based discharge standards for >50 micron or

discharges. Assessment is based on current implementation; potential modifications are identified when appropr

is used to denote that the approach could be used to help evaluate whether predictions from other approaches fall range. “Recommend for national standard development” is our assessment of whether the approach should be cogenerating quantitative organism-based discharge standards at the national level. See the text for explanations of 

Approach / 

Attribute 

Expert Opinion / 

Management 

Consensuses 

Zero Detectable 

Organisms 

Natural 

Invasion 

Rate 

Reaction – 

Diffusion 

Population 

Viability 

Analysis 

Per Ca

Invas

Probab

Current 

implementation Yes No No 

generates Yes Yes (prelim. for (volume (relative Yes 

quantitative CA) based) comparison) 

standards 

Apparent range of 

uncertainty in 

standard 

10,000 fold 

(range of conc. 

proposed in IMO 

negotiations – 

0.01 to 100 org m-3) 

Uncertain since 

detectable conc. 

in samples have 

not yet been 

defined - could 

be as much as 

10,000 fold 

( upper possible 

conc. w/1L vs. 

10 m3 sample) 

100-fold 

(3 experts) 

or 

10,000-fold 

(our analysis) 

About 200 fold 

(approx range 

in “max. safe 

release 

volumes”) 

<2 fold (w/12 spp. 

in ballast) to 

10,000 fold 

(multiple voyages 

– our analysis) 

6-fold (a

coast

or 

12-fold (w

Lake

Key data needs for 

generation of 

quantitative 

standards 

Unknown since 

decision process not 

transparent 

Development of 

statistically 

rigorous 

sampling 

protocol 

Natural 

invasion rates 

in range of 

ecoregions 

Instantaneous 

population 

growth rates 

for a range of 

taxa 

Instantaneous 

population growth 

rates 

& 

instantaneous 

variance of the 

population growth 

rate for a range of 

taxa 

Non

Assumes linear dose 

response 

Unknown since 

decision process not 

transparent 

No 

(assumes a single 

individual can 

become 

established) 

Yes 

No 

(can 

incorporate 

Allee effects) 

No 

(can incorporate 

Allee effects) 

Yes 

89
Approach / 

Attribute 

Expert Opinion / 

Management 

Consensuses 

Zero Detectable 

Organisms 

Natural 

Invasion 

Rate 

Reaction – 

Diffusion 

Population 

Viability 

Analysis 

Per Ca

Invas

Probab

Incorporates invasion 

risk from multiple 

species in a discharge 

Yes? Yes Yes No? Yes Yes 

Incorporates invasion 

risk from multiple 

ship discharges 

Yes? Yes Yes No 

No 

(modify to 

incorporate 

multiple ships?) 

Yes 

Based on historical 

invasion rates No No Yes No No Yes 

Based on population 

dynamics No No No Yes Yes No 

Applicable to all taxa 

and guilds Yes? Yes 

Yes? 

(depends on 

taxa included 

in analysis) 

No 

(limited to 

short-lived 

holoplanktonic 

species) 

Yes? 

(depends upon 

which species the 

pop. data can be 

obtained) 

Yes 

Separates risk 

assessment from risk 

management 

No No? No Yes Yes Yes 

Published in peerreviewed scientific 

literature 

No No No 

Yes 

(extensive 

literature on 

reactiondiffusion 

models) 

No 

(extensive 

literature on PVA 

models) 

No 

(in proc

Recommended for 

national standard 

development 

No 

(use as “reality 

check”) 

No 

No 

(possible use 

as “reality 

check”) 

No 

(use as “reality 

check” for 

holoplanktonic 

species) 

Yes 

(if sufficient pop. 

data available for 

predictions of 

actual vs. relative 

risk) 

Yes 

90
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105
 
 

Appendix A: Overview of Human Health Microbial Standards 

Henry Lee II 

Overview: 

It is beyond the scope of this document and the expertise of the author to critically review the 

microbial human health discharge standards proposed by IMO or other entities (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/beaches/) as well as to reviews on microbes in 

ballast water (e.g., Dobbs and Rogerson, 2005; Drake 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 considered 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) Recreational Waters” in the 1986 “Ambient 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”. The 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), “Some 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. This 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 note that in a presentation by Professor Rob Bragg 

(“Understanding Cholera - A Review”; 

http://www.ufs.ac.za/apps/congress/documents/05/Presentations/107-Prof%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 value with the ballast standards 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 

106
 
standards considered surrogates to help protect against the transport of animal diseases, such as 

viral hemorrhagic septicemia virus (VHS; see http://biology.usgs.gov/faer/vhs.html)? These are 

all laudable objectives but the standards, and the indicators, are likely to differ depending upon 

the most important objective(s). 

Consideration should be given to the design of sampling protocols both during land/ship based 

verification testing and during compliance monitoring. As detailed in the 1986 “Ambient Water 

Quality Criteria for Bacteria”, there are different standards for long-term means and individual 

samples. 

107
 
 Appendix B: Calculation of Coastal 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 discharge 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 calculates 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 discharge 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("DensityVals.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 number of ships with organism concentrations of a 

certain value. The MeanData table contains 354 values with approximate organism
 

concentrations extracted from the table in Minton et al. (2005). 

Indentify the columns and read the ballast water file
 

>col.defs <- c(rep("character", 5),"numeric", 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_Invaders.csv", colClasses = col.defs) 

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Create 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 randomly 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 the PCIP values is written to a 

png file and the 2.5, .5, 97.5 quantile values are calculated 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 normal 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 inoculation from all ships for this run and store it 

 >RandRun$TotalProp[i] <- sum(Prop,na.rm=TRUE)

 # Calcuate the annual per capita probability

 >RandRun$PCIP[i] <- bInfo$TotBWInvaders/(RandRun$TotalProp[i]/3) 

>} 

# Create a file name and write out the 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 annual PCIPs, write the graphic to a png file 

# Create the name of the file to be written
 

>pngFile <- paste(bInfo$Coast, ".png",sep="") 

# Open the png file for writing
 

>png(pngFile) 

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# Create a title for the Historgram based on the name of the coast being processed

 >hTitle <- paste("Histogram of", bInfo$Coast, "Coast Annual\nPer Capita Invasion 

Probabilities") 

>hist(RandRun$PCIP, font=2, font.lab=2,main=hTitle, xlab="Per Capita Invasion Probabilites") 

# add lines for the lower, median and upper 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 for 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 information calculated for each coast 

>CoastInfo=data.frame(CoastName=rep(NA,recCount), shipCount=rep(NA, recCount), 

TotFB=rep(NA,recCount),TotAnnFB=rep(NA,recCount),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 number of records for the current coast ## 

 >CoastInfo$shipCount[j] <-length(CoastData$Coast) 

 ## Get only the records that have foreign ballast 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 water invaders per year for a coast 

 >CoastInfo$TotBWInvaders[j] <- ballastInvaders$invpyr[ballastInvaders$Coast %in% 

CoastInfo$CoastName[j]] 

 ## Calculate the PCIP values for the Coast 

 >CoastInfo[j,] <- calcPCIP(CoastInfo[j,], CoastData) 

>} 

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Write out the results for each coast to a CSV file 

>write.csv(CoastInfo, file = "RegionalPCIP.csv", append = FALSE, na = "NA", row.names = 

TRUE)
 

# Build a vector of values for 3D plot- 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<- CoastInfo$hbPCIP[3] 

# Set the safety factor 

>safetyFactor<- 1 

#Create a matrix to contain the number of invaders 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]*conc[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 Invaders Per Year \n Given Per Capita Invasion 

Probability of", format(probinv,scientific = TRUE, digits=4), " \n West Coast")
 

# Make the plot 

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>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 Develop/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 introductory 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 read input preceded by “#”, which is for user 

documentation. 

Random distributions 

To calculate the confidence interval around a concentration 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 concentrations based on the desired confidence interval 

(alpha = significance level = 1 – CI/100), the total number of observed organisms (events), and 

the total sample volume (person.time). For example, if 0 organisms are observed in a 0.1 m3 

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 1m3

 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, ppois, qpois, and rpois functions. 

These functions allow lots of flexibility for evaluating and developing sampling protocols. 

Poisson distributions are described by a single parameter, λ, which equals both the mean and the 

variance (λ = μ = σ

2

). As the mean of a Poisson distribution increases, the variance also 

increases. For ballast water analyses, λ represents the concentration of organisms in the ballast 

water. For more information about these functions, type the function name preceded by a “?” 

(i.e., ?dpois) into the R console. For the following examples, we assume a sample volume of 1 

3 m . 

113
 

 

 

 

The 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 m3

 sample volume 

containing zero organisms is 36.8%: 

> dpois(0, lambda=1) 


0.3678794 


A plot of the probability distribution 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 organisms. The probability of a 1 m3 

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 inverse of ppois). For example, if the concentration 

of organisms in ballast is 10 m-3, about 95% of 1 m3

 samples will contain 15 or fewer organisms. 

> qpois(0.950, lambda=10) 


15 


The rpois function generates random values from a Poisson distribution with a specified lambda. 

To obtain ten 1 m3 random samples from a population with concentration 1 organism m3

: 

> rpois(10, lambda=1) 


1 0 3 1 2 1 0 0 3 2 


Aggregated distributions 

One way to determine whether a population is aggregated is to compare the observed distribution 

of sample data with an expected 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). Negative 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 techniques using the fitdistr function from the MASS 

114
 
package from replicate samples taken from a population. Once the parameters have been 

estimated, the probability distribution for the negative binomial can be used to develop sampling 

protocols for aggregated populations. The negative binomial functions in R are: dnbinom, 

pnbinom, qnbinom, and rnbinom. 

115