Henry Lee II1

Deborah A. Reusser2

Melanie Frazier1

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. 

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. 

Density Matters: 

Review of Approaches to Setting 

Organism-Based Ballast Water Discharge Standards 

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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
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
3

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). 
4

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
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
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
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 when estimating concentrations. 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., 2009). 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 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. 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 

using laboratory techniques which count the numbers of living organisms. 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 tank or 

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 

organisms with fast population growth rates, reproduction may occur at a faster rate than 

73
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. 

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 good 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 

distribution is that it is defined by a single parameter, λ, which describes both the mean and 

74
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 

Equation 23: ! )( N

e NP

N λ −λ

=

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 

0486.0

3628800

176399

12345678910

)1077.5()1006.3(

!10

)15( )10(

1015 7 11

= = ×××××××××

××× = =

− − e P

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
Equation 24: !

)( )( N

cve NP

− Ncv

=

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 counts can 

change by sampling larger or smaller volumes (Bolker, 2008). 

 

Table 15: Definition of statistical terms. 

Population All the organisms in a population, in this case, all the >50 μm organisms in the 

discharged ballast water. 

Sample A random sample of the population, in this case, a volume of the discharged 

ballast water in which all >50 μm organisms are counted. 

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 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 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. 

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

Negative 

Binomial 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 

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 

76
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. 

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). 

77
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 the large number of samples that will 

have zero detects. In these cases, the estimated concentration is zero, and enormous volumes 

must be sampled to obtain a better estimate of the true concentration. 

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. 

Table 16: Conditions for ballast water sampling scenarios (unless otherwise stated). 

1) In these analyses, we assume discharge standards directly regulate the concentration of 

organisms in ballast discharge. If so, the purpose of sampling is to estimate the true 

concentration of the ballast discharge, referred to as “average based sampling”. An 

alternative is “maximum instantaneous” discharge standards which establish the 

maximum number of organisms that can occur in a random sample. An instantaneous 

discharge standard of <10 organisms sample-1 (with a sample unit is 1 m3

) does not equal 

a concentration based standard of <10 organisms m-3 in terms of the allowable 

concentration of organisms in ballast discharges. The two types of standards have the 

same outcome only when the discharge standard is 0 detectable organisms. The sampling 

protocols for instantaneous discharge standards must consider additional statistical 

factors because the results are very sensitive to the number and volume of the samples. 

2) Organisms are randomly distributed in the ballast discharges and can thus be modeled 

using the Poisson distribution. 

3) We assume ALL organisms in a sample are counted with no human or equipment error. 

Therefore any variation among the samples from a single 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 

78
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 

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. 

Table 17: Probability of detecting ≥ 1 organism for various sample volumes (100 mL to 100 m3) 

and ballast water 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 volume. We 

calculated the UPC when zero organisms were detected in sample volumes ranging from 100 mL 

to 100 m3

 (Table 18). 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 

79
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 

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, 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 about 14 m3

. 

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 

80
confidence. Two obvious results of sampling are: 1) Fail: The number of organisms in the 

sample is large enough that the true concentration likely exceeds the discharge standard; 2) Pass: 

The number of organisms in the sample is small enough that the true concentration likely meets 

the discharge standard. There is also a third, indeterminate category due to the inherent 

stochasticity of sampling. A random sample from a ballast discharge may have a concentration 

that 

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. 

 

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 absolute number of organisms that must be observed in a range of sample 

volumes to determine – using two-tailed 95% confidence intervals – whether the true 

concentration exceeds or meets 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 discharge can be classified as 

exceeding the standard (i.e., concentration > discharge standard). If a single organism is detected 

in a sample volume of ≤2 m3

 then we can be confident that the standard has been exceeded 

81
(Figure 12A, red region) given that the lower value of the 95% confidence interval estimate 

(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 a sample can be classified as meeting the standard 

with the same confidence (i.e. concentration < discharge standard). For a discharge standard of 

0.01 organisms m-3, approximately 370 m3

 of ballast water must be sampled, with zero detects, 

before we can be confident that the tank meets the standard. In this case, the upper value of the 

95% confidence interval estimate (0 to 0.00997 organisms m-3) is less than the discharge 

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) to meet the 

discharge standard. 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 

still more likely to meet the standard than not. Rather, based on this result we can not distinguish 

within our desired confidence whether the discharge standard is met given the 95% confidence 

interval of 0.000068 to 0.015 organisms m-3 (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 the ballast discharge can be classified as passing the standard. 

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 exceed the standard. Green regions indicate total organism counts that 

meet the standard. White regions indicate indeterminate results; counts in this region do not pass 

or fail inspection based on two-tailed 95% confidence intervals. 

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 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 

82
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). 

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. 

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. 

83
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 

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). 

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 

84
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 

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 water 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. 

85
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
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104
 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 

m3

. 

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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 

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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. 

114