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Mermaid:A Shellfish Sanitation Model Providing Additional Metrics for the Classification of Shellfish Growing Areas of Virginia (USA), Managed by the Direct Rule Method

F. S. Conte, A. Ahmadi## Published in

Applied Engineering in Agriculture33(6): 825-839 (doi: 10.13031/aea.12355). Copyright 2017 American Society of Agricultural and Biological Engineers.Submitted for review in March 2017 as manuscript number NRES 12355; approved for publication as part of the International Watershed Technology III Collection by the Natural Resources & Environmental SystemsCommunityof ASABE in September 2017.

The authors are

Fred S. Conte, Aquaculture Extension Specialist, andAbbas Ahmadi, Computer Scientist, Department of Animal Science, University of California, Davis, California.Corresponding author: Fred S. Conte, Department of Animal Science, University of California, One Shields Avenue, Davis, CA 95616; phone: 530-752-7689; e-mail: fsconte@ucdavis.edu.

Abstract.The Virginia Department of Shellfish Sanitation (VDSS) manages shellfish growing areas using the Direct Rule method, by directly comparing the Geometric Mean and Estimated 90^{th}Percentile of fecal coliform concentrations to the U.S. National Shellfish Sanitation Program (NSSP) standard. The agency closes the area to harvest if fecal coliform concentrations exceed the NSSP limit and the area is not reopened until concentrations fall below the NSSP limit. The VDSS originally used the NSSP 3-Tube test (14/49 Standard), and transitioned to the NSSP Membrane Filtration Test (MFT, 14/31 Standard) in August 2007. In this article we focus on a VDSS 13-plus year dataset of fecal coliform concentrations from 127,320 water samples collected from 2,193 sampling stations in 103 shellfish growing areas located in Virginia’s state waters. Our goal is to introduce a new shellfish sanitation model, Mermaid, which provides additional metrics to the NSSP statistical procedures for managing shellfish growing areas under the Direct Rule method, using calculated datasets, with uniform and mixed samples. We also examine if the additional metrics, which are based on the upper limits of Estimated 90^{th }Percentile values of fecal coliform concentrations, increase the health safety of harvested shellfish managed under the Direct Rule method.

Aquaculture, Computer software, Decision support system, Diagnosis, Fecal coliform, Sanitation model, Shellfish harvesting Keywords.Results of this study show that the model’s application of additional statistical metrics to both uniform and mixed samples in calculated datasets, successfully provides more finite decisions regarding the management of shellfish growing areas. These results demonstrate that the application of the national NSSP standards using the Direct Rule method fall short, and Mermaid’s new metrics are more adequate in maintaining food safety for consumption of harvested shellfish. These results reflect similar results of our previous studies using Indirect Rule methods, employed by shellfish sanitation agencies of states of the Pacific, Gulf, and South Atlantic coasts of the United States.

The association between human illness and filter-feeding shellfish (oysters, clams, mussels, scallops) that are exposed to fecal contamination from sewage and other fecal contaminated sources, have been long-established. cites the earlier summaries of illnesses recorded by Macomber from 1884 through 1953, and provides a continuation of reported shellfish-related illnesses through the early 1990s.

Fecal material from warm-blooded humans and other animals often contain viruses, bacteria, and protozoa that are pathogenic to humans, and can be concentrated by shellfish as they filter water while feeding. For example, bacterial pathogens of the genus

Vibriocan result in human gastroenteritis. Other pathogen examples include bacillary dysentery, typhoid fever, cholera, hepatitis A, non-A, non-B enteral hepatitis (hepatitis E), Norwalk, Norwalk-like virus, Snow Mountain agent; and pathogenicEscherichia coli. The most common shellfish and other seafood-related illness reported today are of the Vibrio species causing Vibriosis .Following large numbers of illnesses and death from typhoid fever attributed to the consumption of shellfish in the 1920s, the U.S Public Health Service formed a committee to establish regulations for the sanitary control of shellfish, which ultimately lead to the formation of the National Shellfish Sanitation Program (NSSP) . The NSSP relies on tracking data of reported U.S. shellfish-related illnesses. Originally, two major U.S. databases of seafood-associated illness were maintained by the Center for Disease Control (CDC) Foodborne Disease Outbreak Surveillance Program and a database on shellfish-associated food-borne cases maintained by the Food and Drug Administration (FDA) Northeast Technical Support Unit . Currently, U.S. shellfish illness data are collected and maintained by the CDC Prevention, Cholera and Other Vibrio Illness Surveillance Program, but summary data are only available for limited categories of illnesses, and only in annual reports . National and international summary reports for shellfish related illnesses exist in the literature. However, all summaries are limited by incomplete reporting of marine-borne illnesses, unknown pathogenic etiology of many food-borne cases, and how illnesses are initially reported and summarized .

U.S. shellfish-related illnesses have a two-fold economic impact: the health cost related to human illness and disease, and the economic impact to local economies when shellfish areas are closed because of health-related concerns. The annual health cost of marine-borne disease in the United States is estimated at approximately $1 billion (USD), with seafood-borne disease making up two-thirds of the cost, and one-third resulting from illness from direct exposure to contaminated marine waters . The estimated economic impact of shellfish-growing area closures on local and regional economies, due to health-related concerns, is in the millions of dollars .

The U.S. Federal Food and Drug Administration (FDA) is the national agency with responsibility for protecting the health of shellfish consumers. The FDA has a Memorandum of Understanding with the Interstate Shellfish Sanitation Conference (ISSC) recognizing the ISSC as the primary voluntary national organization of state shellfish regulatory officials, Federal agencies and representatives from industry that provide guidance and counsel for the control of shellfish harvesting. The ISSC provides procedures and a formal structure to establish regulatory guidelines for uniform national application of regulations under the NSSP. Following FDA concurrence, guidelines are published in the NSSP Guide for the Control of Molluscan Shellfish, which consists of a Model Ordinance, supporting guidance documents, recommended forms, and other related materials associated with the NSSP . The Model Ordinance establishes the minimum requirements necessary to regulate the interstate commerce of molluscan shellfish, but individual states may adopt more stringent regulatory standards as long as those standards conform to the principals of the NSSP.

For nearly a century, indicator organisms have been used to assess the microbiological status of water and foods. Originally use in water sanitation programs, their applications have been extended over the years to other products and became important components of the microbiological testing programs for both industry and regulatory agencies .

Using current technology, direct testing for the presence of pathogens in shellfish growing waters is both expensive and impractical. Sanitary monitoring protocols use indicator species to determine the potential presence of pathogens in growing waters because their presence indicates that fecal contamination may have occurred. The four indicator species most commonly used today include total coliforms, fecal coliforms,

Escherichia coli, andEnterococcusbacteria. These bacteria, while not normally pathogenic, are normally found in the intestines and feces of warm-blooded animals, including humans, wildlife, farm animals, and pets .Fecal coliform and total coliform bacteria have evolved as the indicator species of choice to characterize the sanitary quality of shellfish growing areas for over 80 years . Fecal coliform are also the primary indicator species in the United States used to assess sanitary conditions in shellfish growing areas. Although total coliform is still used in assessing shellfish waters, it is not as reliable as fecal coliform to indicate fecal contamination because some species in the total coliform group are naturally present in soils and plant materials . Fecal coliform, as the indicator species of choice, has also been challenged in the literature , and other species have been proposed for evaluation and possible adoption for managing shellfish growing areas. The list of replacement candidates include Male Specific Coliphage , Enterococci , and proposed adoption of the European standard, . However, there are also negative support for these adaptive changes relative to shellfish sanitation , and strong support remains for maintaining fecal coliform as the primary indicator species to characterize the sanitary quality of shellfish growing areas . Although the NSSP considers fecal coliform to be the principal indicator species for shellfish sanitation, the ISSC continues to evaluate other species for additional supportive roles, e.g., the Male Specific Coliphage for viral presence, especially near sewage plants . At present, the definitive documents and authority defining how states regulate U.S. shellfish growing areas are the NSSP Guide for the Control of Molluscan Shellfish, the Model Ordinance, and its supporting guidance documents .

The NSSP mandates that state shellfish authorities shut down shellfish harvesting if water quality in the growing area drops below established food safety levels . The NSSP’s fecal coliform concentration standard for shellfish growing areas, using the Membrane Filter Test (MFT), stipulates that the median or Geometric Mean of fecal coliform concentrations must not exceed 14 Most Probable Number (MPN)/100 mL. The MPN is used for the quantitative estimation of fecal coliform concentration in water samples . The standard also states that the Estimated 90 Percentile of the fecal coliform concentration may not exceed 31 MPN/100 mL. This is known as the “14/31 Standard” for MFT. For the 3-tube test, the NSSP standard is “14/49,” and for the 5-tube test it is “14/43.” The NSSP Model Ordinance requires the use of at least 30 samples to calculate these statistics, and that fecal coliform samples to be collected on a monthly or bi-monthly (every 2 months) schedule using Systematic Random Sampling .

The NSSP establishes bacteriological standards for classification of shellfish growing areas. Shellfish growing area classifications determine when and under what circumstances shellfish may be harvested for human consumption; and include Approved, Restricted, Prohibited, Conditionally Approved, and Conditionally Restricted areas . Approved areas meet NSSP standard year-round. Areas classified with the prefix “Conditionally” may be temporarily closed based on events such as rainfall, river flow, and boating activity that can result in the growing water not meeting the water quality standards. States shellfish regulatory agencies are allowed to use either “Indirect Rule” or “Direct Rule” methods to manage shellfish growing areas, providing the method used conforms to the NSSP and Model Ordinance. The areas classified as Approved, Restricted, or Prohibited are managed using the “Direct Rule” method. The areas classified with the prefix “Conditionally” are managed using the “Indirect Rule” method.

In the Indirect Rule method, state agencies do not make direct decision comparing the Geometric Mean and Estimated 90

^{th}Percentile of fecal coliform concentrations to NSSP standards of 14/31 MPN/100 mL for a MFT or 14/43 MPN/100 mL for a 5-tube test. Instead, they use a conditional-rule such as a rainfall, river flow, river height, or tidal stage to open and close growing areas. For example, if the cumulative daily rainfall data exceeds 30 mm, the shellfish growing area is closed to harvest for five days.In the Direct Rule method, the fecal coliform concentrations are used directly to establish closure rules. For example, if the Estimated 90

^{th}Percentile of fecal coliform concentrations exceeds the NSSP limit of 31 MPN/100 mL for a MFT, the area is closed to harvest until the concentration falls below the 31 MPN/100 mL limit.There are many sanitation models that address watersheds and their impacts on bays and estuaries, including the impacts of fecal coliform. Most sanitation models are Total Maximum Daily Load (TMDL) models that simulate concentrations of fecal coliform to evaluate sanitary conditions in watersheds, rivers, and bays (. Few sanitation models useconcentrations of fecal coliform to evaluate sanitation conditions in shellfish growing areas. These are decision-making tools that aid shellfish regulatory agencies in managing the opening or closing of shellfish harvest areas, or to make decision relative to growing area boundaries. These decision-making sanitation models have to conform to the mandated protocols stipulated in the U.S. NSSP, Model Ordinance. Currently, the only published shellfish sanitation models that conform to these protocols are and . Both these modes use actual concentrations of fecal coliform in their calculations. is used to address changes in closure rules in conditionally approved shellfish growing areas.

Pearlis used for evaluating and managing shellfish growing water closures. TheAquarius,Pearl, andMermaidsanitation models were developed for shellfish growers and state regulatory agencies to reduce risk of human illness due to shellfish consumption.The

Pearlmodel is designed to evaluate bay sanitation conditions and manage shellfish growing area closures. The model can be used in one of two modes. In the stand-alone mode,Pearlcan perform a multi-year analysis using observed fecal coliform data collected from within shellfish growing areas to determine if shellfish harvested from those areas may pose a human health risk for shellfish consumers. Shellfish growing areas that are identified as posing a risk through a stand-alonePearlanalysis are candidates for closure rule adjustments. Run in tandem mode withAquarius,Pearlcan be used to tighten or safely relax closure rules, without increasing risk of illness to shellfish consumers.

Pearlalso increases the sensitivity of the existing NSSP’s closure assessment method by establishing the Pearl limit. To calculate the Pearl limit, first, the upper limit of Estimated 90^{th}Percentile fecal coliform concentrations are calculated using the population means and population standard deviations. Then a line of regression of y (the Estimated 90^{th}Percentile fecal coliform concentrations) over x (the upper limit of Estimated 90^{th}Percentile fecal coliform concentrations) is established in the form of Y = a + bX, where ‘a’ denotes intercept and ‘b’ denotes slope. Both Y and X are in MPN/100 mL. To calculate the Pearl limit, the x value in the above equation is set to the NSSP standard and the Y is calculated as the Pearl limit. The Pearl limit for the Estimated 90^{th}Percentile is therefore defined as the value of the Estimated 90^{th}Percentile of fecal coliform concentration samples at which its upper limit is equal to the NSSP limit.The same procedure can be used to calculate the Pearl limit for the Geometric Mean of the fecal coliform concentrations by establishing a regression line of y (the Geometric Mean of fecal coliform concentrations) over x (the upper limit of Geometric Mean of fecal coliform concentrations), and setting the x value to the NSSP standard for the Geometric Mean.

The

Pearlmodel requires that datasets contain individual water samples of fecal coliform concentrations collected from sampling stations in shellfish growing areas. These datasets are ‘raw’ datasets. TheMermaidmodel is developed to address datasets that that do not contain individual water samples of fecal coliform concentrations, but only summary information of Geometric Mean and Estimated 90^{th}Percentile values, which are calculated using the most recent 30 samples per water sampling station. These are ‘calculated’ datasets. Both thePearlandMermaidmodels use the same logic and have the primary goal to reduce risk of illness to shellfish consumers. appliedPearlto conditionally-approved shellfish growing areas in California, Washington, Texas, Alabama, Florida, and Georgia, and found that the areas are inadvertently managed using thePearlstandard of 8/26 MPN/100 mL and not the NSSP standard of 14/43 MPN/100 mL for 5-tube test. The authors hypothesize that after agencies apply the national standards in conditionally approved harvest areas, and shellfish-related illnesses continue to occur, that the agencies continue to tighten harvest closure rules without applying additional statistics until reported illnesses are reduced.In Virginia, the Department of Health, Division of Shellfish Sanitation (VDSS) manages shellfish growing areas using the Direct Rule method. The VDSS used the NSSP 3-tube test (14/49 Standard) for many years, but in August 2007 transitioned to the NSSP MFT (14/31 Standard), which is a more sensitive test for fecal coliform concentration (VDSS, personal communication). For example, the VDSS directly compares the Geometric Mean and Estimated 90

^{th}Percentile of fecal coliform concentrations to the NSSP standard of 14/31 MPN/100 mL for the MFT and closes the area to harvest if concentrations exceed the 14/31 limit, or when other management factors such as discharges of toxic substances, industrial discharges, or seasonal boating activities, affect water quality. The area is not reopened until fecal coliform concentrations fall below 14/31 MPN/100 mL . The same stipulations are applied to 3-tube test datasets using the 14/49 cutoff standard.The VDSS identifies closed areas as Restricted, Condemned, or Seasonally Condemned. A Restricted Area is a growing area that is closed to shellfish harvesting, unless the shellfish, under special permit, are relayed to a clean area, or depurated before marketing. A Condemned Area is an area that is permanently closed to shellfish harvest. A Seasonally Condemned Area is a growing area that is seasonally closed to shellfish harvesting due to events such as summer boating activity .

Under the VDSS management method, each shellfish growing area may be divided into one or more sections, with each section containing one or more shellfish sampling stations. The geographical boundaries of a shellfish growing area remains the same, but the geographical boundaries of its internal sections may be redrawn each year based on the classification of their shellfish sampling stations as either Approved, Restricted, Condemned, or Seasonally Condemned. This means that a shellfish growing area can contain a mixture of sections, each with different classifications. For example, a shellfish growing area can be open for harvest in its Approved sections, but be closed to harvest in its Condemned sections .

VDSS collects samples minimally six times per year at designated stations throughout the shellfish growing waters in tidal rivers, Chesapeake Bay, and Seaside Eastern Shore. Sampling is scheduled a month in advance so that the samples will be collected randomly with respect to the weather, i.e., under all weather conditions except those that pose a hazard to the crew . These samples are used to generate raw datasets, consisting of real data containing individual fecal coliform concentrations of the water samples, along with their corresponding sampling dates, locality of sampling stations in growing areas, water temperature, salinity, and other environmental information.

VDSS annually uses raw datasets to generate calculated datasets that are used to reclassify the sections within shellfish growing areas. Calculated datasets consist of the Geometric Mean and Estimated 90

^{th}Percentile values of fecal coliform concentrations that are calculated using the last 30 water samples taken for each sampling station. Datasets also contain the start and ending dates for each group of 30 samples, as well as the NSSP limit for the Estimated 90^{th}Percentile. If a sampling station has more than 30 samples on the date of analysis, the VDSS excludes all extra samples from the calculated dataset. For a run with 2,000 sampling station, the calculated dataset can contain at most 60,000 samples. Although over 24,000 water samples are analyzed annually in VDSS laboratories, not all samples are included in the calculated dataset for each run. Most important, calculated datasets contain a column to store the reclassification status of each sampling station as Approved, Restricted, or Prohibited.The goal of this article is four-fold: (1) to introduce a new shellfish sanitation model

Mermaidthat uses calculated datasets when raw datasets are not available; (2) to provide additionalPearlmetrics in the Direct Rule method that allows more finite decisions regarding the opening or closing of shellfish growing areas; (3) to show that in the Direct Rule method, it is safer to use the Pearl limits rather than the NSSP limits for the 3-tube and MFT, and (4) to test theMermaidshellfish sanitation model’s ability to handle both uniform and mixed-test transitional databases of fecal coliform concentration samples, e.g., transitioning from the 3-tube test to the MFT.

Materials and MethodsThe data used in this study are from water samples collected from shellfish-growing areas in Virginia (fig. 1). The VDSS did not provide us with raw data, they only provided calculated data consisting of the Geometric Means and the Estimated 90

^{th}Percentile values of fecal coliform concentration. To overcome this handicap, we developed theMermaidmodel that uses standard formulas to back calculate the population means and population standard deviations from calculated datasets to generate the upper limits for both the Geometric Mean and the Estimated 90^{th}Percentile values of fecal coliform concentration. We received two calculated datasets from VDSS for their annual runs on 15 December 2010 and on 25 April 2016.The first dataset for the run date of 15 November 2010 contains 68,382 samples collected from 2,421 stations. After excluding the inactive stations, and stations with less than 30 samples, we ended up with 62,610 samples from 2,087 stations (62,610 = 30 × 2,087). The second dataset for the run date of 25 April 2016 contains 65,677 samples collected from 2,220 stations. After excluding the inactive stations and stations with less than 30 samples, we ended up with 64,710 samples from 2,157 stations (64,710 = 30 × 2,157). The combined dataset for both run dates contains 134,059 samples (= 68,382 + 65,677), collected by the VDSS from 2,193 sampling stations located in 103 shellfish growing areas over a period of 13 years (from 3 December 2002 to 20 April 2016). After excluding the inactive stations and stations with less than 30 samples, we ended up with 127,320 samples [127,320 = (62,610 = 30 × 2,087) + (64,710 = 30 × 2,157)], collected by the VDSS from 2,193 sampling stations located in 103 shellfish growing areas over a period of 13 years (from 3 December 2002 to 20 April 2016).

The dataset of fecal coliform samples are organized into 4,244 groups of 30 samples by the VDSS. For each group of samples, two statistics were calculated by the VDSS: Geometric Mean and Estimated 90

^{th}Percentile, as mandated by the NSSP. This dataset of calculated values, and not raw data, was provided to us by the VDSS.The

Pearlmodel requires raw data as input and cannot operate with calculated datasets. However, once raw data is loaded into the model,Pearlcan easily calculate the Geometric Mean and Estimated 90^{th}Percentile and their upper limits, and generates diagnostic scattergrams and analytical reports. To overcome the limitation of having only calculated values, we developed a new software model,Mermaid,which usesPearllogics, but works with calculated datasets and generates the Pearl limits and the same scattergrams and outputs as thePearlmodel .

Figure 1. Map showing shellfish growing areas associated with river systems, Chesapeake Bay and Seaside Eastern Shore of Virginia. The insert shows the water sampling stations for these shellfish growing areas . Over 24,000 water samples are analyzed annually in VDSS laboratories for the concentration of fecal coliforms present in the water samples using the 3-Tube Test method and reported as MPN/100 mL. In August 2007, the VDSS begin transitioning to the MFT method for analyzing fecal coliform samples. During transitioning from the 3-Tube Test to the MFT, the VDSS uses hybrid weighted NSSP limits for the Estimated 90

^{th}Percentile of the Fecal Coliform concentrations following the methods of the Maine Department of Marine Resources (DMR), , and approved by the NSSP (NSSP, 2015).The VDSS re-classifies the shellfish growing areas annually by performing the NSSP statistics on a certain date, for example, on 15 December 2010. If the Estimated 90

^{th}Percentile values of fecal coliform concentrations for some of the stations exceed the NSSP standard, the agency redefines boundaries within the growing area to exclude sections that contain the problem stations. These problem sections are classified as Restricted or Condemned. Other sections of the same growing area that contain stations that conform to the NSSP standard are classified as Approved.

StatisticsFor each group of 30 samples of fecal coliform concentrations, as mandated by NSSP, two parameters are already calculated by Virginia’s VDSS: the Geometric Mean and the Estimated 90

^{th}Percentile. TheMermaidmodel first back calculates the arithmetic means and the standard deviations of the sample results, and then using these two parameters, calculates the upper limit of Geometric Mean and the upper limit of the Estimated 90^{th}Percentile using the following equations:a) Back calculate the arithmetic mean of the sample result using logarithms (base 10) by:

(1)

b) Back calculate the arithmetic standard deviation of the sample result using logarithms (base 10) by:

(2)

c) Calculate the upper limit of Geometric Mean at a significance level by:

(3)

d) Calculate the upper limit of Estimated 90

^{th}Percentile at a significance level by:(4)

where

= sample estimate of the arithmetic mean,

s = sample estimate of standard deviation,

n = sample size,

= significance level,

t = t-distribution,

df = degree of freedom.

= Inverse t-Distribution statistics, which is equivalent to Excel function of .

= Inverse Chi-Square Distribution statistics, which is equivalent to Excel function of

The value 1.28 in equation 4 is obtained from the standard normal distribution and is equal to

z_{a=0.10}for one-sided test.e) Calculate the Pearl limit for the Geometric Mean of fecal coliform concentrations by:

y = 0.6524 x + 0.8795 (R

^{2}= 0.9953) (5)where

y = the Geometric Mean of the fecal coliform

concentrations (MPN/100 mL),

x = the upper limit of Geometric Mean of the fecal

coliform concentrations (MPN/100 mL).

f) Calculate the Pearl limit for the Estimated 90

^{th}Percentile of fecal coliform concentrations by:y = 0.6524 x + 0.8795 (R

^{2}= 0.9953) (6)where

y = the Estimated 90

^{th}Percentile of the fecal coliformconcentrations (MPN/100 mL),

x = the upper limit of Estimated 90

^{th}Percentile of thefecal coliform concentrations (MPN/100 mL).

Equations 1 and 2 are back calculated from the NSSP equations for the Geometric Mean and Estimated 90

^{th}Percentile , equation 3 is calculated according to , and equation 4 is calculated according to and .The equations to calculate the upper limits of Geometric Mean and Estimated 90

^{th}Percentile of fecal coliform samples can be simplified for alpha value of 0.10 and sample size of 30. Under these conditions, the Inverse t-Distribution statistic is calculated as 1.311434 and the Inverse Chi-Square Distribution statistic is calculated as 19.767744. Substituting these values in equation#3 yields the following equation for calculating the upper limit of Geometric Mean:(7)

Substituting these values in equation #4 yields the following equation for calculating the upper limit of Estimated 90

^{th}Percentile:(8)

where

= sample estimate of the arithmetic mean,

s = sample estimate of standard deviation.

The state agencies routinely calculate the arithmetic mean and standard deviation of fecal coliform concentration samples. Therefore, the required parameters for these simplified equations to calculate the upper limits of Geometric Mean and Estimated 90

^{th}Percentile values of fecal coliform concentration samples are already available, and these metrics can be easily calculated.

Table 1. NSSP Standards for different laboratory tests used to determine the concentrations of fecal coliform samples collected from shellfish growing areas . Method Geometric

Mean^{[a]}Estimated 90 ^{th}

Percentile^{[a]}3-Tube Test 14 49 5-Tube Test 14 43 Membrane Filtration Test (MFT) 14 31 12-Tube Test 14 28 3-Tube Test, Restricted 88 300 5-Tube Test, Restricted 88 260 Membrane Filtration Test (MFT), Restricted 88 173 12-Tube Test, Restricted 88 173

^{[a]}Both the Geometric Mean and the Estimated 90^{th}Percentile values of the fecal coliform concentration samples are expressed as MPN/ 100 mL.The

Mermaidalgorithm consists of five steps as follows:

- 1. Is the ‘Est 90
^{th}Percentile’ value of the fecal coliform concentration samples above the NSSP standard?- a. Yes: Go to Step 3
- b. No: Go to Step 2
- 2. Is the ‘Est 90
^{th}Percentile’ value of the fecal coliform concentration samples below the Pearl limit or their upper limits below the NSSP limit?- a. Yes: Go to Step 4
- b. No: Go to Step 5
- 3. Classify the shellfish growing area as ‘Closed’ in the Red Zone. Stop
- 4. Classify the shellfish growing area as ‘Open’ in the Green Zone. Stop.
- 5. Classify the shellfish growing area as ‘Closed’ in the Yellow Zone. Stop.
The above algorithm can be applied using the laboratory tests listed in table 1.

ResultsTable 2 shows the weighted NSSP limits for the Estimated 90

^{th}Percentile for the gradual change in data between the 3-Tube Test and the MFT. Before the transition period, when all samples are analyzed using the older 3-Tube Test, the VDSS uses the NSSP limit of 49 MPN/100 mL. After transition, when all samples are analyzed using the newer MFT, the VDSS uses the NSSP limit of 31 MPN/100 mL. During transition, the VDSS uses the hybrid-weighted NSSP limits, changing from 49 to 31 MPN/100 mL, following the method described in .

Table 2. Weighted NSSP limit for the Estimated 90 ^{th}Percentile values of the fecal coliform concentration samples, when transitioning from the 3-Tube Test method to the Membrane Filtration Test method.Samples

3-Tube TestSamples

Member

Filtration

TestLab

RatioWeighted NSSP Limit for

Estimated

90^{th}PercentileWeighted PearlLimit for

Estimated

90^{th}Percentile30 0 30:00 49 33 29 1 29:01 48 32 28 2 28:02 48 32 27 3 27:03 47 32 26 4 26:04 46 31 25 5 25:05 45 30 24 6 24:06 45 30 23 7 23:07 44 30 22 8 22:08 43 29 21 9 21:09 43 29 20 10 20:10 42 28 19 11 19:11 41 28 18 12 18:12 41 28 17 13 17:13 40 27 16 14 16:14 40 27 15 15 15:15 39 26 14 16 14:16 38 26 13 17 13:17 38 26 12 18 12:18 37 25 11 19 11:19 37 25 10 20 10:20 36 24 9 21 09:21 36 24 8 22 08:22 35 24 7 23 07:23 34 23 6 24 06:24 34 23 5 25 05:25 33 22 4 26 04:26 33 22 3 27 03:27 32 22 2 28 02:28 32 22 1 29 01:29 31 21 0 30 00:30 31 21 The hybrid standard is calculated by weighting the relative contributions of each laboratory method used in analyzing samples in the dataset, which is listed in table 2 as lab ratios. The lab ratio is defined as the ratio between the number of samples analyzed using the older 3-Tube Test to the number of samples analyzed using the newly employed MFT. As the number of samples analyzed by the 3-Tube Test is reduced and the number of samples analyzed by the MFT increases, the NSSP limits change over time.

Equation 6 is used to calculate the weighted Pearl limits for the corresponding weighted NSSP limits listed in table 2. Before transition, when all samples are analyzed using the 3-Tube Test, we use the Pearl limit of 33 MPN/100 mL. After transition, when all samples are analyzed using the MFT, we use the Pearl limit of 21 MPN/100 mL. During transition, we use the hybrid weighted Pearl limits, transitioning from 33 through 21 MPN/100 mL (table 2).

Figure 2 shows the relationship between the Geometric Mean values of fecal coliform concentration samples to their upper limits at the alpha level of 0.10 and the sample size of 30 generated by the

Mermaidmodel. The correlation coefficient is very high at 99.53%. To calculate the Pearl limit for the Geometric Mean of fecal coliform concentrations, the value of variable X in equation 5 is set to the NSSP limit.Figure 3 shows the relationship between the Estimated 90

^{th}Percentile values of fecal coliform concentration samples to their upper limits at the alpha level of 0.10 and the sample size of 30 generated by theMermaidmodel. The correlation coefficient is very high at 99.53%. To calculate the Pearl limit for the Estimated 90^{th}Percentile of fecal coliform concentrations, the value of variable X in equation 6 is set to the NSSP limit.Figures 4 through 6 are scattergrams showing the Estimated 90

^{th}Percentiles values of fecal coliform concentration samples. The graphs do not show individual samples, or the individual dates in which they were taken. Instead, each data point represents the calculated statistics of 30 fecal coliform samples collected from a single sampling station over a period of time and is positioned on the scattergram at the time of the last sampling date.Each figure has two scattergrams. The scattergram ‘A’ shows the Estimated 90

^{th}Percentiles values of fecal coliform concentration samples during the transition period from the 3-Tub test method to the MFT test method; and the scattergram ‘B’ shows the Estimated 90^{th}Percentiles values of fecal coliform concentration samples after transition period, when the VDSS switched entirely to the MFT method.Using the NSSP and Pearl limits, the data points in scattergrams of the Estimated 90

^{th}Percentiles of fecal coliform concentration samples are separated into three zones:

- 1. True Positive Zone (Red Zone) – In this zone, the Estimated 90
^{th}Percentile values of fecal coliform concentrations samples are above the NSSP limit. Both Virginia’s VDSS Direct Rule method and thePearlDirect Rule method classify this zone the same: Closed.- 2. False Negative Zone (Yellow Zone) - In this zone, the Estimated 90
^{th}Percentile values of fecal coliform concentrations samples appear between the NSSP limits and the Pearl limits. The Virginia’s VDSS Direct Rule method and thePearlDirect Rule method classify this zone differently: The VDSS classifies as Open, whereasPearlclassifies as Closed.- 3. True Negative Zone (Green Zone) - In this zone, the Estimated 90
^{th}Percentile values of fecal coliform concentrations samples are below the Pearl limits. Both Virginia’s VDSS method and thePearlmethod classify this zone the same: Open.Each data point on these scattergrams represent a single sampling station. The position of each data point relative to the NSSP limit and Pearl limit determines its classification as Approved (open for harvest) or Prohibited (closed for harvest). The scattergrams also display an instantaneous visual representation of their status as appearing on one of the three zones described above, which is not apparent in tabular format.

Figure 2. Relationship between the Geometric Means of fecal coliform concentrations and their upper limits at alpha level of 0.10 and the sample size of 30. The graph is generated by the Mermaidprogram using fecal coliform concentrations. To calculate the Pearl limit for the Geometric Mean of fecal coliform concentrations, the value of X is set to the desired NSSP limit and the corresponding value of Y is the Pearl limit.Figure 4 shows a scattergram of Estimated 90

^{th}Percentiles of fecal coliform concentration samples, collected from Virginia’s shellfish growing areas, in the Red zone. 1,148 of total data points (27%) taken before, during, and after the transition period do not meet the NSSP standard (Estimated 90^{th}Percentile values were greater or equal to the NSSP limit) and the shellfish growing areas are classified as closed by both the VDSS and thePearlDirect Rule methods.

Figure 3. Relationship between the Estimated 90 ^{th}Percentiles of fecal coliform concentrations and their upper limits at alpha level of 0.10 and the sample size of 30. The graph is generated by theMermaidprogram using fecal coliform concentrations. To calculate the Pearl limit for the Estimated 90^{th}Percentile of fecal coliform concentrations, the value of X is set to the desired NSSP limit and the corresponding value of Y is the Pearl limit.Figure 5 shows a scattergram of Estimated 90

^{th}Percentiles of fecal coliform concentration samples, collected from Virginia’s shellfish growing areas, in the Green Zone. 2,592 of 4,244 total data points (61%) taken before, during, and after the transition period meet the Pearl limit (Estimated 90^{th}Percentile values were less than the Pearl limit) and the shellfish growing areas are classified as open by both the VDSS and thePearlDirect Rule methods.Figure 6 shows a scattergram of Estimated 90

^{th}Percentiles of fecal coliform concentrations samples, collected from Virginia’s shellfish growing areas, in the Yellow Zone. 504 of 4,244 total data points (12%) taken before, during, and after the transition period meet the NSSP standard but exceeds the Pearl limit. The shellfish growing areas in this zone are classified as open by The VDSS Direct Rule method, but are classified as closed by thePearlDirect Rule method.

Figure 4. Red Zone: Scattergram, generated by the Mermaidprogram, showing Estimated 90^{th}Percentiles of fecal coliform concentration samples, collected from Virginia shellfish growing areas, which exceed the NSSP limits. Scattergram A shows the Estimated 90^{th}Percentiles values of fecal coliform concentration samples exceeding the weighted NSSP limits during the transition period from the 3-Tub test method to the MFT test method; and the scattergram B shows the Estimated 90^{th}Percentiles values of fecal coliform concentration samples after transition period, when the VDSS switched entirely to the MFT method.Figure 7 shows the pie chart of the Estimated 90

^{th}Percentiles of fecal coliform concentration samples for the Red, Yellow, and Green zones for all data points taken before, during and after the transition period. This figure shows that 27% of data points are in the Red zone (Closed), 61% of data points are in the Green zone (Open), and 12% of data points are in the Yellow zone (disputed data points: Open by VDSS, but Closed byMermaid). A partial list of these data points are shown in table 3. This table has eight columns: Area Name, Area Number, Station Number, Last Date Sampled, Lab Ratio, Estimated 90^{th}Percentile, NSSP Limit, and the upper limit of Estimated 90^{th}Percentile. The first seven columns are taken directly from the calculated datasets provided by the VDSS, but the last column is generated by theMermaidmodel.Table 3 shows a partial list of Virginia’s sampling stations and their corresponding shellfish growing areas, in which the Estimated 90

^{th}Percentile of fecal coliform concentration samples are below the NSSP limit, but their upper limits are above the NSSP standard. Although they meet the NSSP standard, and are deemed open by the VDSS, their data points actually appear inMermaid’sFalse Negative Zone (Yellow Zone), and would be closed using theMermaidDirect Rule method. Table 3 originally contained 343 problem sampling stations, but for brevity is shorten to less than 70 example stations.

VDSS Exceptions to Analysis:On completion of their statistical analysis using the NSSP 90^{th}percentile results, the CDSS employs other overriding factors that alter their final results. These factors may include such events as a contaminating spill, non-seasonal boat mooring, or toxic algal bloom. Based on such factors, the agency determined that 41 of total data points (1%) in the Red zone meet water quality standards and the affected areas were opened; that 373 of 4,244 total data points (9%) in the Green zone did not meet water quality standards and the affected areas were closed; and that 161 of 4,244 total data points (4%) did not meet water quality standards and the affected areas were closed.

Figure 5. Green Zone: Scattergram, generated by the Mermaidprogram, showing Estimated 90^{th}Percentiles of fecal coliform concentration samples, collected from Virginia shellfish growing areas, which meet the Pearl limits. Scattergram A shows the Estimated 90^{th}Percentiles values of fecal coliform concentration samples meeting the weighted Pearl limit during the transition period from the 3-Tub test method to the MFT test method; and the scattergram B shows the Estimated 90^{th}Percentiles values of fecal coliform concentration samples meeting the unweighted Pearl limit after transition period, when the VDSS switched entirely to the MFT method.

DiscussionApplying the

Mermaidmodel and its concepts to state sanitation agency datasets do not replace the statistical procedures of the NSSP Model Ordinance, but employ additional statistical metrics to these procedures and thereby increase the sensitivity and accuracy of the NSSP statistical procedures. In addition, by increasing the sensitivity and accuracy of the NSSP statistical procedures, this process also reduces the risk of shellfish borne illnesses in human population. This is explained by the following:The NSSP mandates calculation of a confidence limit for the mean of fecal coliform concentration to address the increased variability of datasets when shellfish water sampling data collected following intermittent pollution events are combined with data collected under normal conditions. Confidence limits for the mean are an interval estimate of the mean . Interval estimates are often desirable because the estimate of the mean varies from sample to sample. Instead of a single estimate for the mean, a confidence interval generates a lower and upper limit for the mean. The interval estimate gives an indication of how much uncertainty there is in the estimate of the true mean. The narrower the interval, the more precise the estimate.

Confidence limits are expressed in terms of a confidence coefficient. Although the choice of a confidence coefficient is arbitrary, in practice, 90%, 95%, and 99% intervals are often used. The NSSP mandates that the 90% interval be applied. The confidence coefficient is simply the proportion of samples of a given size (30 samples mandated by the NSSP) that may be expected to contain the true mean.

Figure 6. Yellow Zone: Scattergram, generated by the Mermaidprogram, showing Estimated 90^{th}Percentiles of fecal coliform concentrations samples, collected from Virginia shellfish growing areas, which meet the NSSP limits but exceeds the Pearl limits. Scattergram A shows the Estimated 90^{th}Percentiles values of fecal coliform concentration samples meeting the weighted NSSP limits, but exceed the weighted Pearl limits during the transition period from the 3-Tub test method to the MFT test method; and the scattergram B shows the Estimated 90^{th}Percentiles values of fecal coliform concentration samples meeting the unweighted NSSP limit, but exceed the unweighted Pearl limit after transition period, when the VDSS switched entirely to the MFT method.

Figure 7. Pie chart of the percentages of Estimated 90 ^{th}Percentiles of fecal coliform concentrations samples taken before, during and after the transition period appearing inMermaid’sRed, Yellow, and Green zones.The NSSP defines the upper limit of the 90% confidence interval of the mean as the ‘Estimated 90

^{th}Percentile’ of fecal coliform concentrations. This statistic, along with the Geometric Mean or median, is mandated by the NSSP as the standard for sanitary control of shellfish, when evaluating sampling stations for compliance with the NSSP growing area criteria.To increase the accuracy of the NSSP standard, the authors go one step further and calculate a confidence limit for the confidence limit of the mean. That is, we calculate a confidence limit for the NSSP ‘Estimated 90

^{th}Percentile’ of fecal coliform concentrations. Confidence limits are expressed in terms of a confidence coefficient. The confidence coefficient of the ‘Estimated 90^{th}Percentile’ is simply the proportion of samples of a given size (NSSP mandated 30 samples) that may be expected to contain the true NSSP ‘Estimated 90^{th}Percentile’. This is a new concept in shellfish sanitation models, and that is why we consider thePearlandMermaidmodels to be new models. We are not replacing the NSSP standard, but increasing the accuracy of the equations used in the NSSP Model Ordinance by the additional statistics, and hence reducing the risk of shellfish borne illnesses in human populations.

Table 3. Partial list of problem shellfish growing areas. Sampling stations and shellfish growing areas of Virginia that meet the NSSP standard, but not the Pearllimit. ^{[a]}Area Name Area No. Station Last Date Sampled LAB RATIO Est 90 ^{th}PctNSSP Limit Upper Limit Est 90 ^{th}PctBack River 054 54-5B 11/15/2010 0:30 30.8 31 48 Broad and Linkhorn Bays 071 71-14 11/16/2010 0:30 28.4 31 44 Browns Bay and Monday Creek 045 45-16 5 3/15/2016 0:30 29.7 31 46 Bush Park and Sturgeon Creeks 032 32-6 5 4/20/2016 0:30 25.5 31 34 Carter Creek 020 20-8 4/20/2016 0:30 20.7 31 32 Cherrystone Inlet 088 88-18 10/12/2010 3:27 30.6 32 44 Chesapeake Bay 014 14-8 5 4/14/2016 0:30 22.2 31 33 Chesconessex Creek 079 79-7 3/21/2016 0:30 29.4 31 44 Chuckatuck Creek 062 62-8 11/22/2010 0:30 27.9 31 40 Coan River 008 8-28 5 4/5/2016 0:30 21.9 31 35 Corrotoman River 021 21-9 3/29/2016 0:30 23.3 31 34 Craddock Creek 083 83-3X 11/4/2010 12:18 35.9 37 51 Dividing Creek 015 15-8 9/22/2010 0:30 24.8 31 38 East River 041 41-5B 12/6/2010 0:30 27.8 31 42 Farnham Creek 024 24-3 11/8/2010 0:30 27.0 31 40 Gardner, Jackson and Bonum Creeks 006 6-7 11/2/2010 0:30 28.1 31 41 Gaskins and Owens Ponds 011 11-1 12/8/2010 0:30 27.3 31 42 Great Wicomico River 013 13-3B 11/30/2010 0:30 27.7 31 40 Gwynn Island 036 36-18 12/2/2010 0:30 30.7 31 48 Horn Harbor and Dyer Creek 039 39-B 4/7/2016 0:30 24.4 31 38 Hungars and Mattawoman Creeks 086 86-27 10/7/2010 6:24 24.8 34 35 Hunting and Deep Creeks 077 77-8 8/19/2010 11:19 28.3 37 42 Indian, Dymer and Tabbs Creeks 016 16-32 4/19/2016 0:30 30.5 31 42 Lagrange and Robinson Creeks 028 28-9 4/18/2016 0:30 21.3 31 31 Lancaster, Deep Creek 023 23-9 11/8/2010 0:30 23.4 31 35 Little Bay and Antipoison Creek 017 17-7 11/15/2010 0:30 30.0 31 45 Little Wicomico River 010 10-9Z 12/6/2010 0:30 24.9 31 38 Locklies and Mill Creeks 031 31-11 11/17/2010 0:30 26.3 31 38 Lower Machodoc Creek 005 5-16 11/2/2010 0:30 24.1 31 36 Lynnhaven Bay 070 70-7 11/16/2010 0:30 30.2 31 44 Messongo and Guilford Creek 076 76-23 4/14/2016 0:30 29.3 31 43 Monroe Bay – Monroe Creek 002 2-3 5 11/4/2010 0:30 22.9 31 33 Nandua and Curratuck Creek 082 82-9 4/18/2016 0:30 25.8 31 37 Nansemond River 063 63-8 12/2/2010 0:30 23.4 31 34 Nassawadox Creek 085 85-5I 3/22/2016 0:30 29.7 31 40 Nomini and Currioman Bay 004 4-23 5 11/3/2010 0:30 24.0 31 34 North River 042 42-6 8 11/22/2010 1:29 23.0 31 35 Occohannock Creek 084 84-11A 11/4/2010 8:22 34.0 35 51 Old Plantation and Elliotts Creeks 090 90-8 10/12/2010 5:25 32.5 33 47 Onancock and Matchotank Creeks 080 80-8 9/20/2010 10:20 31.7 36 48 Pagan River 061 61-4 3/22/2016 0:30 29.4 31 42 Piankatank River, Lower 034 34-6 11/29/2010 0:30 21.6 31 31 Piankatank River, Upper 035 35-33 11/29/2010 0:30 23.8 31 33 Pocomoke Sound 075 75-N9 8/23/2010 12:18 30.0 37 43 Poquoson River and Back Creek 053 53-8 4/13/2016 0:30 27.7 31 40 Potomac River: Coan River 009 9-4 5 4/18/2016 0:30 27.0 31 40 Pungoteague Creek 081 81-6 5A 4/18/2016 0:30 27.1 31 38 Rappahannock River: 027 27-4 7A 4/18/2016 0:30 20.2 31 31 Rappahannock River: Wares Wharf 026A 26A-2 11/18/2010 0:30 29.5 31 45 Rosier Creek 001A 1A-6 4/4/2016 0:30 22.3 31 33 Sarah Creek and Perrin River 046 46-8B 12/7/2010 0:30 26.4 31 38 Seaside: Bogues and Shells Bays 099 99-7A 4/6/2016 0:30 25.2 31 36 Seaside: Finney and Folly Creeks 097 97-2V 9/13/2010 5:25 25.1 33 37 Severn River 044 44-18 3/1/2016 0:30 21.5 31 32 Stutts, Queens and Whites Creeks 037 37-6 12/2/2010 0:30 27.0 31 39 The Gulf 087 87-9 12/16/2015 0:30 27.7 31 37 Totuskey and Richardson Creeks 025A 25A-2 4/11/2016 0:30 25.0 31 37 Ware River 043 43-17 11/22/2010 0:30 29.3 31 46 Warwick River and Deep Creek 058 58--L76 11/29/2010 0:30 21.9 31 32 Whiting and Meachim Creeks 030 30-8A 11/17/2010 0:30 28.8 31 42 Winter Harbor and Garden Creek 038 38-8 4/7/2016 0:30 21.7 31 33 Yeocomico River 007 7-50 5 11/1/2010 0:30 22.3 31 33 York River: Camp Peary to Yorktown 051 51-27 12/8/2010 0:30 21.7 31 31

^{[a]}The Estimated 90^{th}Percentile of fecal coliform concentration samples are below the NSSP limit, but their upper limits are above the NSSP standardBoth the

MermaidandPearlmodels can calculate the Pearl limits and generatePearlscattergrams using laboratory tests listed in table 1.Mermaidis designed to use calculated datasets of fecal coliform concentrations, whereasPearlis designed to use raw datasets. Because thePearlalgorithm is incorporated into theMermaidmodel, this allowsMermaidto determine the upper limits of both the Geometric Mean and the Estimated 90^{th}Percentile of fecal coliform concentrations, and thereby calculate the Pearl limits.The Pearl limit is the value of the Estimated 90

^{th}Percentile of fecal coliform concentration samples at which its upper limit is equal to the NSSP limit as shown in figures 2 and 3, and calculated by equations 5 and 6. In these figures and equations, to determine the Pearl limit, the value of X is set to the NSSP limit and the corresponding value of Y is the Pearl limit. For example, to find the Pearl limit for the Geometric Mean of fecal coliform concentrations using the MFT, you have to find a value whose upper limit is equal to the NSSP limit of 14 MPN/100 mL, which in this example is 10 MPN/100 mL (eq. 5 and fig. 2). To find the Pearl limit for the Estimated 90^{th}Percentile of fecal coliform concentrations using the MFT, you have to find a value whose upper limit is equal to the NSSP limit of 31 MPN/100 mL, which in this example is 21 MPN/100 mL (eq. 6 and fig. 3). The high degree of accuracy in calculating Pearl limit is shown by the coefficient of determination (R^{2}= 0.9953) and corresponding correlation coefficient (r = 0.9976).The Pearl limits for various values of NSSP limits are shown in table 2. In this table, the method described in is used to generate the weighted NSSP limits for the Estimated 90

^{th}Percentile values of the fecal coliform concentration samples; and equation 6 is used to generate the weighted Pearl limits for corresponding weighted NSSP limits. Before transition, when all fecal coliform samples are analyzed using the 3-Tube Test, the Pearl limit for the Estimated 90^{th}Percentile values is calculated as 33 MPN/100 mL. After transition, when all samples are analyzed using the MFT, the Pearl limit is calculated as 21 MPN/100 mL. During transition, the weighted Pearl limit for the Estimated 90^{th}Percentile are also changed gradually from 33 to 21 MPN/100 mL, based on the changes in the corresponding weighted NSSP standards for the Estimated 90^{th}Percentile values (49 to 31 MPN/100 mL).

Mermaid’sPearl limit provides additional statistical metrics for opening or closing shellfish growing areas. Using both the Pearl limit and the NSSP limit, the data points of fecal coliform concentration samples can be classified in three zones: Data points from shellfish growing areas appearing in the Red Zone (True Positive Zone) exceed both the NSSP limit and Pearl limit, and these areas are closed for shellfish harvest by both the NSSP and Pearl limits. Data points from shellfish growing areas appearing in the Green Zone (True Negative Zone) are below both the NSSP limit and Pearl Limit; and these areas or opened for harvest of shellfish by both the NSSP and the Pearl limit. The disputed data points from shellfish growing areas appearing in the Yellow Zone (False Negative Zone) appear below the NSSP limit, but are above the Pearl limit. These shellfish areas are open for harvest using the VDSS direct rule method, but are closed using thePearlDirect Rule method. Using the Pearl limit, shellfish from areas with fecal coliform concentrations appearing in the Yellow Zone are not considered safe for human consumption.Figures 4 through 6 are scattergrams showing the Estimated 90

^{th}Percentile values of fecal coliform concentration samples collected from Virginia’s shellfish growing areas. The NSSP limits are depicted as a solid line and the corresponding Pearl limits are represented by a dotted line. During the transition period, these lines are not straight, but vary in orientation based on the lab ratio of data points. If all 30 samples in a single data point are analyzed using the 3-Tube Test, the NSSP limit for that data point is depicted as 49 MPN/100 mL; and the corresponding Pearl limits is depicted as 33 MPN/100 mL. However, if all 30 samples in a single data point are analyzed using the MFT, the NSSP limit is depicted as 31 MPN/100 mL and the corresponding Pearl limit is depicted as 21 MPN/100 mL. For the mixed samples (results from 3-Tube Test and MFT), the NSSP limit is depicted as a value between 31 and 49 MPN/100 mL and the corresponding Pearl limit is depicted as a value between 21 and 31 MPN/100 mL.Figure 4 shows Estimated 90

^{th}Percentile values that exceed both the NSSP limits and the Pearl limits; all appearing in the True Positive Zone (Red Zone). Both the VDSS Direct Rule method and thePearlDirect Rule method are in agreement; and the growing areas are designated as Closed.Figure 5 shows Estimated 90

^{th}Percentile values that are below both the NSSP limits and the Pearl limits; all appearing in the True Negative Zone (Green Zone). Both the VDSS Direct Rule method and thePearlDirect Rule method are in agreement; and the growing areas are designated as Open.Figure 6 that shows Estimated 90

^{th}Percentile values that appear below the NSSP limits, but above the Pearl limits, provides contrasting results. These data points appear in the False Negative Zone (Yellow Zone), and are designated as Open under the VDSS Direct Rule method, but are designated as Closed under thePearlDirect Rule method.The principal difference between the VDSS and

PearlDirect Rule methods is in the interpretation of data points appearing in the False Negative Zone (Yellow Zone). Although the Estimated 90^{th}Percentile values of fecal coliform concentration samples in this zone are below the NSSP limit, their upper limits exceed the NSSP limit and would appear in the True Positive Zone (Red Zone).The pie chart in figure 7 illustrates the percentages of Estimated 90

^{th}Percentiles of fecal coliform concentrations samples taken during the transition period from the 3-Tub test method to the MFT test, and after total transition to the MFT. It shows the percentage distribution between data points appearing in the True Positive (27%), True Negative (61%), and False Negative (12%) Zones. The VDSS andPearlDirect Rule methods agreed in 88% of data points and disagreed with about 12%, and those confined to data points appearing in the False Negative Zone (Yellow Zone). Consuming shellfish products harvested from shellfish growing areas whose Estimated 90^{th}Percentile values of fecal coliform concentration samples appears in the False Negative Zone (shown in fig. 6) pose a public health risk, and can be avoid by using the following rule:Rule:

To open a shellfish growing area for harvest, under the Direct Rule method, the Estimated 90^{th}Percentile values of the fecal coliform consecrations samples must appear below the Pearl limit. Or, the Upper Limit of Estimated 90^{th}Percentile values of the fecal coliform consecrations samples must appear below the NSSP limit.In the first portion of our analysis, we demonstrate the model’s ability to successfully handle mixed datasets using fecal coliform samples collected during the transition period, which were analyzed by VDSS using two different methods: the 3-Tube Test and the MFT. In the second portion of our analysis, we demonstrate the

Mermaidmodel using fecal coliform samples collected after the VDSS transition period, when all fecal coliform samples were analyzed by the VDSS using the MFT method. In applying both single test and transitional (NSSP weighted) test datasets of fecal coliform concentrations, we demonstrateMermaid’sability to determine and illustrate disagreements between the VDSS method that use NSSP limits, and the more sensitive Pearl limits, in redefining the sectional boundaries within growing areas based on the reclassification of the sampling stations (fig. 7, table 3).The results of

Mermaid’sapplication to the VDSS datasets using thePearlequations for the calculation of upper limits for both Geometric Mean and Estimated 90^{th}Percentile, and results using weighted Pearl limits for the mixed datasets, are consistent with results obtained in our previous shellfish sanitation studies applying these same equations to other state datasets (.

Conclusion

- The
Mermaidshellfish sanitation model successfully evaluates sanitary conditions of shellfish growing areas managed under the Direct Rule method using calculated datasets as opposed to raw datasets of fecal coliform concentrations.- The model successfully handles both uniform and mixed-test, transitional databases of fecal coliform concentration samples.
- The
Mermaidmodel provides state agencies that use the Direct Rule method with additional, more sensitive statistical metrics to manage shellfish growing areas. This is accomplished by calculating the upper limit of the Estimated 90^{th}Percentile values of fecal coliform concentrations, which are used in turn to calculate the more sensitive Pearl limit.- The Pearllimit can be used to determine the appropriate classification and geographical boundaries of a mixture of sections, each with different classifications, within a single growing area.
- We believe that the additional
Pearlstatistical metrics allow for more finite decisions regarding the opening or closing of shellfish growing areas managed under the Direct Rule method and increases the health safety of harvested shellfish.- Most important,
Mermaidmeets the necessary criteria for a shellfish sanitation model in that it conforms to the mandated protocols stipulated in the NSSP, Model Ordinance.

AcknowledgementsOur thanks are extended to Keith Skiles, Director of Shellfish Sanitation; Adam Wood, Marine Scientist; Evan Yeargan, Marine Scientist; Eric Aschenbach, Growing Area Manager; and Todd Egerton, Marine Scientist Supervisor of the Virginia Department of Health, Division of Shellfish Sanitation for providing the dataset used in this study. This study was partially supported by a grant from the USDA grant #2008-38500-19230 from the USDA-NIFA through the Western Regional Aquaculture Center.

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