Applying multi-scale occupancy models to infer host and site ...

JGLR-00845; No. of pages: 10; 4C: Journal of Great Lakes Research xxx (2015) xxx–xxx

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Applying multi-scale occupancy models to infer host and site occupancy of an emerging viral fish pathogen in the Great Lakes Emily R. Cornwell a,⁎,1, Gregory B. Anderson b,1,2, Destiny Coleman a, Rodman G. Getchell a, Geoffrey H. Groocock a, Janet V. Warg c, Angela M. Cruz c, James W. Casey a, Mark B. Bain b, Paul R. Bowser a a b c

Aquatic Animal Health Program, Department of Microbiology and Immunology, College of Veterinary Medicine, Cornell University, Ithaca, NY 14853, USA Department of Natural Resources, Bruckner Hall, Cornell University, Ithaca, NY 14853, USA National Veterinary Services Laboratories, VS, APHIS, USDA, Ames, IA 50010, USA

a r t i c l e

i n f o

Article history: Received 29 May 2014 Accepted 22 December 2014 Available online xxxx Communicated by Ed Rutherford Index words: Multi-scale occupancy model Reversible Jump Markov chain Monte Carlo qRT-PCR Viral hemorrhagic septicemia virus Viral surveillance Virus isolation

a b s t r a c t Emerging pathogens in wildlife are being described at an increasing rate, but the methods used to describe their dynamics in wildlife populations have been slow to develop. Understanding pathogen prevalence and risk factors for infection are critical first components of developing wildlife disease management. However, the estimation of these attributes can be biased by imperfect detection of the pathogen. In this study, we adopt a multi-scale site occupancy model to estimate the probability of pathogen detection when the diagnostic test is imperfect, host detection is imperfect, and detection can be measured at multiple scales. In addition, this model allowed the comparison of different diagnostic tests for pathogen presence. We then applied this model to the detection of viral hemorrhagic septicemia virus (VHSV) in wild fish populations in the Great Lakes. We show that VHSV is still widely distributed in the Great Lakes, and that a multi-scale model can identify additional risk factors to those identified by previous logistic regression approaches. We also estimate detection probabilities using molecular and traditional virological methods. Although our approach has several limitations, it has important implications in the management and modeling of VHSV and other emerging pathogens in aquatic wildlife. © 2015 Published by Elsevier B.V. on behalf of International Association for Great Lakes Research.

Introduction Estimation of pathogen prevalence and risk factors for infection are critical components in management of diseases in wild populations. There is evidence that pathogens can drive species diversity (Holt and Dobson, 2006) and have an effect on community dynamics at multiple ecological scales (Tompkins et al., 2011). However, the estimation of both prevalence and risk factors is complicated by imperfect detection of the pathogen. At an organismal level, a diagnostic test can miss a truly infected individual (a false negative result), resulting in an underestimation of true prevalence. Alternatively, a diagnostic test may detect a pathogen in a host that is truly not infected (a false positive result), resulting in an overestimation of pathogen prevalence. The same phenomenon can occur at the population and/or community level as well, where non-detection at the population level may not mean that the population is truly free of the pathogen. This can be especially

⁎ Corresponding author. Tel.: +1 607 253 4028. E-mail address: [email protected] (E.R. Cornwell). 1 These authors contributed equally to this work. 2 Present address: Department of Fish and Wildlife Conservation, 106 F Cheatham Hall, College of Natural Resources and Environment, Virginia Tech, Blacksburg, VA 24061-0321, USA.

problematic if infected individuals are not sampled with the same frequency as healthy individuals. Site occupancy models are a robust suite of ecological models that separate the observation process of species detection from the state process of site occupancy (MacKenzie et al., 2002, 2006). These models have been applied to the issue of imperfect detection of pathogens (Thompson, 2007; Lachish et al., 2012) to show that prevalence can be underestimated given different detection methods. However, traditional occupancy models estimate occupancy at one scale, whereas, viral surveillance is often interested in quantifying both the risk factors of individuals and the prevalence within a population and comparing that prevalence among locations. This multi-scale inference can be performed in two ways: (1) additional multilevel structure can be incorporated using random effects or (2) an additional state variable can be incorporated in the site occupancy procedure. The latter formulation was developed by Nichols et al. (2008) and Mordecai et al. (2011) and has been used to simultaneously account for imperfect detection and availability for detection (i.e., site use) when estimating the occurrence of a species across the landscape. Applying this model to pathogen presence would address many of the current limitations to estimating pathogen prevalence and risk factors in wild populations. Viral hemorrhagic septicemia virus (VHSV) is the etiologic agent of the World Organisation for Animal Health (OIE) reportable disease of fish, viral hemorrhagic septicemia (VHS). Over the past thirty years,

http://dx.doi.org/10.1016/j.jglr.2015.01.002 0380-1330/© 2015 Published by Elsevier B.V. on behalf of International Association for Great Lakes Research.

Please cite this article as: Cornwell, E.R., et al., Applying multi-scale occupancy models to infer host and site occupancy of an emerging viral fish pathogen in the Great Lakes, J. Great Lakes Res. (2015), http://dx.doi.org/10.1016/j.jglr.2015.01.002

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E.R. Cornwell et al. / Journal of Great Lakes Research xxx (2015) xxx–xxx

the known host range of VHSV has expanded dramatically, reaching 82 species (World Organisation for Animal Health, 2009). During this time the known geographic range of this virus has also expanded to include the Atlantic coasts of Europe and North America, the Pacific coasts of Japan and North America, and, in 2003, the Laurentian Great Lakes (Elsayed et al., 2006). Surveillance efforts for VHSV have focused on active surveillance demonstrating freedom from disease, identifying risk factors, and passive surveillance (USDA-APHIS-VS Centers for Epidemiology and Animal Health National Surveillance Unit, 2009). Active surveillance efforts have resulted in detection of virus in new species (Frattini et al., 2011) and in additional locations (Cornwell et al., 2011). These efforts have allowed for preliminary modeling of infection dynamics, including predictive factors for infection (Cornwell et al., 2012). However, surveillance to date has not accounted for imperfect detection. In this study, we adapt a multi-scale site occupancy model (Nichols et al., 2008; Mordecai et al., 2011) to estimate host occupancy and collection occupancy while accounting for imperfect pathogen detection. For the purposes of this study, we define host occupancy as the presence of virus in the fish and collection occupancy as the presence of virus at a collection site. Moreover, this method allows the direct comparison of multiple detection methods of virus presence within fish hosts. We applied this modeling strategy to a large-scale virus surveillance effort for VHSV across all five Great Lakes and connecting waterways in order to (1) identify potential risk factors of individuals, (2) estimate apparent prevalence in collections made in the study area, and (3) identify correlates of viral presence both within fish and within a collection.

(Ambion, Applied Biosystems, Carlsbad, California) and immediately frozen at −80 °C for VHSV testing by qRT-PCR. The remaining tissues were split evenly into three sterile, nucleic acid free microcentrifuge tubes. If the remaining tissues mentioned above were too small to add to three tubes, a portion of gonad or muscle was also added. Two microcentrifuge tubes were archived at −80 °C for future use and one microcentrifuge tube was sent to the USDA-APHIS National Veterinary Services Laboratories (NVSL). If a fish was dissected on Monday– Wednesday, samples were sent to NVSL packed on wet ice (i.e. they were not subjected to an additional freeze–thaw cycle) for immediate testing for virus isolation in cell culture. Due to shipping constraints, samples from fish dissected on Thursday and Friday were immediately frozen at − 80 °C and sent to NVSL on dry ice the following Monday (these samples were subjected to an additional freeze-thaw cycle). Additionally, the large volume of samples sent required that some samples originally sent on wet ice be frozen at − 80 °C upon arrival at NVSL. These samples were included with the dry ice samples for purposes of analysis because they were also subjected to an additional freeze– thaw cycle. There was no significant difference in the mean tissue weight (a low tissue weight was an indicator of the presence of gonad or muscle in the sample tube) between samples subjected to one or two freeze–thaw cycles (t = 0.93, p = 0.35). Although initially all samples sent to NVSL were tested regardless of the qRT-PCR results, eventually due to the large volume of samples being received, only samples that tested positive by qRT-PCR were tested by virus isolation in cell culture. Testing for viral hemorrhagic septicemia virus

Material and methods Study design and sample collection Fish were collected between 12 May 2010 and 1 July 2010. Six sites were chosen in each of the five Laurentian Great Lakes as well as one site in each connecting waterway (Niagara River, Detroit River, Lake St. Clair, and St. Mary's River) and 18 sites in the St. Lawrence River based on known or predicted availability of yellow perch (Perca flavescens) and round goby (Neogobius melanostomus) (Bain et al., 2010), availability of data on previous VHSV prevalence (Bain et al., 2010; Cornwell et al., 2011), distance from other sites, and availability of boat access (total number of sites = 51; Fig. 1). Round goby and yellow perch have been targeted in other surveillance efforts (Bain et al., 2010; Cornwell et al., 2011, 2012) because round goby tend to have a higher prevalence of VHSV while yellow perch tend to have a low to moderate prevalence of VHSV. A unique site was defined as a site greater than 1 km away from any other site. At each site, attempts were made to collect 60 yellow perch, 60 round goby, and 60 individuals of other species. This sample size was selected because if VHSV was not detected at a site, it allowed for 95% confidence that the site prevalence in that species or group of species was 5% or less (Simon and Schill, 1984; Fosgate, 2009). Fish were collected and dissected as described in Cornwell et al. (2012). Briefly, fish were collected by electrofishing. Electrofishing was conducted until an adequate number of each species was collected or until 4 h had elapsed, whichever came first. At sites where 60 yellow perch or round gobies were unable to be collected additional species were collected to attempt to reach a total number of fish collected per site of 180. The boat and all collection equipment were disinfected with a 1% solution of household bleach and allowed to dry between each sampling site. Collected fish were euthanized and transported frozen to Cornell University where they were dissected using instruments disinfected with 10% household bleach between each fish. A new sterile scalpel blade was used for each fish. A small portion of each dissected tissue (anterior kidney, posterior kidney, spleen, heart, and liver; total weight approximately 0.05 g) was placed into a sterile, nucleic acid free 2 mL homogenizing tube (BioSpec Products, Bartlesville, Oklahoma) containing 200 μL RNAlater®

Two methods were used to test for VHSV: a qRT-PCR assay developed by Hope et al. (2010) and virus isolation in cell culture. For testing by qRT-PCR, viral RNA was isolated using MagMax magnetic bead extraction (Life Technologies, Carlsbad, California). Each sample was thawed and kept on ice until extraction. Ninety-six samples were extracted at a time, in approximately the order of collection, such that samples remained stored in RNAlater® at − 80 °C for no more than one month. One 1.3 mm chrome steel bead (BioSpec Products) and 200 μL sterile HMEM-10 cell culture media (Minimal Essential Medium with Hanks' salts prepared with 10% fetal bovine serum, penicillin [100 IU/mL], streptomycin [100 μg/mL] and HEPES buffer [1 M 0.015 mL/mL] [Gibco, Invitrogen, Carlsbad California]) were added to each tube and samples were homogenized for 1 min using a Mini-Beadbeater-16 (BioSpec Products). Immediately after homogenization, samples were returned to ice until loading onto the extraction plate. Extraction was performed using a MagMax™-96 viral isolation kit (Ambion by Life Technologies) using the protocols described in the kit (AMB1836) and extraction program AM1836_DW_50_V2. Eluted RNA was immediately placed in sterile, nucleic acid free microcentrifuge tubes following extraction and frozen at −80 °C. RNA quantity and quality were assessed just prior or just after samples were loaded onto the qRT-PCR plate using a NanoVue spectrophotometer (GE Healthcare, Piscataway, New Jersey). The qRT-PCR assay used was that reported by Hope et al. (2010) with slight modifications described in Cornwell et al. (2012). All samples were initially run in duplicate. If VHSV was detected in only one replicate, a third replicate assay was performed. For the occupancy model, each assay was considered a replicated survey of virus occupancy status. Virus isolation in cell culture was performed at the National Veterinary Services Laboratories following OIE guidelines for virus isolation using Epithelioma papulosum cyprini cells (World Organization for Animal Health, 2009). Data analysis To compare the agreement between virus isolation and qRT-PCR with one or two freeze–thaw cycles, we performed traditional,

Please cite this article as: Cornwell, E.R., et al., Applying multi-scale occupancy models to infer host and site occupancy of an emerging viral fish pathogen in the Great Lakes, J. Great Lakes Res. (2015), http://dx.doi.org/10.1016/j.jglr.2015.01.002

E.R. Cornwell et al. / Journal of Great Lakes Research xxx (2015) xxx–xxx

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Fig. 1. Map of sites sampled during this study. All sites except those in the St. Lawrence River are shown in A. Sites in the St. Lawrence River are shown in B. Sites where the four species used in the site-occupancy model were collected and tested positive for VHSV are indicated by a circle with a cross in the center. Sites where those fish were collected but no VHSV was found are indicated by a circle with a dot in the center. Sites that were sampled but none of the four species used in the site-occupancy model were collected are indicated by an empty circle.

frequentist analyses on the data. Specifically, we calculated sensitivity (the probability a sample that was positive by virus isolation would test positive by qRT-PCR), specificity (the probability a sample that was negative by virus isolation would test negative by qRT-PCR), positive predictive value (the probability that a sample that tests positive by qRT-PCR will test positive by virus isolation), and negative predictive value (the probability that a sample that tests negative by qRT-PCR will also test negative by virus isolation). These were calculated using OpenEpi (Dean et al., 2012). In order to deal with the complex multi-level structure of the data set, we used a multi-scale occupancy model (Nichols et al., 2008) formulated as a hierarchical state-space model (Royle and Kery, 2007; Mordecai et al., 2011) to estimate collection occupancy (ψ), individual occupancy (θ), and virus detection (p). In this approach, two submodels are used to decompose the latent or partially observed process of collection occupancy (i.e., the virus being present in the collection taken during the visit to a locality) and individual occupancy (i.e., the

virus being present in an individual in a collection given the collection is occupied) from the observational data (i.e., repeated detections using replicate tests within fish). The state process model was composed of two equations: a collection occupancy model and an individual occupancy model. Collection occupancy (zi) was represented as a Bernoulli random variable with probability ψi, where i indexes the N different collections (i = 1, 2, … N). Because the number of individuals sampled in each collection differed, the submodel for collection occupancy was offset using the natural log of the number of individuals sampled. The binary state of individual occupancy by the virus given collection occupancy (uij|zi) was represented as a Bernoulli random variable with probability θij, where j indexes the V different individuals sampled (j = 1, 2, … V) in a collection. In order to estimate these parameters, the observation process was modeled as a Bernoulli random variable with probability pijk conditional on individual and collection occupancy, where k indexes the S replicate tests of an individual (k = 1, 2, … S).

Please cite this article as: Cornwell, E.R., et al., Applying multi-scale occupancy models to infer host and site occupancy of an emerging viral fish pathogen in the Great Lakes, J. Great Lakes Res. (2015), http://dx.doi.org/10.1016/j.jglr.2015.01.002

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E.R. Cornwell et al. / Journal of Great Lakes Research xxx (2015) xxx–xxx

Table 1 Species collected during surveillance for viral hemorrhagic septicemia including apparent prevalences by qRT-PCR and cell culture. For susceptibility, susceptibility demonstrated in wild fish (W; World Organisation for Animal Health, 2009), or by experimental infection (E) is specified. Total length is recorded in mm; weight is recorded in grams. Confidence intervals (CIs) are 95% exact binomial CIs. NA indicates no fish of this species were tested for VHSV by viral isolation in cell culture. Species

Susceptibility to VHSV

Median total length, mm (range)

Median weight, g (range)

Number tested by qRT-PCR

Apparent prevalence (%) by qRT-PCR (95% CI)

Alewife (Alosa pseudoharengus)

Unknown Yes (W)

Bluegill (Lepomis macrochirus)

Yes (W, Ea)

Bluntnose minnow (Pimephales notatus)

Yes (W)

13.0 (2–157) 15.5 (11–121) 60.8 (6–207) 7.1 (3–10) 28.4 (18–46) 202.7 (26–548) 38.6 (14–114) 14.5 (5–60) 17.1 (14–20)

61

Black crappie (Pomoxis nigromaculatus)

120.0 (72–181) 100.0 (94–192) 134.0 (66–201) 85.0 (63–94) 145.0 (123–165) 235.0 (126–310) 153.0 (106–191) 132.0 (90–200) 119.5 (110–129) 82.0 (66–108) 69.5 (65–74) 85.0 (66–100) 101.0 (85–120) 190.5 (92–460) 225.0

5.8 (3–13) 4.4 (3–4) 4.6 (3–7) 19.6 (13–25) 75.4 (9–98) 174.4

6

378.5 (344–420) 104.0 (58–199) 113.0 (95–253) 101.0 (66–113) 70.0

549.0 (419–726) 10.3 (3–101) 29.5 (16–363)

4

20.3 (6–36) 4.6

12

165.0 (68–201) 178.0

36.6 (3–99) 54.4

29

140.0 (86–269) 111.0 (78–146) 79.0 (64–130) 143.0 (92–164) 94.0 (93–95) 58

36.7 (9–330) 35.3 (12–62) 5.7 (1.3–20) 30.7 (10–52) 7.9 (8–8) 1

74

65.0 (61–70) 112.0 (60–178) 113.0 (85–194) 132.0 (44–352) 78.0 (49–220) 77.5 (60–92) 178.0 (61–489)

3.1 (3–5) 30.8 (5–157) 18.1 (8–69) 55.3 (3–553) 7.2 (2–218) 6.6 (4–13) 88.3 (3–2091)

5

6.6 (2.1–15.1) 0 (0–45.1) 5.6 (3.3–8.8) 0 (0–7.2) 0 (0–20.6) 29.1 (22.0–37.0) 0 (0–13.3) 0 (0–25.9) 0% (0–77.6) 0 (0–39.3) 0 (0–77.6) 26.3 (10.3–49.1) 0 (0–52.7) 12.5 (2.2–35.5) 0 (0–95.0) 0 (0–52.7) 18.2 (8.8–31.6) 0 (0–5.4) 0 (0–22.1) 0 (0–95.0) 0 (0–9.8) 0 (0–95.0) 4.1 (1.0–10.6) 0 (0–39.3) 0 (0–19.3) 0 (0–20.6) 0% (0–77.6) 0 (0–95.0) 0 (0–45.1) 5.2 (3.2–8.0) 0 (0–13.3) 6.6 (5.1–8.3) 28.4 (26.0–31.0) 0 (0–15.3) 11.2 (8.2–14.8)

b

c

Brook trout (Salvelinus fontinalis)

Yes (W , E )

Brown bullhead (Ameiurus nebulosus)

Yes (W)

Brown trout (Salmo trutta)

Yes (W, Ec)

Burbot (Lota lota)

Yes (W)

Coho salmon (Oncorhynchus kisutch)

Yes (W, Ec)

Common shiner (Notropis cornutus)

Unknown

Creek chub (Semotilus atromaculatus)

Unknown

Emerald shiner (Notropis atherinoides)

Yes (W)

Eurasian ruffe (Gymnocephalus cernuus)

Unknown

Fallfish (Semotilus corporalis)

Unknown

Freshwater drum (Aplodinotus grunniens)

Yes (W)

Golden redhorse (Moxostoma erythurum)

Unknown

Golden shiner (Notemigonus crysoleucas)

Unknown

Goldfish (Carassius auratus)

Unknown

Green sunfish (Lepomis cyanellus)

Unknown

Hornyhead chub (Nocomis biguttatus)

Unknown

Lake trout (Salvelinus namaycush)

Yes (Wb, Ec)

Lake whitefish (Coregonus clupeaformis)

b

Yes (W ) c

Largemouth bass (Micropterus salmoides)

Yes (W, E )

Longear sunfish (Lepomis peltastes)

Unknown

Longnose dace (Rhinichthys cataractae)

Unknown

Longnose sucker (Catostomus catostomus)

Unknown

Mimic shiner (Notropis volucellus)

Unknown

Ninespine stickleback (Pungitius pungitius)

Unknown

Pugnose minnow (Opsopoeodus emiliae)

Unknown

Pumpkinseed (Lepomis gibbosus)

Yes (W)

Rainbow trout (Oncorhynchus mykiss)

Yes (W, Ec)

Rock bass (Ambloplites rupestris)

Yes (W)

Round goby (Neogobius melanostomus)

Yes (W)

Slimy sculpin (Cottus cognatus gracilis)

Unknown

Smallmouth bass (Micropterus dolomieu)

Yes (W, Ea)

5 269 40 13 141 21 10 2

2 19 4 16 1

44 54

1

1

6 14 13 2 1

343 21 955 1251 18 357

Number tested by virus isolation

4 5 229 40 0 139

Apparent prevalence (%) by virus isolation (95% CI) 0 (0–52.7) 0 (0–45.1) 0.4 (0.02–2.1) 0 (0–7.2) NA

0

0 (0–2.1) 0 (0–23.8) NA

0

NA

1

0 (0–95.0) NA

11

0 17 0 16 1 0 41 52 12 0 1 0 74

0 (0–16.2) NA 0 (0–17.1) 0 (0–95.0) NA 0 (0–7.0) 0 (0–5.6) 0 (0–22.1) NA 0 (0–95.0) NA

0

0 (0–4.0) 0 (0–45.1) 0 (0–95.0) 0 (0–95.0) NA

0

NA

5

0 (0–45.1) 0.3 (0.02–1.6) NA

5 1 1

306 0 493 973 0 238

0.6 (0.2–1.6) 5.3 (4.1–6.9) NA 0.4 (0.02–2.1)

Please cite this article as: Cornwell, E.R., et al., Applying multi-scale occupancy models to infer host and site occupancy of an emerging viral fish pathogen in the Great Lakes, J. Great Lakes Res. (2015), http://dx.doi.org/10.1016/j.jglr.2015.01.002

E.R. Cornwell et al. / Journal of Great Lakes Research xxx (2015) xxx–xxx

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Table 1 (continued) Species

Susceptibility to VHSV

Median total length, mm (range)

Median weight, g (range)

Number tested by qRT-PCR

Apparent prevalence (%) by qRT-PCR (95% CI)

Spoonhead sculpin (Cottus ricei)

Unknown Unknown

Spottail shiner (Notropis hudsonius)

Yes (W)

Trout-perch (Percopsis omiscomaycus)

Yes (W)

White perch (Morone americana)

Yes (W)

White sucker (Catostomus commeersonii commeersonii) Yellow perch (Perca flavescens)

Unknown

3.2 (3–4) 7.4 (6–11) 8.5 (2–11) 5.4 (3–10.7) 115.5 (11–267) 11.4 (5–139) 26.5 (2–429)

2

Spotfin shiner (Cyprinella spiloptera)

62.5 (62–63) 87.0 (76–94) 97.0 (60–107) 76.0 (61–119) 202.5 (95–243) 103.0 (72–225) 130.0 (17–287)

0 (0–77.6) 0 (0–52.7) 0 (0–7.8) 0 (0–34.8) 0 (0–8.0) 0 (0–3.3) 13.1 (11.1–15.2)

a b c

Yes (W, Ec)

4 37 7 36 89 1048

Number tested by virus isolation

Apparent prevalence (%) by virus isolation (95% CI)

0

NA

4

0 (0–52.7) 0 (0–10.9) 0 (0–95.0) 0 (0–8.0) 0 (0–8.2) 0.2 (0.04–0.8)

26 1 36 35 814

Goodwin et al. (2012). This species is considered susceptible by the OIE, but is not regulated in North America by USDA-APHIS. Kim and Faisal (2010).

Although most collections came from a unique locality (i.e., locality was only sampled once), a few localities were sampled on replicate visits (i.e., multiple collections) in order to identify temporal variability of virus presence. Furthermore, each locality sampled for the virus was nested within a basin within the Great Lakes (e.g., Lake Huron basin). These two spatial structures could possibly induce a dependent structure within our analysis. Therefore, in order to weigh the evidence of a spatial structure within the data, we evaluated three different spatial components to the model using multi-level mixed models: (1) no spatial dependence, (2) site level dependence, and (3) basin level dependence. Each spatial scenario was fit with the full model (i.e., all covariates), and the weight of evidence was calculated using the Deviance Information Criterion (DIC; Spiegelhalter et al., 2002). DIC is a Bayesian analog to the Akaike's Information Criterion and is an estimate of the expected predictive error present within the model, with lower DIC values being better than higher values. It is not the actual value of the DIC that is important but rather the differences between the value for the model of interest and that for competing models. To judge whether this model strategy was appropriate for the dataset, we calculated a Bayesian p-value (i.e., a posterior predictive check; Gelman and Hill, 2007; Kéry, 2010) using the sum of the absolute residuals. The Bayesian p-value compares the lack of fit of a model for the actual data set with the lack of fit of the model when fitted to simulated datasets that were generated under the distributional assumptions of the models with the parameter estimates obtained from the analysis of the actual data set. Simulated datasets were created at each Markov chain Monte Carlo (MCMC) iteration (n = 200,000), and the sum of the absolute residuals was used as a discrepancy measure. We used this model to test three distinct types of hypotheses: detection of VHSV, fish occupancy, and collection occupancy. With regard to detection of VHSV, we hypothesized that qRT-PCR would have the highest detection probability because it has been suggested to be up to 100 times more sensitive than viral isolation in cell culture (Hope et al., 2010). We also hypothesized that the detection probability using virus isolation in cell culture would be affected by sample handling. Freeze– thaw cycles are thought to decrease the sensitivity of detection using virus isolation (Arkush et al., 2006) and VHSV is stable at 4 °C in freshwater for up to one year (Hawley and Garver, 2008); thus our a priori expectation was that samples stored on wet ice for no more than 24 h would have the highest detection probability, followed by samples stored on wet ice during transport then frozen, and samples immediately frozen on dry ice. For fish occupancy, we hypothesized that bigger fish would have a higher probability of occupancy and examined this using three covariates: total length, weight, and their interaction. For collection occupancy, we hypothesized that collection in the St. Lawrence River

would have a higher probability of virus occupancy than any other sites based on surveillance comparing Lake Ontario and the St. Lawrence River (Cornwell et al., 2012). Additionally, based on work by Eckerlin et al. (2011), we hypothesized that there would be seasonal variation in collection occupancy. This was represented in our models by air degree day (calculated using records from the closest weather station to the collection site and beginning 1 January 2010 with a base temperature of 10 °C). To account for the possibility that this relationship could be quadratic, we included the 2nd order polynomial term in our model. Finally, given the strong influence of temperature on viral replication and fish immune system function, we hypothesized that collections in more northern lakes would have a lower probability of virus occupancy. We used collection site latitude to represent this factor. In order to weigh the evidence for these alternative hypotheses regarding collection occupancy, individual occupancy and virus detection, we performed a model selection procedure using Reversible Jump Markov chain Monte Carlo (RJMCMC; Green, 1995) using the Jump plug-in (Lunn et al., 2006, 2009) of WinBUGS version 1.4.3 (Spiegelhalter et al., 2003), which explores the parameter and model space. In this procedure, posterior model probabilities are estimated as the proportion of times that a Markov chain is in any given model (King et al., 2010). Although this approach requires the specification of a hierarchical prior distribution in order to calculate posterior model probabilities, we specified a relatively diffuse prior for each submodel of the hierarchical statespace model described above. For ψi, θij and pijk, we specified a hierarchical truncated Normal prior on the logit transformed expected value (e.g.,   ψi for collection occupancy) with a mean specified as a linear ln 1−ψ i

combination of the covariates present in the sub-model (i.e., Xβ where X is a matrix of covariates and β is the vector of logistic model coefficients) and a standard deviation specified as a Uniform distribution bounded by 0 and 100. This prior was truncated between −21 and 21 to increase convergence of MCMC runs. For each model coefficient we specified a hierarchical Normal prior with a mean of zero and a standard deviation with a Uniform prior with a minimum of 0 and a maximum of 100. This prior formulation was chosen due to sensitivity issues with a non-hierarchical Normal prior (Normal with a mean of zero and a standard deviation of 1.5 [King et al., 2010]); however, estimates from the hierarchical Normal prior were relatively invariant to changes in the prior on the standard deviation (maximum of the Uniform increased from 100 to 1000 and 10,000). For model selection using RJMCMC, we specified a Binomial prior with a probability of 0.5 and the number of trials equal to the number of covariates for each model. All models were fit in WinBUGS version 1.4.3, which utilizes a MCMC algorithm. MCMC simulations were run for 200,000 iterations on three

Please cite this article as: Cornwell, E.R., et al., Applying multi-scale occupancy models to infer host and site occupancy of an emerging viral fish pathogen in the Great Lakes, J. Great Lakes Res. (2015), http://dx.doi.org/10.1016/j.jglr.2015.01.002

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E.R. Cornwell et al. / Journal of Great Lakes Research xxx (2015) xxx–xxx

Table 2 Comparison of the agreement between virus isolation (VI) and qRT-PCR when samples for virus isolation are subjected to one or two freeze–thaw cycles. Number of freeze–thaw cycles for virus isolation One Two

qRT-PCR positive qRT-PCR negative qRT-PCR positive qRT-PCR negative

VI positive

VI negative

10 0 48 2

294 884 331 2051

chains with a burn-in of 75,000. RJMCMC simulations were run for 2,500,000 iterations on two chains with a burn-in of 2,000,000 and each chain was thinned by a rate of 5 (every 5th iteration was saved). Although thinning is inefficient and can reduce precision (Link and Eaton, 2012), thinning was necessary given the large amount of memory required to store each chain for the RJMCMC simulations. After the iterations were complete, models were exported from WinBUGS to R (R Development Core Team, 2011) using the package R2WinBUGS (Sturtz et al., 2005) and convergence was assessed using the Brooks– Gelman–Rubin diagnostic statistic (Gelman and Rubin, 1992; Brooks and Gelman, 1997). Results A total of 5090 fish representing 42 species were collected and tested for VHSV by qRT-PCR and 3,565 fish by virus isolation; 56 of the fish tested by qRT-PCR and 30 of the fish tested by virus isolation were excluded from analysis because either the site or the collection date was

not able to be confirmed. Six hundred sixty-nine fish tested positive for VHSV by qRT-PCR and 60 by virus isolation in cell culture. Apparent prevalence across species by qRT-PCR ranged from 0 to 29.1% and from 0 to 5.3% by virus isolation in cell culture (Table 1). In preliminary, frequentist analyses of these data (using a Wilson score), there was no significant difference in sensitivity between samples subjected to one (sensitivity = 100%, 95% CI: 72.3–100.0) versus two (sensitivity = 96%, 95% CI: 86.5–98.9) freeze–thaw cycles. Similarly, there was no significant difference in negative predictive value (NPV) between samples subjected to one (NPV = 100%, 95% CI: 99.6–100.0) versus two (NPV = 100%, 95% CI: 99.7–100.0) freeze–thaw cycles. The specificity and positive predictive value of qRT-PCR compared to virus isolation was greater in samples subjected to two freeze–thaw cycles (specificity = 86.1%, 95% CI: 84.7–87.4; positive predictive value = 12.7, 95% CI: 9.7, 16.4) than in those subjected to one cycle (specificity = 75%, 95% CI: 72.5–77.4; positive predictive value = 3.3%, 1.8–5.9) (Table 2). Four species that were collected in large numbers (n N 300) at multiple sites, rock bass, smallmouth bass, yellow perch, and round goby, were used in the multi-scale occupancy model. The median viral load (viral N gene copies per 50 ng RNA) detected by qRT-PCR of fish that tested positive for VHSV was 1.6 in rock bass (n = 63; range: 2.3 × 10− 2–2.9 × 105) 1.2 in smallmouth bass (n = 44; range: 3.1 × 10− 2–1.2 × 105), 2.0 for yellow perch (n = 140; range: 6.2 × 10− 2–5.3 × 106) and 14.6 in round goby (n = 341; range: 1.6 × 10−2–2.1 × 107). Using the full model, there was no indication of lack of fit, and all Bayesian p-values were between 0.42 and 0.49 (Fig. 2). Additionally, using DIC values, a model without additional multi-level structure was best supported for all species (Table 3).

Fig. 2. Posterior predictive check of the multi-scale occupancy model for (A) Ambloplities rupestris, (B) Neogobius melansotomus, (C) Micropterus. dolomieu, and (D) Perca flavescens. Discrepancy measures are based on the sum of the absolute residuals. A well fitting model has an equal number of circles on either side of the line.

Please cite this article as: Cornwell, E.R., et al., Applying multi-scale occupancy models to infer host and site occupancy of an emerging viral fish pathogen in the Great Lakes, J. Great Lakes Res. (2015), http://dx.doi.org/10.1016/j.jglr.2015.01.002

E.R. Cornwell et al. / Journal of Great Lakes Research xxx (2015) xxx–xxx

7

Table 3 Relative support for different model structure for multi-scale occupancy models. Model support is evaluated using the Deviance Information Criterion, calculated as the sum of the mean deviance and the effective number of parameters (shown in parentheses). Model structure

A. rupestris

M. dolomieu

P. flavescens

N. melanostomus

No random effects Site level random effects Basin level random effects

502.69 (219.05) 539.25 (256.03) 525.75 (232.32)

245.73 (83.57) 298.75 (135.24) 320.97 (150.36)

973.76 (418.27) 1125.77 (567.98) 1115.71 (557.63)

1386.94 (362.38) 1396.92 (371.78) 1390.81 (365.81)

Posterior estimates from the multi-scale occupancy model suggested that no viral detection method was perfect (Fig. 3). Estimates of virus detection differed substantially between species; however, no one species showed higher detection rates than other species by both virus isolation in cell culture and virus detection by qRT-PCR. Based on posterior model probabilities from the RJMCMC procedure, there was very little model uncertainty (i.e., one model with N0.99 probability) for the different alternative hypotheses regarding detection probability for three species: rock bass, yellow perch, and round goby. For these species, a full sub-model including all of the covariates of detection was best supported (posterior probability N 0.99). However, two different sub-model structures demonstrated considerable support for smallmouth bass: (1) a sub-model containing all detection covariates (posterior probability = 0.44) and a sub-model excluding a difference between wet ice and wet then frozen treatments for detection (posterior probability = 0.54). For all species, posterior estimates suggested that qRT-PCR was much more sensitive at detecting VHSV when present than virus isolation in cell culture. Mean model averaged posterior estimates ranged from 0.52 to 0.90, depending on the species, with a 95% highest posterior density (HPD) from 0.3 to 0.98 (Fig. 3). Detection of VHSV using qRT-PCR was higher for round goby ( x = 0.9; 95% HPD = 0.79–0.98) and smallmouth bass ( x = 0.8; 95% HPD = 0.62–0.98) than yellow perch (x = 0.6; 95% HPD = 0.47–0.75) or rock bass (x = 0.5; 95% HPD = 0.30–0.72). In a manner similar to that of qRT-PCR, posterior estimates of detection using virus isolation in cell culture varied between the different species and among the different sample treatments. Counter to our hypotheses, for all species mean posterior detection estimates of the wet then frozen treatments and the dry ice treatments were higher than the wet ice treatment (Fig. 3). For smallmouth bass, the difference between wet ice and dry ice was substantial; however, the 95% HPD was also fairly large (Fig. 3). Compared to the posterior model probabilities of the hypotheses regarding detection, fish occupancy showed a modest amount of model

uncertainty. Generally, for all species no one sub-model had a high posterior model probability (Table 4); however the marginal probability, a measure of variable importance, was relatively high for the regression coefficient for total length for round goby (N0.99). Based on the averaged posterior mean (2.0; 95% HPD = 0.73–3.31), we expect the probability that an individual round goby is occupied, given the collection is also occupied, to increase as the size of the individual increases. Total length was also a relatively important variable for rock bass and yellow perch (marginal probabilities of 0.47 and 0.29, respectively), but the magnitude of the posterior means was much smaller, of the opposite sign, and the 95% HPD overlapped zero (−0.35 and − 0.12; 95% HPD: −1.41–0.01 and −1.12–0.20, respectively). In addition to total length, for some species, weight also had a modest marginal probability. However, the posterior means were small with a 95% HPD that substantially overlapped zero. Using the estimated latent state node for conditional fish occupancy, we estimated fish occupancy to be lowest for rock bass (x = 0.1; 95% HPD = 0.08–0.11) and highest for round goby (x = 0.3; 95% HPD = 0.15–0.18; Fig. 4). At the collection occupancy level, there was a large amount of submodel uncertainty, with no one sub-model holding a substantial amount of weight. The parameters' marginal probabilities showed that several covariates were important in describing the patterns of VHSV presence; however, these marginal probabilities differed between the four species (Table 5). For all species, the covariate degree day had a high marginal probability; however, this probability was smaller for smallmouth bass and round goby (0.72 and 0.76, respectively). The model averaged posterior means for this parameter ranged between − 2.24 and − 4.38 with 95% HPD ranging from − 11.52–0.00. Using these estimates, we expect that collections made later in the season have a lower probability of hosting at least one individual that is infected with VHSV. The regression coefficient for latitude was also an important parameter for rock bass, yellow perch, and smallmouth bass. Posterior means suggest that collections made in more northern

Fig. 3. Posterior estimates of detection probability for different methods and sample treatments for (A) Ambloplities rupestris, (B) Neogobius melanostomus, (C) Micropterus dolomieu, and (D) Perca flavescens. Posterior means (circles) are shown with 68% (bold lines) and 95% (thin lines) highest posterior densities.

Please cite this article as: Cornwell, E.R., et al., Applying multi-scale occupancy models to infer host and site occupancy of an emerging viral fish pathogen in the Great Lakes, J. Great Lakes Res. (2015), http://dx.doi.org/10.1016/j.jglr.2015.01.002

8

E.R. Cornwell et al. / Journal of Great Lakes Research xxx (2015) xxx–xxx

Table 4 Posterior marginal probabilities for covariates of fish occupancy for Ambloplities rupestris, Micropterus dolomieu, Perca flavescens, and Neogobius melanostomus. TL represents total length. Parameter

A. rupestris

M. dolomieu

P. flavescens

N. melanostomus

^ TL B ^ Weight B

0.47

0.17

0.29

N0.99

0.32

0.19

0.44

0.25

^ TLWeight B

0.07

0.24

0.34

0.14

climates are expected to have a lower probability of occupancy. For smallmouth bass and round goby, the covariate representing sites in the St. Lawrence River was a relatively important predictor of collection occupancy (marginal probability = 0.69 and 0.95). Additionally, collection occupancy is also expected to increase in the St. Lawrence River compared to collections made in other drainages of the Great Lakes (Fig. 5). Based on estimated latent state node for collection occupancy, we estimated the true proportion of collections occupied for each species to be lowest for yellow perch (x = 0.42; 95% HPD = 0.40–0.48) and highest for round goby (x = 0.79; 95% HPD = 0.78–0.82).

Discussion This study demonstrates that VHSV is endemic within fish populations of the Laurentian Great Lakes and periodic episodes will most likely occur when large populations of naïve fish are exposed to infected fish. Of the 5090 fish collected in this study, 13% of all fish collected tested positive for VHSV genotype IVb by qRT-PCR and/or virus isolation in cell culture. Virus was detected in all water bodies tested except Lake Superior and the St. Mary's River (Fig. 1). This suggests that VHSV continues to be a useful pathogen to study viral pathogen dynamics in aquatic systems because it is widely distributed and affects a large range of teleost hosts. Additionally, we were able to apply a multiscale model for four species, use this model to estimate detection probabilities for two different methods, identify correlates of virus presence among fish and among sites, and estimate the true (not perfectly observed) state of virus occupancy of individuals. Although several species had high apparent prevalences (Table 1), many of these species were not collected in sufficient numbers to obtain a very precise estimate of prevalence. Of the four species collected in higher numbers and used for further analysis in this manuscript, round gobies had the highest apparent prevalence. This is similar to what has been observed in other VHSV surveillance studies (Bain et al., 2010; Cornwell et al., 2012). That this species consistently shows the highest proportion of infected fish suggests that it may be serving as a reservoir for VHSV within wild fish populations. Round goby overlap in habitat with yellow perch, smallmouth bass, and rock bass as well as many other species collected in this study. Smallmouth bass also had a relatively high prevalence among collections; this may be related to the high prevalence observed in round goby because Eckerlin et al. (2011) have reported a direct, positive relationship between the prevalence of VHSV in round goby and the prevalence in

smallmouth bass, and smallmouth bass diet can include round goby when their habitats overlap. As suggested by Hope et al. (2010), Frattini et al. (2011), and Cornwell et al. (2012), the results of this study showed that qRT-PCR was more sensitive than virus isolation in cell culture. As a result, when cell culture is considered to be the gold standard (as in Table 2), the specificity of qRT-PCR appears to be low. This is especially true when the level of virus present is low, which was the case in the vast majority of samples in this data set. Although this increased sensitivity is beneficial from a surveillance standpoint, the qRT-PCR assay used in this study cannot distinguish between infectious virus and defective viral particles (as long as they contain RNA) so it is possible that not all of the fish that tested positive by qRT-PCR in this study were harboring infectious virus. However, false negatives are still possible with the qRT-PCR assay, at both an individual and site level. Despite this, detection rates were relatively high for all species when multiple tests were run. For rock bass, the species with the lowest detection probability, the probability of detection with a single qRT-PCR test was 0.5 and increased to 0.7 when samples were tested twice and to 0.9 when samples were tested three times. The difference in detection probabilities is most likely due to differences in viral loads. The median viral load detected in round goby was much higher than the median viral load detected in any other species tested, and the detection probability for one qRT-PCR test in round goby was also higher than any other species tested (0.9). This problem is similar to abundance induced heterogeneity in detection observed in traditional occupancy models; however, models that account for the additional source of detection heterogeneity (i.e., Royle and Nichols, 2003; Royle, 2006) often require many more survey replicates. Freezing has been shown to lower the number of infective viral particles of VHSV (Arkush et al., 2006) and virus stability in water at 4 °C can be up to one year (Hawley and Garver, 2008). However, in this study samples subjected to two freeze–thaw cycles were more helpful in predicting virus detection than those subjected to a single freeze– thaw cycle. This suggests that rapid freezing of samples at − 80 °C is more important than avoiding an additional freeze–thaw cycle. The detection probability in samples stored at 4 °C then frozen was also higher than those stored on wet ice. This may be a testing bias because these samples were more likely to be tested by viral isolation in cell culture because they had already tested positive by qRT-PCR. The infectivity of another rhabdovirus, Infectious hematopoietic necrosis virus (IHNV) is known to decrease during storage at 4 °C (Hostnik et al., 2002). Overall, individual fish characteristics (length, weight, etc.) are not very helpful in predicting occupancy status. The one exception for this was in round goby, where total length was a good predictor of virus occupancy. This is in contrast to the analysis for round goby reported in Cornwell et al. (2012) where total length was not a significant predictor of virus occupancy in this species. Interestingly, in this study larger fish were more likely to test positive for VHSV than smaller fish. Eckerlin et al. (2011) found the opposite when assessing smallmouth bass, where smaller fish were more likely to test positive. The mechanism behind our finding might be due to the fact that larger fish are more likely to aggregate and engage in potentially stressful activities, such as spawning, even though they may be less susceptible to infection.

Fig. 4. Estimated (A) proportion of fish occupied and (B) proportion of collections occupied by VHSV. Posterior means are represented with black circles and are shown with 68% (bold lines) and 95% (thin lines) highest posterior densities.

Please cite this article as: Cornwell, E.R., et al., Applying multi-scale occupancy models to infer host and site occupancy of an emerging viral fish pathogen in the Great Lakes, J. Great Lakes Res. (2015), http://dx.doi.org/10.1016/j.jglr.2015.01.002

E.R. Cornwell et al. / Journal of Great Lakes Research xxx (2015) xxx–xxx Table 5 Posterior marginal probabilities for covariates of fish occupancy for Ambloplities rupestris, Micropterus dolomieu, Perca flavescens, and Neogobius melanostomus. SLR represents the St. Lawrence River. Parameter

A. rupestris

M. dolomieu

P. flavescens

N. melanostomus

^ DegreeDay B ^ B 2

0.91

0.72

0.97

0.76

0.34

0.40

0.25

0.15

^ Latitude B ^ SLR B

0.80

0.64

0.78

0.10

0.46

0.69

0.43

0.95

DegreeDay

These contrasting findings suggest that a site occupancy model, accounting for the multi-scale structure inherent in sampling multiple species at multiple locations, might be more sensitive at identifying important predictive factors. The relationship between total length and virus occupancy was likely observed in round goby and not in other species because we were able to sample a larger range of size classes in round goby than in other species. Degree day was moderately predictive of site occupancy in all four species. This is likely because VHSV replication is highly temperature dependent, occurring between 4 and 20 °C. Additionally, degree day may also be a good proxy for other parameters that are expected to be predictive, but difficult to measure such as fish immune status. Degree day also accounts for previous temperature conditions prior to sampling at a given site. This finding is important, because tracking degree days can be used to maximize the probability of detecting virus during surveillance. In this study, we used air degree days because it was not possible to measure local water temperatures at all locations throughout the year. We expect that degree days calculated using local water temperatures would be even more predictive. In round goby, the presence of a site in the St. Lawrence River was a good predictor of site occupancy. The prevalence in this species in the St. Lawrence River has been consistently high (Cornwell et al., 2012) suggesting that there may be unique

9

dynamics of VHSV within this species in the St. Lawrence River that warrant further investigation. The methodologies in this study had many limitations. First, although the multi-scale occupancy model allowed the unbiased estimation of true virus state of individuals within a collection, we were unable to estimate the true virus state of the locations we visited. Instead, we were only able to have an unbiased estimation of the state of the collection made. Because this study did not focus on the estimation of virus detection at the site scale, we were unable to determine if the random sample of fish collected at each site was representative of the population at the site. Two situations which could potentially bias this random sample are detection of different species at a location is not equal and detection of individuals that are infected is not equal to detection of individuals that are not infected. In order to estimate this potential bias, several replicate samples would be required over a period where the virus state of the species within the site did not change. Such a design would require a non-lethal sampling technique (Cornwell et al., 2013) that was not available during the time this study took place. Additionally, the cross sectional design of this study did not allow estimation of incidence and it is possible that seasonal changes in virus prevalence, such as the long-term changes documented by Eckerlin et al. (2011) may have an effect on the reported prevalence estimates. Emerging pathogens in wildlife are being described at an increasing rate (Smith et al., 2009). Non-native species, such as round goby, can play a role in the amplification of emerging pathogens by serving as reservoirs for endemic pathogens or by introducing new pathogens (Poulin et al., 2011). Thus it is critical to be able to predict factors that can be used to (1) identify the likelihood of detection when conducting viral surveillance and (2) target management practices for the greatest effect. In this study, we have shown that a multi-scale site-occupancy model can be adapted to virus surveillance in wild fish populations and can identify additional predictive factors compared to a logistic regression approach by accounting for the complex multi-scale nature of the

A

B

C

D

Fig. 5. Posterior mean effect of degree day for St. Lawrence River Sites (Grey) and all other sites (Black) for A) Ambloplities rupestris, (B) Neogobius melanostomus, (C) Micropterus dolomieu, and (D) Perca flavescens. Estimates are shown with the mean values of all other covariates.

Please cite this article as: Cornwell, E.R., et al., Applying multi-scale occupancy models to infer host and site occupancy of an emerging viral fish pathogen in the Great Lakes, J. Great Lakes Res. (2015), http://dx.doi.org/10.1016/j.jglr.2015.01.002

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E.R. Cornwell et al. / Journal of Great Lakes Research xxx (2015) xxx–xxx

sampling. However, our approach had many limitations, including a potentially biased estimation of viral presence at a site. Therefore, the spatial and temporal inferences made should be approached with caution, and more research and model development are needed to be able to estimate viral presence at multiple scales. The recent single survey occupancy estimation procedure developed by Lele et al. (2012) holds particular promise. Additionally, the non-lethal sampling described by Cornwell et al. (2013) would enable the ability to have several replicate visits to a site in the form of repeated measures in order to estimate site occupancy. Acknowledgments We thank Emily Nash, Deidre Hayward, and Geofrey Eckerlin for assistance in collecting fish; Sandra LaBuda, Po Ting Wong, Rebecca Fellman, Chelsea Bellmund, Lindsay Glasner, Phoebe Clark, and Jimmy Todhunter for assistance with fish dissections; Greg Wooster for technical assistance; and Dr. John Farrell and the SUNY ESF Thousand Islands Biological Station for field and sampling support. Funding was provided by the United States Department of Agriculture Animal and Plant Health Inspection Service Cooperative Agreement10-9100-1294-GR. References Arkush, K.D., Mendonca, H.L., McBride, A.M., Yun, S., McDowell, T.S., Hedrick, R.P., 2006. Effects of temperature on infectivity and of commercial freezing on survival of the North American strain of viral hemorrhagic septicemia virus (VHSV). Dis. Aquat. Org. 69, 145–151. Bain, M.B., Cornwell, E.R., Hope, K.M., Eckerlin, G.E., Casey, R.N., Groocock, G.H., Getchell, R.G., Bowser, P.R., Winton, J.R., Batts, W.N., Cangelosi, A., Casey, J.W., 2010. Distribution of an invasive aquatic pathogen (viral hemorrhagic septicemia virus) in the Great Lakes and its relationship to shipping. PLoS One 5, e10156. http://dx.doi.org/ 10.1371/journal.pone.0010156. Brooks, S., Gelman, A., 1997. General models for monitoring convergence of iterative simulations. J. Comput. Graph. Stat. 7, 434–455. Cornwell, E.R., Eckerlin, G.E., Getchell, R.G., Groocock, G.H., Thompson, T.M., Batts, W.N., Casey, R.N., Kurath, G., Winton, J.R., Bowser, P.R., Bain, M.B., Casey, J.W., 2011. Detection of viral hemorrhagic septicemia virus by quantitative reverse transcription polymerase chain reaction from two fish species at two sites in Lake Superior. J. Aquat. Anim. Health 23, 207–217. Cornwell, E.R., Eckerlin, G.E., Thompson, T.M., Batts, W.N., Getchell, R.G., Groocock, G.H., Kurath, G., Winton, J.R., Casey, R.N., Casey, J.W., Bain, M.B., Bowser, P.R., 2012. Predictive factors and viral genetic diversity for viral hemorrhagic septicemia virus type IVb infection in Lake Ontario and the St. Lawrence River. J. Great Lakes Res. 38, 278–288. Cornwell, E.R., Bellmund, C.A., Groocock, G.H., Wong, P.T., Hambury, K.L., Getchell, R.G., Bowser, P.R., 2013. Fin and gill biopsies are effective nonlethal samples for detection of Vrial hemorrhagic septicemia virus genotype IVb. J. Vet. Diagn. Investig. 25, 203–209. Dean, A.G., Sullivan, K.M., Soe, M.M., 2012. OpenEpi: Open Source Epidemiologic Statistics for Public Health. Available at:. www.OpenEpi.com. Eckerlin, G.E., Farrell, J.M., Casey, R.N., Hope, K.M., Groocock, G.H., Bowser, P.R., Casey, J., 2011. Temporal variation in prevalence of viral hemorrhagic septicemia virus type IVb among upper St. Lawrence River smallmouth bass. Trans. Am. Fish. Soc. 140, 529–536. Elsayed, E., Faisal, M., Thomas, M., Whelan, G., Batts, W., Winton, W., 2006. Isolation of viral hemorrhagic septicemia virus from muskellunge, Esox masquinongy (Mitchell), in Lake St. Clair, Michigan, USA reveals a new sublineage of the North American genotype. J. Fish Dis. 29, 611–619. Fosgate, G.T., 2009. Practical sample size calculations for surveillance and diagnostic investigations. J. Vet. Diagn. Investig. 21, 3–14. Frattini, S.A., Groocock, G.H., Getchell, R.G., Wooster, G.A., Casey, R.N., Casey, J.W., Bowser, P.R., 2011. A 2006 survey of viral hemorrhagic septicemia (VHSV) virus type IVb in New York State waters. J. Great Lakes Res. 37, 194–198. Gelman, A., Hill, J., 2007. Data Analysis Using Regression and Multi-Level/Hierarchical Models. Cambridge University Press, Cambridge, United Kingdom. Gelman, A., Rubin, D.B., 1992. Inference from iterative simulation using multiple sequences. Stat. Sci. 7, 457–472. Goodwin, A.E., Merry, G.E., Noyes, A.D., 2012. Persistence of viral RNA in fish infected with VHSV-IVb at 15 °C and then moved to warmer temperatures after the onset of disease. J. Fish Dis. 35, 523–528. Green, P.J., 1995. Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82, 711–732.

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Please cite this article as: Cornwell, E.R., et al., Applying multi-scale occupancy models to infer host and site occupancy of an emerging viral fish pathogen in the Great Lakes, J. Great Lakes Res. (2015), http://dx.doi.org/10.1016/j.jglr.2015.01.002