MARINE ECOLOGY PROGRESS SERIESMar Ecol Prog Ser

Vol. 531: 221–239, 2015doi: 10.3354/meps11349

Published July 2

INTRODUCTION

Marine diseases are a strong selective force in theworld’s oceans, and can have significant and long-lasting economic and ecological consequences (Burgeet al. 2014, Lafferty et al. 2015). Oyster diseases in -

cluding MSX (Ford & Tripp 1996, Ford & Bushek2012), dermo (Ragone Calvo et al. 2003, Bushek et al.2012), OsHV-1μVar (=oyster herpesvirus) infection(Segarra et al. 2010, Paul-Pont et al. 2014) and Roseo-varius (=juvenile) oyster disease (Davis & Barber1999, Maloy et al. 2007) have caused high mortality in

© Inter-Research 2015 · www.int-res.com*Corresponding author: dmunroe@hsrl.rutgers.edu

Outcomes of asymmetric selection pressure and larval dispersal on evolution of disease resistance:

a metapopulation modeling study with oysters

Daphne M. Munroe1,*, Eric N. Powell2, Susan E. Ford1, Eileen E. Hofmann3, John M. Klinck3

1Haskin Shellfish Research Laboratory, Rutgers University, 6959 Miller Ave., Port Norris, NJ 08349, USA2Gulf Coast Research Laboratory, University of Southern Mississippi, 703 East Beach Drive, Ocean Springs, MS 39564, USA

3Center for Coastal Physical Oceanography, Department of Ocean, Earth and Atmospheric Sciences, 4111 Monarch Way, 3rd Floor, Old Dominion University, Norfolk, VA 23529, USA

ABSTRACT: Marine diseases are a strong selective force that can have important economic andecological consequences. Larval dispersal patterns, selective mortality and individual growthrates can modulate metapopulation responses to disease pressure. Here, we use a modelingframework that includes distinct populations, connected via larval transport, with varying diseaseselection pressure and connectivity to examine how these dynamics enhance or inhibit the evolu-tion of disease resistance in metapopulations. Our system, oysters and MSX disease, is one inwhich disease resistance is highly and demonstrably heritable. Simulations show that under con-ditions of population isolation (i.e. local retention of larvae) and strong disease selection, popula-tions rapidly evolve genetic disease resistance. Varying the patterns of larval dispersal alone dou-bles the time for evolution of disease resistance. Spatially varying disease in the absence of larvaldispersal leaves some populations unable to respond to the disease, whereas adding larval disper-sal slows the response of populations under strong selection and speeds the response in popula-tions under low selection when fitness is based on relatively limited genetic structure (‘juvenile fitness’ in our simulations). Under spatially variable disease pressure, larval dispersal generates afourfold greater variance in fitness outcomes across the dispersal patterns tested. In a meta -population, populations experiencing lower selection pressure will tend to slow the developmentof other, more heavily selected populations. This suggests that conservation efforts aimed atimproving overall metapopulation resistance in the face of marine diseases should target thosepopulations under modest or high disease pressure, rather than protecting those experiencing lowselective pressure.

KEY WORDS: Larval dispersal · Metapopulation dynamics · Connectivity · Disease · Oyster ·Resistance · Structured population model · Genetic adaptation · Evolution

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Mar Ecol Prog Ser 531: 221–239, 2015

wild-harvested and aquacultured populations, whichhas translated into major economic and ecologicallosses (Mann et al. 2009, Lafferty et al. 2015). Exam-ples of catastrophic disease mortality can also befound in crustacean fisheries (Shields 2012, Lafferty etal. 2015) as well as in other taxa such as abalone(Friedman et al. 2014, Lafferty et al. 2015), echino-derms (Scheibling & Hennigar 1997) and corals (Pat-terson et al. 2002, Kim & Harvell 2004), where massivedie-offs have been associated with disruption of eco-logical functioning (Altizer et al. 2003, Miner et al.2006). The economic and ecological consequences ofdisease in these open (dispersive) populations illus-trates that a greater understanding of the mechanismsand rates of possible development of genetic resist-ance to disease at a metapopulation level would im-prove management and mitigation of losses.

The rate at which evolution of resistance occurs iscontrolled jointly by the strength of selection for sur-vival (Kingsolver et al. 2001), the heritability of resist-ance (Fisher 1930) and the degree of genetic connec-tivity between a given population and others undervarious selection pressures (Sanford & Kelly 2011).Spatially variable selective pressure within a meta -population may drive genetic divergence among sub-populations experiencing different levels of se lec-tion (Feng & Castillo-Chavez 2006, Dégremont et al.2010). Alternatively, in cases where a selection (dis-ease) refuge exists spatially (Hofmann et al. 2009,Bushek et al. 2012) or temporally (Harding et al. 2005,Powell et al. 2012), development of genetic resistancein the metapopulation could be inhibited (Ford et al.2012) through continual input of unselected genotypesfrom refuge areas. This genetic connectivity amongsubpopulations via larval dispersal creates a homoge-nizing influence that tends to mix selected and unse-lected genotypes and slow the influence of local selec-tion pressure (Sanford & Kelly 2011). Thus, we maypredict that species with high rates of dispersal shoulddisplay lower spatial genetic structure and relativelyslow evolution of resistance. In practice, this has notbeen demonstrated as clearly as would be expected(Weersing & Toonen 2009, Selkoe & Toonen 2011); infact, the only clear pattern that exists regardingpelagic larval duration and genetic structure is thenull pattern that species with direct development (i.e.no larval dispersal) have high spatial genetic structure(Weersing & Toonen 2009, Kelly & Palumbi 2010).Larval dispersal of varying pelagic duration createsgenetic mixing; however, the specific relationship between larval duration and evolution of disease re -sistance within spatially structured metapopulationsremains unclear.

Metapopulations consist of any number of opensubpopulations connected by larval dispersal, andhave local selective pressures that are heteroge-neous in time and space (Kritzer & Sale 2004). Thisvariability has the potential to create uncertainty inmetapopulation response to selection. Observationof, and experimentation with, these processes ofselection pressure and genetic response on an eco-logically relevant scale are challenging if not impos-sible to fully execute. One hindrance for experimen-tation is that direct observation of larval dispersalpresents a number of challenges (Piggott et al. 2008,White et al. 2010). Increasingly, connectivity matricesgen erated from biophysical models are being used to predict larval dispersal in marine metapopulations(North et al. 2008, Haase et al. 2012, Narváez etal. 2012a,b). These connectivity patterns have beenused to successfully predict population genetic struc-ture in coral reef metapopulations, allowing directcomparisons between simulated and empirical geneticpatterns (Galindo et al. 2006, Kool et al. 2011, Fosteret al. 2012); however, these studies used neutral alle-les and thus failed to include the effect of selection intheir calculations. The combined influence of spa-tially varying selective pressure and larval dispersal(connectivity) is more complex, but has importantconsequences for adaptation and evolution (Sanford& Kelly 2011).

For more than half a century, eastern oysters Crass-ostrea virginica have been affected by MSX disease,caused by the protozoan pathogen Haplosporidiumnelsoni. Eastern oysters have shown the ability torapidly develop resistance to disease and mortalitycaused by H. nelsoni in both ‘common garden’ field-challenge experiments (Haskin & Ford 1979, RagoneCalvo et al. 2003) and in wild populations (Ford et al.2009, 2012). In the Delaware estuary, a large portionof the oyster population is managed as a state fishery(Powell et al. 2011a) and annual quantitative assess-ments have provided a detailed account of populationabundance and disease prevalence from 1953 untilthe present day (Ford & Haskin 1982, Powell et al.2008). H. nelsoni is intolerant of low salinity andtherefore the strong salinity gradient that exists inthe Delaware estuary generates a corresponding dis-ease gradient (Ford & Bushek 2012, Powell et al.2012) such that oyster populations in the upper estu-ary (low salinity) experience lower disease pressure,whilst lower estuary populations in higher salinityexperience higher disease pressure. The salinity gra-dient in the estuary creates a corresponding gradientin oyster growth, such that growth is faster in highersalinity (Kraeuter et al. 2007). It is as yet uncertain

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how these environmentally-driven spatial gradientsin disease pressure and oyster demographics, in com -bination with variable larval dispersal (Narváez et al.2012a) influence the evolution of disease resistance.

Here, we investigate the hypothesis that spatiallyvarying disease selection, local demography and larval dispersal influences metapopulation genetic-connectivity dynamics and the evolution of diseaseresistance using a framework that includes an indi-vidual-based model that simulates an eastern oystermetapopulation. We parameterized the model usingthe comprehensive long-term data from oyster fish-ery stock assessments in the Delaware estuary (Pow-ell et al. 2011a) and historical data on the oyster stockresponse to MSX disease pressure (see Hofmann &Ford 2012 and other papers in the same volume foran overview). The modeling framework includes dis-tinct populations that can be manipulated by varyinglevels of selective disease pressure and connectivityvia larval transport.

MATERIALS AND METHODS

The model

The Dynamic Population Genetics Engine (DyPoGEn)(Munroe et al. 2012, 2013a,b, Powell et al. 2011b,c) isa numerical model that simulates the genetic struc-ture and population dynamics of a metapopulation.We parameterized the model to simulate a metapop-ulation containing 4 connected populations of east-ern oysters Crassostrea virginica in the Delawareestuary (Fig. 1). In the model, each simulated popula-tion is composed of multiple cohorts of oysters whosepopulations interact via larval dispersal. Larvae (off-spring) are created annually from parent pairs viaindependent assortment of parental genotypes tosimulate meiosis and random egg fertilization. Thelarvae produced in each population can remainwithin the source population (local retention, sensu

Hogan et al. 2012) or disperse to any of the other pop-ulations, in which the conditions for growth and sur-vival can differ. No larvae are lost from the system,and all are constrained to settle within 1 of the 4 pop-ulations. The general characteristics of each popula-tion are given in Table 1.

DyPoGEn has 3 basic components: (1) a post-settle-ment population dynamics sub-model that containsparameterizations for growth, mortality and repro-duction; (2) a larval sub-model that contains parame-terizations for larval mortality, larval exchange andearly juvenile survival and (3) a gene sub-model thatdescribes each individual in terms of its geneticstructure to which differential fitness and survival

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Fig. 1. Locations and depths (m) of eastern oyster Crassostreavirginica populations in Delaware estuary used in modelsimulations. Inset shows location of fished beds in Delawareestuary, and the Delaware estuary on the Atlantic Coast of

the USA. Map modified from Munroe et al. (2013c)

Population1 2 3 4

Abundance (millions of oysters)a 492 395 868 197Average adult natural mortality ratea 8% 10% 16% 26%Natural juvenile mortality ratea NDb 8% 23% 47%von Bertalanffy growth parameters (k / L∞)c NDb 0.175/110 0.26/125 0.23/140aFrom Powell et al. (2011a); bND: L∞ estimated from stock assessment dataa; juvenile mortality and k assumed equal toPopulation 2; cFrom Kraeuter et al. (2007): L∞ in mm, k in yr−1

Table 1. Characteristics for each of the 4 eastern oyster Crassostrea virginica populations used in the metapopulation simulations, based on recently observed dynamics in the fished oyster stock in Delaware estuary (2000 to 2010). ND: no data

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probabilities can be applied to individual genotypes.Additional details of the single population modelstructure and formulation (on which our metapopu -lation model is based) are given in Powell et al.(2011b,c). The model processes, including specifica-tions for growth, reproduction and mortality, havebeen described previously (see Munroe et al. 2012,2013a,b), and population abundances in the modelwere maintained high enough to minimize the influ-ence of genetic drift. In this study, we include a geno-type−phenotype interface that interprets individualgenotypes in terms of fitness, which then influencesthe post-settlement sub-model. This permits the feed -back between genotype and phenotype that allowsfor selection. For brevity, we describe only thosenovel components of the model that were previouslyundescribed, and the mechanisms by which the pre-viously described model processes are influenced bythe genotype−phenotype interface.

Post-settlement population dynamics

MSX disease is thought to cause oyster mortality in2 ways (Ford et al. 1988). The first is by high andrapid mortality of naïve individuals, and the second isa result of prolonged (chronic) disease in individualsthat have experienced selection but are still carryingthe parasite (Ford 1985, Ford & Haskin 1987, Fordet al. 1988, 1999). For the purposes of the presentmodel, this difference is imposed on populations suchthat juveniles are considered naïve and therefore ex -perience high, rapid mortality, whereas adults (havingsurvived initial mortality episodes) experience lower,chronic exposure mortality. Thus, the probability ofmortality of an individual oyster (PMort) is calculatedas the combined probability of juvenile mortality (PJuvMort) and adult mortality (PAdultMort):

(1)

where PJuvMort is calculated as:

(2)

and PAdultMort depends on the age of the animal (Age,in years) as follows:

(3)

The probability of mortality is modulated by theindividual’s age and fitness (FitFac). For young oys-ters, FitFacJuv generates an increasing probability ofmortality relative to the genetic disease resistance

of an individual at a given age as dJuvMort (whichvaries from 0 under conditions of low disease pres-sure to 2.2 in high disease pressure; Fig. 2A); how-ever, as age increases, the probability of mortalitydecreases (Fig. 2A). In older oysters, FitFacAdultspecifies a probability range of mortality depend-ing on the degree of genetic disease resistance asdAdultMort (varies from 0 in low disease pressure to17.8 in high disease pressure) and dAdultSpread-Mort (varies from 0 in low disease pressure to 6 inhigh disease pressure). Likewise, for oysters olderthan approximately 3 yr, as age increases, the proba-bility of mortality increases (Fig. 2A).

Genetic structure and fitness

Definition of fitness

Fitness is often defined as the number of reproduc-ing offspring that a parent produces (Charnov et al.2007). Only a small fraction of an oyster populationspawns successfully, and many recruits fail to spawnsuccessfully before they die. Whether a recruit willreproduce is controlled by its growth rate, which controls lifetime spawning potential by influencingsize-at-age (e.g. Galvani & Slatkin 2004) and the age-dependent mortality rate. Size-at-age in the modelis assigned using a von Bertalanffy relationship(Kraeuter et al. 2007). In this study, age-dependentmortality is influenced by selection. For simplicity,we use modifiers to the term ‘fitness’ to refer to 3 sub-sets of this overall process. The term ‘juvenile fitness’refers to the genetic complement of any oyster withan age

Munroe et al.: Disease resistance and oyster metapopulation genetic connectivity

as having significant shifts in genotype frequencywithin families after being exposed to MSX disease-caused mortality. Some of these alleles may confer agreater increment in survival than others; however,the data currently available are insufficient to pro-vide more than a ranking of selection pressure asso-ciated with each allele. Which loci influence juvenilemortality and which modulate adult mortality is alsounknown. Based on evidence from multiple selectiontrials using laboratory-produced cohorts, Haskin &Ford (1979) suggested that a single locus, randomlydistributed within the population could be responsi-ble for evolution of MSX disease resistance. Usingdata obtained from previous disease selection exper-iments, which demonstrated strong selection duringthe first (juvenile) year of exposure of naïve stocks(Haskin & Ford 1979, Ford & Haskin 1987), we deter-

mined that the ob served selection forMSX disease resistance in juvenilescould not be simulated appropriatelyunless selection in juveniles was influ-enced by only a single, highly influen-tial locus; consequently, we assignedthe locus with the strongest selection(i.e. the largest differential betweenAA and AB genotypes) to juvenile fitness (Table 2). The remaining 14loci were assigned to alleles associ-ated with adult fitness, consistent withGuo’s observations of the number ofloci involved. Further support for theassignment of multiple loci to adult fitness is found in the observation ofslower development of disease re -sistance in later generations of se -lection (Haskin & Ford 1979). Thedecreasing rate of disease resistancedevelopment is most easily explainedby a multiple locus selection process(e.g. Powell et al. 2012). For the pur-poses of this study, the importance ofthis information is to establish (1) thatselection pressure for survival throughearly life stages of a naïve stock isstrong, (2) that a large number of locimay be involved in the adult selectionprocess and (3) that these loci are distributed among the majority of thechromosomes (Table 2).

Genotype−phenotype interface

The genetic structure of each oyster is defined by10 pairs of chromosomes (Wang et al. 2005); for com-putational convenience, we assigned 4 genes to eachchromosome and 2 alleles per gene. Thus, each ani-mal is specified by 40 loci, with the genotypes per-mitted at each locus being AA, AB and BB. To initiateeach simulation, an initial population is created witha defined genetic structure. Alleles on loci not in -volved in disease resistance are assigned to be A or Brandomly, and act as neutral alleles. A single locus isused to confer disease resistance which results fromearly exposure of naïve animals (here termedjuvenile fitness) and 14 loci are used to specify adultfitness. Generally, alleles conferring disease resist-ance are present at low frequency in an uninfectedpopulation; that is, these alleles are not favored byselection in the absence of disease (e.g. Detilleux

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Fig. 2. Probability of mortality for an individual eastern oyster Crassostreavirginica as the oyster ages, showing how the probability changes (A) hold-ing fitness constant at 0.4 but varying disease pressure, and (B) with age of

the oyster, holding disease constant (high) but varying fitness

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2005, Powell et al. 2012). Since the actual allele fre-quencies in the naïve population are unknown, weinitially implemented both juvenile and adult fitnessat a 1:9 ratio of A:B alleles. Verification against obser-vations (see ‘Results’) supports this choice for adults;however, the 1:9 allele frequency failed to provide anadequate response for the juvenile trait. Thus, we ini-tiated the juvenile fitness allele frequency assumingHardy-Weinberg equilibrium (50:50 ratio) based onthe work of Haskin & Ford (1979). The etiologicalagent of MSX disease, Haplo sporidium nelsoni, wasintroduced; that is, MSX is not a naturally occurringdisease in C. virginica (Burreson et al. 2000), andthus there was no prior selection for or against the al-lele conferring juvenile re sistance in the population.

In these simulations, the 15 loci are assigned anallele fitness as described in Table 2, based on thedesignation of A for the allele conferring diseaseresistance and B for the alternative allele. Note thateach is given a weight relative to 1.0, which is as -signed to the AA homozygote, in keeping with theearlier caveat that only the relative ranking of effecton disease resistance among genotypes can currentlybe assigned with any degree of confidence. The locusand chromosome to which each gene is assigned arereported in Table 2.

Juvenile fitness for an individual oyster is deter-mined by the fitness value that corresponds to itsgenotype at locus 11 (Table 2), whereas adult fitnessis the average of the 14 values corresponding to its

genotype from each of the loci conferring adult dis-ease resistance (Table 2). Most oyster loci have morethan 2 alleles (Launey & Hedgecock 2001, Wang &Guo 2007). For these simulations, we assume thatonly one of these alleles is associated with diseaseresistance, so that a 2-allele configuration can beused, with the second allele representing the host ofalleles having no influence on disease resistance. Weassume no epistasis, having limited information tothe contrary (e.g. Sokolova et al. 2006), although epi -stasis is a common occurrence in Crassostrea spp.(Hedgecock et al. 1995, 1996). In some cases, the simple average of the maximum or minimum valuesof allele fitness for the designated loci may define arange narrower than 0 to 1, inclusive. From Table 2,for example, an animal with a BB genotype at thejuvenile locus has a juvenile fitness of 0.179, whereasan animal with genotype BB at all 14 adult loci wouldhave an adult fitness value of 0.292. Therefore, toscale the genotypes on a range from 0 to 1, the mini-mal and maximal fitnesss values obtained for boththe juvenile locus, and the adult fitness obtainedfrom the 14 loci are standardized to values of 0 and 1;any genotype falling between 0 and 1 is standardizedwithin the 0-to-1 continuum by interpolation. Boththe final juvenile and adult fitness values for eachanimal, then, have an easily quantifiable distinctionbetween the least and most fit animals; a value be -tween 0 and 1, inclusive.

Hosts might evolve in response to a pathogen suchas H. nelsoni in 1 of 3 ways: decreased susceptibility(the inability to become infected), increased resistance(control of pathogen proliferation once infected), orincreased tolerance (lack of disease despite infection;Ford 1988, Boots & Bowers 1999). For our purposes,fitness is used as a summary response; that is, we donot try to represent the 3 ways that the evolution ofresponse to disease might occur. In the model, selec-tion simply operates by controlling variation in theprobability of death at a given age based on an individual’s value of fitness (either FitFacJuv or Fit-FacAdult, depending on the age of the animal), asspecified in Eqs. (1) & (2).

Simulations

Simulations in this study include a single-popula-tion selection trial case (with which the genotype/phenotype response of a series of cohorts was tuned)plus a range of metapopulation simulations using 4populations and covering a range of disease pres-sures, larval connectivity patterns and local demo-

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Locus Chromosome Life stage Relative fitnessAA AB BB

1 2 Adult 1 0.726 0.5042 3 Adult 1 0.556 0.1623 4 Adult 1 0.554 0.3904 4 Adult 1 0.561 0.3255 5 Adult 1 0.952 0.4236 6 Adult 1 0.419 0.1317 6 Adult 1 0.496 0.2498 7 Adult 1 0.424 0.1529 7 Adult 1 0.412 0.29410 8 Adult 1 0.566 0.08911 9 Juvenile 1 0.385 0.17912 9 Adult 1 0.531 0.43913 9 Adult 1 0.969 0.39514 10 Adult 1 0.469 0.26015 10 Adult 1 0.622 0.389

Table 2. Relative eastern oyster Crassostrea virginica allelefitness values and chromosome locations for each of the 15loci associated with MSX disease resistance. Each is refer-enced to the assumed maximum fitness of 1 for the AA geno-type. Relative fitness values are based on unpublished dataprovided by X. Guo (Haskin Shellfish Research Laboratory,

Rutgers University)

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graphic conditions. All simulations initiate with a fullydeveloped oyster population structure (a normalrange of size, sex and age frequencies as described inPowell et al. 2011a) in each population, and were runfor 100 yr.

I. Selection trial case

The selection trial case simulates a single cohort ofoysters, and is designed to reflect the populationresponses that resulted from a series of controlledlaboratory selection experiments which generated arelatively rapid and repeatable evolution of resist-ance to MSX disease-caused mortality in the oystersof Delaware Bay (Haskin & Ford 1979). In these labo-ratory-based trials, parental stock was taken fromwild oyster populations in the estuary. These parentswere bred, and the offspring (F1) were put in cages inthe estuary where they were exposed for 3 yr to rela-tively high natural levels of MSX disease. The surviv-ing offspring were then returned to the laboratoryand bred to generate the second generation (F2). TheF2 generation was again exposed to naturally highdisease levels in cages in the estuary for 3 yr beforereturning the survivors to the laboratory for breedingagain to generate the next generation (F3). Thisselection experiment was performed multiple timesby researchers at the Haskin Shellfish Research Laboratory over more than 2 decades with relativelyconsistent responses, such that survival increased (onaverage) with each generation (Haskin & Ford 1979).Results of those repeated selection experiments aresummarized by Haskin & Ford (1979), and averagemortality curves from these experiments are used totune the selection pressure of disease in the model byaltering the way that mortality depends on FitFacand the relative fitness of alleles. Tuning is accom-plished by a single cohort model run, in which thatcohort is exposed to high rates of disease selection,and oysters are allowed to reproduce only once intheir lifetime (at 3 yr of age). This allowed direct com-parison of the observed survival curves with simu-lated survival of each cohort to tune selection pres-sure and oyster mortality in the model, ensuringmodel selection pressure reflected the observed re -sponses to MSX disease of initially naïve populations.Pathological examinations revealed that H. nelsoniwas present, and heavy, in oysters during that timeand that MSX disease was the major cause of mortal-ity; other oyster diseases (including dermo) were notmajor sources of mortality during that period (Ford &Haskin 1987).

II. Metapopulation simulations: varying disease,larval and demographic conditions

The following sections describe the ways that dis-ease pressure, larval connectivity and local demo-graphic conditions are varied in simulations. Allmetapopulation scenarios include 4 spatially distinctpopulations of oysters, connected to one another bylarval dispersal. In the simulated metapopulation,each population has distinct characteristics of diseasepressure, larval export and local demography (i.e.growth rate and carrying capacity), thereby allowingthe model to represent spatial gradients in thesecharacteristics. Each combination of population-levelsettings for these categories (disease pressure, larvaldispersal and local demography) is fully crossed withthe others, resulting in a total of 24 metapopulationsimulations (Fig. 3).

(a) Disease pressure. Two disease conditions aresimulated, both of which employ constant diseasepres sure over time. In one condition, disease pres-sure is high and constant throughout all populations,thereby simulating a situation without spatial dynam-ics in disease pressure. In the other condition, diseasepressure varies along an estuarine gradient wheredisease is high in Population 4 (high salinity) andgrades to very low in Population 1 (low salinity)(Fig. 2A).

(b) Larval dispersal. Larval connectivity matricesspecifying larval dispersal in the larval sub-modelinclude 6 distinct patterns, 5 of which are hypotheti-cal and 1 of which represents a Delaware estuarine-based pattern obtained from connectivity matricescalculated by Narváez et al. (2012a,b) using theRegional Ocean Modeling System (ROMS; Haid -vogel et al. 2000). The hypothetical patterns of dis-persal are described in greater detail below and areshown in Fig. 4 (also see Munroe et al. 2012, 2013a,bfor description of the larval sub-model and behaviorof neutral alleles in a metapopulation under various dispersal patterns).

For any given larval dispersal pattern, the samedispersal matrix is used in each simulated year. Thecontrived patterns of dispersal include one in whichno connectivity occurs among populations (i.e. all larvae are locally retained) and all larvae self-recruit.A second contrived larval dispersal pattern has lar-vae dispersed evenly among all populations (homo -genous full mixing). In the downbay larval cascade(directional dispersal) case, larvae do not move‘upbay’ from their birth population but instead mostlarvae disperse to the adjacent population downbay.The inverse (an upbay cascade) is also used. The

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more realistic larval disper-sal condition—the estuarinelarval dispersal—is basedon transfer probabilitiesfrom Lagrangian larvaltracking simulations as pre-viously discussed. In a finalcontrived dispersal pattern,this estuarine pattern isinverted.

(c) Population demogra-phy. Two patterns of pop u -lation demography are sim -ulated: in both, local popula-tion dynamics remain con-stant for the duration of the100 yr simulation (i.e. localgrowth rate and carryingcapacity does not changeover time). In one patternof demography, all 4 popu -lations are set to havethe same conditions of localgrowth rate and carryingcapacity, thereby simulatinga case without spatial varia-tion in local demographics.Thecontrastingpattern variesgrowth rate and carryingcapacity among populationssuch that growth rate andcarrying capacity are low inPopulation 1 (low salinity),grading to high in Popula-tion 4 (high salinity). Thispattern agrees well with theobserved conditions alongthe estuarine gradient inDelaware Bay that occurredduring the period 2000 to2010 (Kraeuter et al. 2007,Powell et al. 2008, 2009).

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Fig. 3. All combinations in -cluded in the simulations re -ported in this study. Left column:levels of disease selection; center column: levels of eastern oyster Crassostrea virginica larval dispersal; right column:levels of local demographics.All combinations of levels are simulated, as represented by the

lines connecting the levels

Fig. 4. Dispersal matrices for the 6 eastern oyster Crassostrea virginica larval dispersalpatterns used in simulations: (A) local retention, (B) even dispersal, (C) estuarine disper-sal, (D) inverted estuarine dispersal, (E) downbay cascade and (F) upbay cascade. Colorcorresponds to the number of larvae dispersed from the population listed on the y-axis to

the population on the x-axis

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Analysis

To assess the relative influence of changes in levelsof model population processes among the simula-tions, we use analysis of variance (ANOVA) to rankthe population processes (disease pattern, larval dis-persal and demographics) for each simulation outputin each population (Ginot et al. 2006). The changein both juvenile and adult fitness from time zero to25, 40, 60 and 100 yr for each population and eachsimulation is used as a summary metric representingthe genetic response of the population over time.Change in fitness was the response variable in eachANOVA that included first-order interactions only,where the dependent variables were the levels ofpopulation parameters in each simulation. Specifi-cally, the levels of dependent variables were: whethera gradient in selection pressure was present (2 lev-els), the various larval connectivity patterns (6 lev-els), whether a gradient in local growth and carryingcapacity was specified (demographics: 2 levels), andwhich population was being observed (4 levels).ANOVA was used here simply as a means to rank therelative influence of changes in the population para -meters of interest, rather than as a direct test of sig-nificance. For each ANOVA, variables that are sig -nificant (p < 0.05) are ranked from highest to lowestaccording to the associated F-statistic.

RESULTS

Comparison of simulated and observed selection trials

Oyster fitness in the single cohort selection trialcase responded rapidly to disease exposure. A simu-lation using the genotype fitness values shown inTable 2 and high disease pressure modifiers in themortality equations (Eqs. 1 & 2) generated an initialunselected cohort of oysters that experience veryhigh mortality early in life when exposed to disease.This high rate of juvenile mortality in unselected oys-ters agrees well with the average response of naïvepopulations observed during multiple selection ex -periments performed at the Haskin Shellfish Re -search Laboratory (Haskin & Ford 1979, our Fig. 5).Subsequent generations of the simulated selectiontrial (generations 2 and 4) show greatly reduced earlymortality compared to the unselected cohort, reflect-ing a rapid phenotypic response to selection pres-sure, although not as rapid as the average responsefrom selection experiments. The same is true for mortality rates in later life stages; between simulated

selection trial generation 2 and 4, a large reduction inthe cumulative mortality is observed 3 and 4 yr afterexposure. The rate at which older oysters die (theslope of the lines in Fig. 5) increases slightly from onecohort to the next. Again, this increase is not as pro-nounced as was observed for average experimentalcohorts (Haskin & Ford 1979).

Metapopulations

Influence of varied disease pressure

When all populations experience homogeneouslyhigh disease selection pressure, the entire metapop-ulation steadily and relatively rapidly evolves higherfitness (shown by solid lines in Fig. 6). Juvenile fit-ness doubles from about 0.4 to 0.8 in all populationsin 30 yr, whilst adult fitness doubles from about 0.05to 0.1 in one-third of the time (10 yr). The differencesin the initial fitness values between juvenile andadult fitness are due to the different initial allele fre-quencies and varied fitness weighting of differentloci (Table 2). When spatially heterogeneous diseasepressure exists across the metapopulation (dottedlines in Fig. 6), a much slower fitness response is ob -served. Spatially varying disease pressure amongpopulations generates a doubling of juvenile fitnessin about 100 yr, whilst adult fitness barely increasesover the same duration.

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Fig. 5. Cumulative mortality curves from multiple easternoyster Crassostrea virginica disease selection experiments(data from Haskin & Ford 1979, their Fig. 2) shown with solidlines. Cumulative mortality for simulated ‘selection trial’

oysters shown with dashed lines

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Influence of varied larval dispersal

All 4 populations evolve a rapid increase in juve-nile fitness and a constant increase in adult fitnesswhen no larval dispersal occurs, with disease pres-sure homogeneously high and demographic condi-tions constant (heavy black line in Fig. 7). In thesimulation with no larval dispersal, all 4 populationsdemonstrate identical patterns in evolution of fit-ness, verifying that the disease and demographyparameterizations in each of the 4 isolated popula-tions are influencing phenotypes and genotypesconsistently. Therefore, allowing larval dispersal tovary while holding disease pressure and demo -graphy constant means that dispersal is the only

character (of the simulations shown withthe thinner lines in Fig. 7) that generates achange in the fitness response of eachpopulation. Allowing any pattern of larvaldispersal tends to slow the juvenile fitnessresponse of the population. Under condi-tions of no larval dispersal, the popula-tions double juvenile fitness in approxi-mately 15 yr, whereas allowing larvaldispersal slows the doubling to approxi-mately 25 yr. The response of adult fitnessdoes not show the same pattern. Instead,allowing larval dispersal tends to generatea relatively constant and matching in -crease in adult fitness relative to the nolarval dispersal case. One might expectthat the directional larval dispersal pat-terns (upbay and downbay dispersal)should be differentially beneficial for populations at either end of the baywidemetapopulation; however, this is not ob -served. The upbay and downbay dispersalpatterns generate juvenile fitness re -sponses that are more similar to eachother than to those generated by theremaining dispersal patterns in bothupbay (Popu lation 1) and downbay (Popu-lation 4) populations.

Influence of varied population demo-graphics

When population demographics areequal among all populations in themetapopulation and all experience highdisease pressure, all 4 populations steadilyevolve higher fitness (shown by solid lines

in Fig. 8). Both juvenile and adult fitness double,from about 0.4 to 0.8, and 0.05 to 0.1 respectively, inall populations in approximately 30 yr. Metapopula-tion conditions in which all else is held constantexcept spatially hetero geneous demography amongpopulations (dotted lines in Fig. 8) show a similarresponse of fitness in each population compared tothe homogenous demography case.

ANOVA ranks

The influence of changes in disease pressure(homogeneous to heterogeneous) ranked higher thanchanges in other variables throughout the duration of

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Fig. 6. (A) Juvenile and (B) adult fitness over time for each of the 4 east-ern oyster Crassostrea virginica populations from simulations withhomogeneous high disease pressure (solid lines) and with a gradient indisease pressure (heterogeneous case; dotted lines). Simulations plottedhere with both homogeneous and heterogeneous disease pressure have

even larval dispersal and homogeneous population demographics

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the simulation for both juvenile and adult fitness(Fig. 9). Varying larval dispersal also ranked consis-tently high, especially for fitness responses in the first40 yr (generations). The interaction of selection andlarval dispersal also ranked high for both juvenileand adult fitness, whereas the interaction of demo-graphics and larval dispersal ranked relatively highwhen con sidering change in adult fitness only (Fig. 9).Under conditions of heterogeneous disease pressure,larval dispersal tends to speed the increase in fitnessin unselected (low disease) populations (Fig. 10A,C),and slow the increase in fitness in heavily selected(high disease) populations (Fig. 10B,D). Larval dis-persal patterns that are the most evenly mixed leadto the most rapid evolution of fitness of all populationsunder conditions of heterogeneous disease pressure(Fig. 10).

DISCUSSION

In any ecosystem, a number of factors play a role inthe dynamics of population genotype, including sup-ply-side factors such as larval dispersal, and post-settlement factors such as selection and growth rate.The model described here provides a way to considerthese factors together and to assess their relativeimportance to selection for disease resistance in ameta population over time. Neutral alleles can bemaintained homogeneously in a metapopulationwith very little larval dispersal (Munroe et al. 2012);however, if a diversifying selection is present in onepart of a metapopulation, we would expect that theselected allele will change in frequency over time(Dégremont et al. 2010). The simulations performedhere show that pattern, with alleles conferring a

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Fig. 7. (A,B) Juvenile and (C,D) adult fitness over time for the most ‘upbay’ eastern oyster Crassostrea virginica population(Population 1; A,C) and the most ‘downbay’ population (Population 4; B,D) under conditions of varying larval dispersal. Linesin each plot are from simulations wherein only larval dispersal varies and disease and demography are held constant amongpopulations (homogeneous high disease and homogeneous demography). Heavy black line shows the case of no larval disper-

sal; remaining lines show each of the larval dispersal patterns used (see Fig. 3)

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selective advantage increasing in frequency overtime, and the alleles not linked to fitness (neutralalleles) remaining at about 50:50 (data not shown) inthe metapopulation over time.

Selection trial simulations

Cumulative mortality within a single selection trialcohort matched results obtained empirically fromrepeated selection trials. We tuned fitness and selec-tion associated with the allele parameters in themodel to obtain simulation results that reflectedthese selection experiments; we argue that this tun-ing is appropriate for 2 reasons. First, these simula-tions are meant to follow the metapopulationresponse to disease exposure of a naïve meta -population, and the laboratory-based experiments

were initiated using naïve oysters (those that had notpreviously been exposed to MSX disease; Haskin &Ford 1979). Second, observations made on wild pop-ulations during the initial 3 yr of the MSX epizootic inDelaware Bay documented mortality rates in wildoyster spat and recruits that follow the mortality ofsequential generations shown in Fig. 5 (Haskin &Ford 1979), suggesting that the cohort re sponsedemonstrated in the experimental observations wasalso evident in wild naïve populations. The alleleparameters that generate a simulation reflective ofthe observed oyster mortality curves made duringthose re peated selection experiments is one in whichthe allele that is strongly selected against in early life(the first 2 yr) is initiated at 50% frequency in thenaïve population. This initial frequency distributionallows for strong selection before reproduction andsupports the suggestion of Haskin & Ford (1979,

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Fig. 8. (A) Juvenile and (B) adult fitness over time for each of the 4 eastern oyster Crassostrea virginica populations from simulations with homogeneous demographic conditions (solid lines) and an estuarine gradient in demographic conditions(heterogeneous case; dotted lines). Lines in each plot are from simulations wherein only conditions of demography change;both homogeneous and heterogeneous demographic simulations use estuarine larval dispersal and homogeneous high

disease pressure

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Fig. 9. Ranks of each factor and first-order interactions (y-axis) at 4 timepoints along each simulation (x-axis) for juvenile (left panel) andadult (right panel) eastern oysterCrassostrea virginica fitness. Darkercolors: factors with a stronger in -fluence on the change in fitness ata given time (i.e. higher ranks);white squares: non-significant fac-tors. Ranks are calculated based onANOVA with change in fitness as

the response variable

Fig. 10. (A,B) Juvenile and (C,D) adult eastern oyster Crassostrea virginica fitness over time for Populations 1 and 4 under con-ditions of varying larval dispersal and spatially varying disease pressure. Lines in each plot are from simulations wherein onlylarval dispersal varies and disease and demography conditions are held constant. Disease conditions follow a gradient from

low disease upbay (Population 1) to high disease downbay (Population 4). See Fig. 7 legend for further description

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p. 61) that ‘a population of oysters that has neverbeen ex posed to MSX contains a random distributionof those genes which will determine its capacityto deal with disease’. The full complement of 15 al lelesassociated with resistance to mortality due to MSXdisease allowed for a rapid and high early mortalityin highly susceptible individuals, followed by aslower further response in indi viduals that survivedthe early exposure (Fig. 2). This condition agreeswith observations made by Ford et al. (1988, p. 41),who hypothesized a ‘rapid early mortality in unse-lected stocks… induced by a toxin and later mortalityassociated with loss of condition and impaired physi-ological functioning’. Thus, our model performanceagrees with the most robust datasets available thatdocument the response of naïve Crassostrea vir-ginica to MSX disease.

Metapopulation simulations

These simulations show varied genotypic and phenotypic responses of a metapopulation to diseaseselection pressure under spatially varying conditionsof disease pressure and larval dispersal. Biophysicallarval dispersal models have proven useful in pre-dicting the dynamics of population genetics throughtime. Galindo et al. (2006) used biophysically-basedlarval connectivity matrices to simulate the devel -opment of population genetics over time in a Carib-bean broadcast spawning coral. Likewise, Kool et al.(2011) used a larval dispersal model with a geneticmatrix model to predict coral population geneticstructure over time. Munroe et al. (2012, 2013a,b)used an individual-based metapopulation geneticsmodel with biophysically estimated larval dispersalpatterns to simulate genetic connectivity of estuarineoysters. All of these studies were able to simulatespatial genetic population structure for sessile mar-ine invertebrate populations; however, all used neu-tral allele conditions and failed to include the influ-ence of spatially heterogeneous selection pressure.Our results provide a unique integration of the role ofsupply (larval dispersal) and post-settlement (selec-tion and growth) processes on genetic dynamics in amarine system.

Spatially varying disease pressure

Spatial variability in selection pressure has thegreatest influence on the overall change in fitness ofa metapopulation (Fig. 9). In simulations where dis-

ease pressure is changed from homogeneously highto spatially varying, the ability of the meta populationto respond to disease is slowed considerably by theinclusion of populations with lower disease pressure(Fig. 6). Larval dispersal of unselected genotypesfrom populations in low disease conditions restricts(slows) development of fitness in the remaining pop-ulations, including those under high selection pres-sure. When selection pres sure is controlled (modu-lated) by the environment, as is the case for oystersin the Delaware estuary where a dominant upbay/downbay gradient in salinity controls the diseasepressure (Haskin & Ford 1982) and larval dispersalallows all populations to be connected (Narváez et al.2012a), the environmental gradient will tend to main-tain unselected alleles in the metapopulation anddecrease the capacity for the metapopulation toevolve re sistance to the disease.

The results of our simulations support the sugges-tion by Ford et al. (2012) that the presence of diseaserefuges (Hofmann et al. 2009) within a metapopu -lation could slow or prevent that metapopulationfrom developing resistance to disease. Munroe et al.(2013b) raised similar concerns in considering theappropriate application of Marine Protected Areas(likewise for oyster sanctuaries, Rodney & Paynter2006 and no-take reserves, Mroch et al. 2012) as acomponent of oyster restoration plans. The limitedsuccess of disease-tolerant oyster strains introducedinto the wild emphasizes the importance of under-standing the relationship of spatial variations inselection, dispersal and demography (Hare et al.2006). In our simulations, conditions of consistentlyhigh disease selection pressure generate a relativelyrapid increase in overall metapopulation fitness, par-ticularly for the case of no larval dispersal. This rapidresponse is consistent with observations made inDelaware Bay after an extensive selective mortalityevent in 1985/1986 that resulted from a prolongedperiod of drought. The low river flow conditions during the drought increased salinity in the upperreaches of the estuary, thereby allowing elevatedprevalence of MSX disease for all portions of themetapopulation including areas previously consid-ered disease refuges (Ford & Bushek 2012, Ford et al.2012). The result of this extensive and strong selec-tion event was a relatively disease-resistant meta -population in Delaware Bay, despite the continuedpresence of the disease agent, Haplosporidium nel-soni. In contrast to the general success of larval sur-vival during dispersal predicted by Lagrangian parti-cle simulations for 1985/1986 (Narváez et al. 2012b),our results suggest that for such a rapid response to

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occur, these drought years may have also been timesof reduced larval survival and dispersal and/or rela-tively high larval retention locally. However, Narváezet al. (2012b) also demonstrated that the timing ofoyster spawning relative to the tidal cycle can havean impact on larval survival and the amount of localretention, with neap tides generating more localretention relative to spring tides; a prediction thatagrees with patterns observed in spawning and re -tention of clam larvae (Carriker 1961, Chícharo &Chícharo 2001). Therefore, elevated local retentionin 1985/1986 may have been a result of a large cohortfrom a successful spawn occurring during neap tides.

We can contrast the rapid development of MSXdisease resistance in the Delaware estuary metapop-ulation in the mid-1980s to the slower developmentof resistance to the same disease in the ChesapeakeBay. Oyster populations in the Chesapeake tend tobe found in higher abundances in portions of theestuary where lower salinity protects them fromMSX disease (Carnegie & Burreson 2011). Thesepopulations, existing under lower disease pressure,exhibit lower disease resistance (Carnegie & Burre-son 2011), and are connected through larval disper-sal with other, more heavily selected populationsin the estuary (North et al. 2008). In agreement withMann et al. (1991), our simulations show that con -nectivity among populations under varying diseasese lection pressure retards overall development of disease resistance. Another factor that has failedto produce a similar metapopulation level responsein oyster disease resistance in Chesapeake Bay isdrought. The Chesapeake metapopulation has a muchmore complex larval connectivity pattern because ofthe numbers of tributaries and resulting hydro -dynamics (North et al. 2008) than the basically fun-nel-shaped Delaware estuary. This more complexmetapopulation structure may mean that events suchas drought may have a lower chance of generatingrapid evolutionary events such as that observed inthe Delaware estuary. It should be noted that recentevidence shows some disease resistance may bedeveloping in wild populations in the ChesapeakeBay (e.g. Wreck Shoal in the James River; Carnegie& Burreson 2011).

In our simulations, spatially varying disease pres-sure slows, but does not completely halt, the evolu-tion of increased fitness in populations. Consideringthat initial MSX mortality began in 1959 in Chesa-peake Bay (Andrews 1964), our simulations showthat after 50 yr of exposure, fitness could increase byapproximately 40 to 50% under spatially varying dis-ease conditions (Fig. 6). Carnegie & Burreson (2011)

also noted the presence of a gradient in resistancecoincident with the gradient in disease pressure; thisis also predicted in our model where, in a given year,the population under the highest disease pressurehas a slightly higher juvenile fitness than the popula-tion under low pressure (Fig. 6). An important out-come of these simulations, in contrast to other popu-lation dynamics models that consider source−sinkdynamics but do not consider spatially varied selec-tion pressure within the meta population (Lipcius etal. 2008), is the suggestion that populations in areasof higher disease pressure (e.g. higher salinity populations) should be protected when the goals of protection are to facilitate development of diseaseresistance. In a fully connected metapopulation,regardless of the prevailing larval dispersal pattern,populations experiencing lower selection pressurewill tend to slow the development of other moreheavily selected populations. This suggests that ef -forts intended to protect specific populations (e.g.sanctuaries) would be best targeted at those popula-tions under modest or high disease pressure to allowthose populations to thrive and possibly begin to sup-ply a selected (disease-resistant) genetic contributionto the overall meta population. This strategy agreeswith that suggested for certain Chesapeake Bay oyster populations (Carnegie & Burreson 2011).

Larval dispersal

During selection trial exposure experiments thatused oysters from locations around the estuary andexposed them to heavy disease, all responded to thedisease consistently, regardless of the disease pres-sure they had experienced locally (Haskin & Ford1979). This consistency among populations regard-less of local disease pressure agrees with the fitnessresponse that our simulated populations experiencewhen larval dispersal among populations occurs(Figs. 6 & 8) and further supports that these popula-tions are well connected through larval dispersal.

Development of disease resistance in meta -populations has been examined in other species ofbroadcast-spawning molluscs. Black abalone is awell-studied example in which populations havedemonstrated variable responses to disease pressure(Friedman et al. 2014), with some populations failingto develop resistance to disease. The severity ofabalone infection and mortality due to withering syn-drome is tightly linked to temperature (Ben-Horin etal. 2013); therefore, environmental heterogeneity intemperature could result in spatially varying disease

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pressure among populations. Larval dispersal frompopulations experiencing lower disease pressurecould explain the slower-than-expected rates of de -velopment of disease resistance in some populations.

Selection is the driver of genetic change whilst lar-val dispersal has a homogenizing influence (Sanford& Kelly 2011). In general, this was shown in our simulations. Any connectivity among differentiallyselected populations tended to slow the fitness re -sponse of heavily selected populations, and speedthe response of less selected populations. As such,we could expect that the most evenly dispersed lar-val pattern should generate the most homogenizing,or slowest rate of selection. This was true for our larval dispersal simulations, where the longest timeto double juvenile fitness was seen in the ‘even’ and‘estuarine’ larval mixing simulations (those simula-tions where all populations exchange larvae evenly;Fig. 7A,B) and ‘even’ and ‘estuarine’ larval mixinggenerated the most intermediate (average) rate of fit-ness change when a gradient in disease pressure waspresent (Fig. 10A,B). Similarly, we might expect thatthe 2 cascading larval dispersal patterns (upbay,downbay) should show opposite results when appliedto a metapopulation with a spatial gradient in diseasepressure, such that a downbay larval cascade shouldallow for greater influence of unselected genotypes(slower fitness response) because disease selection inthe upbay population is low, and an upbay larval cas-cade should allow for greater influence of selectedgenotypes (faster fitness response) because diseaseselection downbay is high. The downbay cascadeshowed this pattern, and the upbay cascade initiallyshowed a rapid evolution of fitness, but fitness de -clined around year 12, possibly due to limited larvalsupply from downbay because the downbay popula-tion abundance became constrained by limited re -cruits and high mortality (Fig. 10).

IMPLICATIONS

The importance of understanding the ecologicalprocesses that facilitate or hinder evolution of diseaseresistance is elevated by the possibility that diseaseoutbreaks are increasing in frequency and severitydue to climate change and other anthropogenic fac-tors (Harvell et al. 1999, 2002, Lafferty et al. 2004,Burge et al. 2014). Our rapidly increasing detectioncapacity and more robust monitoring networks haveconfounded our ability to distinguish the artefacts ofincreased intensity of observation from true trends ofincreasing outbreaks (Lafferty et al. 2004). None -

theless, compelling examples of well-documenteddiseases in marine molluscs, sponges, mammals, andeven marine diseases in humans show that increas-ing water temperature and other anthropologicalstressors including pollutants and ocean acidificationhave the capacity to affect the severity and frequencyof marine disease outbreaks (Lafferty 2009, Burge etal. 2014). In addition to changes in severity, climatechange has the potential to influence the spread ofmarine diseases. Northward progression of MSX disease outbreaks since it was first observed in theDelaware estuary in 1957 (Haskin et al. 1966) is aclassic example that has been linked with increasingtemperature (Hofmann et al. 2001). The northwardprogression of the disease is associated with epi-zootic oyster mortality events over the 30 yr followinginitial detection that have caused massive economicburdens to fishing communities along the east coastof the United States (Burreson & Ford 2004). As dis-ease intensity changes and species’ ranges (both hostand disease) extend with changing climate, we mustconsider the importance of understanding the mech-anisms and rates of response in newly exposed popu-lations and their capacity to develop resistance.

Acknowledgements. We are indebted to the late Hal Haskinand David Bushek for the depth of knowledge providedfrom their long-term work on the dynamics of MSX andother diseases in oysters. We also extend our gratitude toXiming Guo, who provided genotype advice that was thebasis for tuning modeled fitness parameters. Thanks toDiego Narváez for insightful conversations about larval dispersal patterns, and Aboozar Tabatabai for sharing map-ping codes. Funding was provided by the National ScienceFoundation (OCE-6022642 and OCE-0622672). Three anony -mous reviewers provided constructive commentary that im -proved the manuscript.

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Editorial responsibility: Romuald Lipcius, Gloucester Point, Virginia, USA

Submitted: October 6, 2014; Accepted: May 13, 2015Proofs received from author(s): June 10, 2015

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