LETTER Bioenergetic theory predicts infection dynamics of human

schistosomes in intermediate host snails across ecological

gradients

David J. Civitello,1*

Hiba Fatima,2 Leah R. Johnson,3

Roger M. Nisbet4 and

Jason R. Rohr5

Abstract

Epidemiological dynamics depend on the traits of hosts and parasites, but hosts and parasites areheterogeneous entities that exist in dynamic environments. Resource availability is a particularlydynamic and potent environmental driver of within-host infection dynamics (temporal patterns ofgrowth, reproduction, parasite production and survival). We developed, parameterised and vali-dated a model for resource-explicit infection dynamics by incorporating a parasitism module intodynamic energy budget theory. The model mechanistically explained the dynamic multivariateresponses of the human parasite Schistosoma mansoni and its intermediate host snail to variationin resources and host density. At the population level, feedbacks mediated by resource competi-tion could create a unimodal relationship between snail density and human risk of exposure toschistosomes. Consequently, weak snail control could backfire if reductions in snail density releaseremaining hosts from resource competition. If resource competition is strong and relevant toschistosome production in nature, it could inform control strategies.

Keywords

Density dependence, energy budget, parasite production, parasitism, reproduction, resources.

Ecology Letters (2018) 21: 692–701

INTRODUCTION

Parasitic diseases of humans and wildlife are emerging andresurging at an unprecedented rate and parasitism can havedramatic effects on ecosystem function, conservation, agricul-ture and human health (Morens et al. 2004; Bekerman &Einav 2015). Indeed, human, livestock and wildlife health aretightly linked because many of the most impactful infectiousdiseases of humans are vector-borne or zoonotic [i.e. involve anonhuman host (Wolfe et al. 2007)]. Given this strong linkbetween human and wildlife disease, it is critical to under-stand disease dynamics in nonhuman hosts, especially thosethat can transmit parasites to humans.Predicting disease dynamics requires an understanding of the

traits of both hosts and parasites. Individual-level traits, such ashost susceptibility and parasite reproduction, drive population-and community-level disease dynamics (Anderson & May1986). However, hosts and parasites are not uniform entitiesthat exist in constant environments. Instead, organisms and theenvironment are heterogeneous across space and time. Muchtheory has focused on how infection success and epidemiologi-cal dynamics are influenced by intrinsic drivers (e.g. infectiongenetics or the ability to produce toxins (Agrawal & Lively2002) or environmental factors (Mordecai et al. 2013). A frame-work that integrates intrinsic and extrinsic drivers couldenhance our ability to predict and manage disease outbreaks.

Resource availability is a powerful and dynamic environmentaldriver of disease. Parasites steal resources from their hosts to fueltheir own growth and reproduction. Thus, starving hosts can beresource-limiting environments for parasites (Sepp€al€a et al.2008). Conversely, well-provisioned hosts may deploy energeti-cally costly immune defences (Sheldon & Verhulst 1996). Thesemechanisms can lead to positive, negative or unimodal (hump-shaped) relationships among host resource acquisition, parasitereproduction, transmission and the virulence of infection (Cress-ler et al. 2014). In natural populations, per capita resource acqui-sition rates are extremely variable because they depend onresource density and quality, competition among consumers andabiotic factors (Hargrave et al. 2011). Bioenergetic theory mech-anistically links how organisms acquire and use energy. By for-malising the role of hosts and parasites as resource consumers,bioenergetic theory for infection could predict how epidemiologi-cal traits respond to the variation in densities of hosts andresources that occurs across space and during epidemics.Here, we develop bioenergetic theory for infection dynamics

using a case study of the human parasite Schistosoma mansoni(Sambon) and its snail intermediate host Biomphalaria glabrata(Say). More than 250 million humans are infected with schisto-somes, which disproportionately harm children (Hotez et al.2014). Humans become infected following contact with cercariae,larval schistosomes released by intermediate snail hosts, in fresh-water environments. Cercarial production rates of individual

1Department of Biology, Emory University, 1510 Clifton Rd NE, 30322 Atlanta,

GA,USA2Global Health Institute, Duke University, Durham, NC, USA3Department of Statistics, Virginia Polytechnic Institute and State University,

Blacksburg, VA, USA

4Department of Ecology, Evolution, and Marine Biology, University of Califor-

nia, Santa Barbara, UCSB, 93106 Santa Barbara, CA, USA5Department of Integrative Biology, University of South Florida, 4202, East

Fowler Ave., 33620 Tampa, FL, USA

*Correspondence: E-mail: dcivite@emory.edu

© 2018 John Wiley & Sons Ltd/CNRS

Ecology Letters, (2018) 21: 692–701 doi: 10.1111/ele.12937

snails depend on key intrinsic and extrinsic factors, for examplesnail size, resource quantity/quality and population density(Coles 1973; Keas & Esch 1997; Sandland & Minchella 2003).Building from well-tested metabolic theory for free-living organ-isms (Kooijman 2010), we constructed a model that predicts sev-eral quantitative aspects of within-host infection dynamics byexplicitly tracking the acquisition and use of resources by snailsand parasites. We parameterised the model using an experimentthat manipulated food resources and tracked growth, reproduc-tion, parasite production and survival for snail hosts. Finally, wevalidated the model by simulating infection dynamics for individ-ual hosts experiencing different levels of intraspecific competitionand comparing these predictions to the results of another experi-ment that manipulated host and resource density, and therefore,the intensity of resource competition.

MATERIALS AND METHODS

Model construction

Our model builds on the ‘standard’ model of Dynamic EnergyBudget (DEB) theory for a free-living organism (Kooijman2010). The model tracks changes in the abundance of foodresources in the environment, F, and several host traits: physi-cal length, L (defined here as maximum shell diameter andproportional to the cube root of structural biomass); thescaled density of energy reserves, e; and resources invested inmaturity/development, D, and in reproduction, RH. All quan-tities are modelled through time for an individual host usingcoupled differential equations. We added two modules to thisstandard DEB model to track a within-host population ofparasites and host survival respectively. Within each host, wetrack the change in parasite biomass, P, and the resourcesinvested in parasite reproduction, RP. To model mortality wefollow Gergs & Jager (2014) and introduce a variable repre-senting repairable ‘damage’, with instantaneous hazard rateassumed proportional to damage. In the Supplement, we

present the derivation of dynamic equations for the scaleddamage density, d, and the cumulative mortality hazard, H,for hosts. The model structure is in Fig. 1, Eqs 1–10, statevariables and parameters listed in Table S1, subscripts H andP distinguish host and parasite variables and parameters.

dF

dt¼ �iML2fH ð1Þ

dL

dt¼ gYVE

3vj�aMe� mV þmREMdð ÞvL

gþ e

� �ð2Þ

de

dt¼ aM

vEMLfH � eð Þ � iPMfP

EMp ð3Þ

dD

dt¼ ð1� j�ÞC�mDD ifD\DR

0 ifD�DRð4Þ

dRH

dt¼ 0 ifD\DR

ð1� j�ÞC�mDD ifD�DRð5Þ

dP

dt¼ YPEiPMfPð1� rPÞ �mPð ÞP ð6Þ

dRP

dt¼ cRPYPEiPMfPrP ð7Þ

dddt

¼ HvL3

dRP

dtþ kR 1� eð Þ � kRd� 3d

L

dL

dtð8Þ

dH

dt¼ hb þ hd max d� d0; 0ð Þ ð9Þ

PðSurvivalÞ½t� ¼ e�HðtÞ ð10ÞHosts consume food, F, from the external environment at a

rate determined by the product of three terms: their maximumsurface area-specific ingestion rate, iM; a Type II functionalresponse, fH, with half saturation constant, Fh, and their physicallength squared (which is proportional to surface area; eqn 1).Hosts assimilate energy from food into an energy ‘reserve’, withyield of reserves on food YEF. The maximum assimilation rate,aM, is the product of the maximum ingestion rate and the yieldof reserves on food. Hosts use these reserves to build two typesof biomass : structure (which performs vital functions andrequires maintenance at rate mV) and reproductive matter (re-serve biomass that has been irreversibly committed to offspring).The reserve dynamics in the absence of parasitism are derivedfrom an assumption of ‘weak homeostasis’ (Kooijman 2010).Hosts allocate a constant portion, j, of mobilised reserves, C, tosomatic (vs. reproductive) processes. Hosts grow in length basedon the energetic costs of growing new structural biomass, deter-mined by the yield of structure on reserves, YVE, and the differ-ence between energy mobilised for somatic processes and thecosts of somatic maintenance and repair (eqn 2). Energy nomi-nally allocated to reproduction is used by juveniles for develop-ment, D (eqn 4). Reproduction begins upon achieving thedevelopmental threshold for reproduction, DR, and developmen-tal status is maintained at the specific ratemD.Our model adds a module describing consumption of

reserves by a population of parasites (if infected; eqn 3). Themodule is a parsimonious, general representation of infection

Figure 1 Schematic representation of a dynamic energy budget model (DEB)

for a free-living organism (grey) containing a parasite population (black).

DEB theory tracks the assimilation, A, of food resources, F, from the

environment into energy reserves, E. Energy reserves are then committed, C,

to somatic or reproductive processes according to a fixed fraction allocation

rule, j. Once allocated, reserves pay maintenance costs and any energy

surpluses fuel increases in structural biomass/biovolume (represented here as

length, L) or reproduction, RH. Here, we introduce a parasite population, P,

with three potential effects (black). Parasites consume host reserves (solid

line), stealing resources that were destined for host growth and reproduction.

Parasites (and/or the host’s response to infection) can alter the host’s

allocation to growth and reproduction (dashed line). Parasites also produce

propagules, RP, that disperse from the host (dotted line).

© 2018 John Wiley & Sons Ltd/CNRS

Letter Bioenergetic theory for infection dynamics 693

energetics that incorporates several features of snail–schisto-some biology (Th�eron 1981b; a; Kostova & Chipev 1991).Following a seminal DEB model of infection that has beenexamined qualitatively (Hall et al. 2007, 2009), we representthe parasite as a population, rather than as a change to thehost’s parameter values (e.g. Llandres et al. 2015), becauseschistosomes greatly increase in number during infection. Fol-lowing infection, parasite biomass (eqn 6) increases throughthe ingestion and assimilation of host reserves, following aType II functional response, fP, with a half saturation coeffi-cient, eh, maximum mass-specific ingestion rate, iPM, and yieldof parasite biomass on host reserve, YPE. Parasite biomassalso decreases through maintenance at a specific rate mP. Aproportion, rp, of the assimilated reserve is allocated to para-site reproduction, while the rest, (1–rp), is allocated to parasitebiomass growth. A reader with experience in DEB theoryshould note that this population representation could also beobtained by assuming (1) that individual parasites are ‘V1-morphs’ (Kooijman 2010), (2) rapid equilibration of reservedensity and (3) rapid turnover of reserves. These latter twoassumptions parallel those underlying the ‘DEBkiss’ approxi-mation of standard DEB (Jager et al. 2013).The allocation proportion rp itself is assumed to increase as a

sigmoid function of parasite density within the host, with aninflection point at ph (Table S1). This parasite allocation func-tion reflects within-host density dependence in parasite growthand limitations of physical space. Furthermore, it influences thetiming of parasite reproduction and the maximum density ofparasite biomass within host tissue (G�erard et al. 1993). Para-site offspring biomass increases from parasite allocation toreproduction, with the relative yield of parasite reproductionbiomass on assimilated reserve, cRP. In addition, infection canmodulate the host’s realised allocation between soma andreproduction, j�, with parasite density-dependent manipulationrate, a, yielding an effective allocation rule, j� = min(j + aP).Thus, parasites may affect the host’s energy budget in twodirect ways: direct consumption of host reserves and by modu-lating the host’s energy allocation rule. If infection diverts hostallocation from reproduction to growth, then it can catalysetwo widespread phenomena: parasitic castration, the rapidreduction/cessation of reproduction by infected hosts, and hostgigantism, increased growth of infected hosts relative to unin-fected hosts (Hall et al. 2007; Lafferty & Kuris 2009).We assume that hosts die from damage caused by low

energy reserve density, ‘reserve depletion’, or emerging para-site offspring. Therefore, we implemented extensions of thestandard DEB model to account for mild and severe hoststarvation caused by low reserve density, and linked theseextensions to a survival module that tracks mortality riskcaused by damage from starvation and parasite emergencebased on the stochastic death model of the Generalized Uni-fied Threshold model of Survival (GUTS) framework (Gergs& Jager 2014). Scaled damage density, d, increases due to therelease of parasite offspring with damage intensity, Θ. Thedamage repair rate, kR, determines the rate of damage causedby reserve depletion and the damage repair. Damage densityalso decreases through dilution by growth (eqn 8). Damagerepair by hosts may be energetically costly, and we assumethat these costs, mR, are a specified component of somatic

maintenance for the host. The cumulative hazard, H, experi-enced by hosts increases with the background hazard rate, hb,and a linear function of damage density beyond a threshold,d0, with hazard coefficient hd (eqn 9). Host survival probabil-ity, P(Survival[t]) is a negative exponential function of cumu-lative hazard, H, (eqn 10). Several derived parameters andfunctions simplify the presentation of the model or the statis-tical analysis (Table S1). When we fit these models to data(see the Supplement for additional details), we assumed thatbiomass invested in host or parasite reproduction are immedi-ately released as eggs or parasite propagules, with carbon con-tent per host egg, eH, or parasite propagule, eP.

Resource supply experiment

We manipulated resource supply rates and tracked thegrowth, reproduction, parasite production and survival ofsnail hosts weekly to parameterise our model. We factoriallycrossed exposure of randomly selected 28-day-old Biom-phalaria glabrata snails (NMRI strain, length = 4.66 � 0.05SE) to parasites (0 or 8 freshly hatched miracidia of Schisto-soma mansoni [NMRI strain] for 24 h in 5 mL HHCOMBOlake water media) and resource supply rates (0.6875, 1.375,2.75, 5.5, 11 or 16.5 mg C dry weight per twice-weekly feedingof high quality food). We fed snails a homogenised blend of6 g dry powdered organic Spirulina algae (Now Organics,Bloomingdale, IL, USA) and 6 g fish flakes (Omega OneFreshwater Flakes, OmegaSea, Painsville, OH, USA) in 1 gagar dissolved in 100 mL deionised water (diet was 47% Cand 10% N; NC2100 Elemental Analyzer, CE Elantech Inc.,Lakewood, NJ, USA). The number of replicates per supplyrate differed for exposed (n = 16) and unexposed (n = 5) treat-ments. We excluded exposed hosts from the analysis if theynever released cercariae (33% of exposed hosts) because wecould not definitively detect successful infection. In almost allcases, visual diagnosis confirmed that these hosts were unin-fected. Therefore, these exclusions are unlikely to bias esti-mates of parasite production from infected hosts. Thisexclusion resulted in samples sizes of n = 10–12 infected hostsfor each resource treatment, which decreased through time ashosts died (see Supplement for additional details).

Resource competition experiment

We followed identical methods as in the resource supplyexperiment with the following changes. We marked andexposed focal 28-day-old snails (length: 4.30 � 0.06 SE) andmanipulated resource supply rates (5.5, 11 or 16.5 mg C dryweight per feeding) and the abundance of uninfected con-specifics (0, 1, 3, 5 or 7 21-day-old snails, length: 3.76 � 0.04SE; due to numerical limitation of 28-day-old individuals, 16replicates per zero competitor treatment and eight replicatesfor all other treatments). We also established parasite-freereplicates containing 1, 2, 4, 6 or 8 uninfected 21-day-oldsnails (length 3.47 � 0.05 SE, four replicates per treatment).We also added three replicates to generate ‘replacement’ con-specifics for experimental replicates if an uninfected competi-tor died prior to the focal host (in an infected treatment) orbefore the end of the experiment (in an unexposed treatment).

© 2018 John Wiley & Sons Ltd/CNRS

694 D. J. Civitello et al. Letter

This resulted in initial samples sizes of n = 4–11 for eachtreatment with an infected focal host except for the high food– 1 conspecific treatment, which had n = 1, and n = 4 for allparasite-free replicates (N = 146).

Model parameterisation, performance and validation

We parameterised our model of infection dynamics by simu-lating infections and comparing predictions for host length,cumulative host and parasite reproduction, and host survivalsimultaneously for each infected and uninfected host in theresource supply experiment in a Bayesian framework (see Sup-plement for additional details on priors, likelihood model andMCMC sampling). We assessed model performance with theconcordance correlation coefficient, rc (for length, reproduc-tion and parasite production), and the area under the receiveroperating characteristic, AUC (for survival), calculated sepa-rately for each time series from all observations (i.e. across allindividual trajectories; Hanley & McNeil 1982; Lin 1989). Wevalidated the model by challenging it to predict the results ofthe resource competition experiment in which we factoriallymanipulated resource availability and the density of unin-fected conspecifics for focal infected or uninfected hosts. Forthe validation step, we simulated life history trajectories forinfected focal hosts and uninfected competitors as well as theuninfected groups based on the posterior distribution derivedfrom the first experiment only, with the experimental condi-tions (host density and resource supply) imposed for eachtreatment treated as known. Specifically, we modified the fooddynamic equation to include depletion of food by all compet-ing hosts according to their size-dependent feeding rates. Wecalculated rc and AUC values as above for these a priori pre-dictions for each observation. Additionally, to generate oursecond set of predictions, we refit the model to both data setssimultaneously as described above, which is equivalent to fit-ting the model to the second experiment using the joint poste-rior distribution of parameters from the first experiment asthe prior for the second, subject to the numerical accuracy ofthe MCMC (Kruschke 2014). We conducted analyses withreplicate MCMC chains after discarding a burn-in. We usedthinned chains for computational efficiency to calculate theposterior mean solution for the dynamical system and 99%posterior credible intervals around this mean.

Epidemiological consequences of resource-dependent cercarial

production

We used a general epidemiological model to investigate howresource-dependent cercarial production could alter the effi-cacy of snail control programmes for the control of humanrisk of exposure. The model, a variant of that in Civitello &Rohr (2014), tracks the densities of resources, R, susceptiblesnail hosts, S, infected snail hosts, I, and human-infectiouscercariae, C, in the aquatic environment:

dR

dt¼ r 1� R

K

� �R� fR Sþ Ið Þ ð11Þ

dS

dt¼ efR Sþ qIð Þ � dS� bSM ð12Þ

dI

dt¼ bSM� dþ vð ÞI ð13Þ

dC

dt¼ r Rð ÞI�mC ð14Þ

Resources grow logistically with a maximal growth rate, r,and carrying capacity, K. Resources are consumed by both hostclasses following a linear functional response with feeding rate f(eqn 11). Susceptible hosts increase based on resource con-sumption by both host types with conversion efficiency e, andinfected hosts exhibit partial castration, with a relative repro-ductive rate 0 ≤ q ≤ 1 (eqn 12). Susceptible hosts decreasethrough background mortality at rate d and infection with mir-acidia, at constant density M, with transmission rate b. Infectedsnails increase from transmission and die at an elevated ratedue to parasite virulence, v (eqn 13). Free-living cercariae arereleased into the environment by infected hosts according to afunction that may depend on resource density, r(R) (eqn 14).Cercariae die with a background mortality rate, m. We com-pared two cercarial release functions: constant production, inwhich release is independent of resources (eqn 15) andresource-dependent production, in which cercarial release is alinear function of resource availability (eqn 16):

r Rð Þ ¼ r ð15Þr Rð Þ ¼ rR ð16Þnoting that eqn 16, embodies qualitatively our findings shownin Fig. 2e.

RESULTS

Model parameterisation – resource supply experiment

We parameterised our model with an experiment that manip-ulated resource availability and tracked the growth, repro-duction, parasite production and survival of snail hosts.Across the 24-fold gradient of resource supply rates, finallength and reproduction of uninfected snail hosts increased2.7- and c. 6000-fold respectively (Fig. 2a and c). Similarly,final length of infected hosts increased 2.4-fold and lifetimereproduction by infected hosts increased from 0 to c. 120eggs over this gradient (Fig. 2b and d). Cumulative parasiteproduction by infected hosts increased c. 60-fold across thesupply gradient (Fig. 2e). Survival of uninfected hostsincreased with resource supply, but infection increased hostmortality (Fig. 2f and g). The fitted bioenergetic modelexplained the vast majority of variation in these quantities(see Fig. S1 and Table S2 for marginal posterior distributionsand highest posterior density estimates of all parameters).Concordance correlation coefficients, rc, spanned 0.75–0.98for the growth, reproduction and parasite production timeseries. The model predicted more rapid mortality of infectedhosts than was observed, which likely reflects the compromiseof fitting seven time series simultaneously. Nonetheless, AUCvalues for host survival were moderate, spanning 0.75–0.81(Fig. 2). Infection permanently reduced snail reproduction,but it temporarily boosted growth relative to uninfected hosts(Figs 2, S2). Ultimately, however, infected hosts were smallerthan uninfected hosts.

© 2018 John Wiley & Sons Ltd/CNRS

Letter Bioenergetic theory for infection dynamics 695

Model validation – resource competition experiment

Parameterised with the resource supply experiment, the modelpredicted strong indirect negative effects of host density on hostgrowth, reproduction and parasite production that are enhanced

under low resource supply rates (Fig. S3). The results of theexperiment echoed these predictions. For example, cercarial pro-duction increased with resource supply, yet competition from upto seven uninfected conspecifics reduced lifetime cercarial pro-duction of focal hosts by c. 40-fold relative to the competitor-freetreatments in the lowest supply rate (Fig. 3d) and c. 20-foldunder higher supply rates (Fig. 3e–f). There were similarly strongeffects of resource supply and competition on host growth andreproduction (Fig. S3), as well as growth and reproduction byinfection-free control groups (Fig. S3). These predictionsmatched the observed infection dynamics well, the AUC was highfor host survival (AUC = 0.78), and rc values were high for hostgrowth (all rc ≥ 0.87) and moderate for cercarial production(rc = 0.76) and host reproduction (rc = 0.64–0.79; Fig S3).Fitting the model to the resource supply and resource competi-

tion experiments jointly improved the match to the data, and rcvalues for infected hosts improved to 0.89 for growth, 0.94 forcercarial production and 0.68 for reproduction, while AUCincreased to 0.89 for survival (Fig. 3). Model predictions for thedynamics of growth (rc = 0.93) and reproduction (rc = 0.78) byunexposed snail hosts also improved (Fig. S4; see Fig. S1 formarginal posterior distributions of parameters). Despite changesto some parameter estimates, this parameterisation retained anextremely strong fit to the resource supply experiment (Fig. S5).

Epidemiological consequences of resource-dependent cercarial

production

The constant production and resource-dependent productionmodel variants both yield analytically tractable equilibria. Forboth models, the equilibria for R, S, and I are identical(eqs 17–19):

R� ¼ ðdþ vÞðdþMbÞefðdþ vþMbqÞ ð17Þ

S � ¼ r dþ vð Þ efK� d�Mbð Þ dþ vð Þ þ efKMbqð Þef 2K dþ vþMbð Þ dþ vþMbqð Þ ð18Þ

I� ¼ rMb efK� d�Mbð Þ dþ vð Þ þ efKMbqð Þef 2K dþ vþMbð Þ dþ vþMbqð Þ ð19Þ

For the constant-production model, C� (Eq. 20) follows indirect proportion from the density of infected hosts:

C�CP ¼ rrMb efK� d�Mbð Þ dþ vð Þ þ efKMbqð Þ

mef 2K dþ vþMbð Þ dþ vþMbqð Þ ¼ rmI� ð20Þ

In contrast, for the resource-dependent production model,C� (eqn 21) becomes a function of both I� and R�:

C�RDP ¼

rrMb dþ vð Þ dþMbð Þ efK�d�Mbð Þ dþ vð Þþ efKMbqð Þe2f 3Km dþ vþMbð Þ dþ vþMbqð Þ2

¼ rmI�R�

ð21Þ

The equilibrium density of resource, R�, drives the uni-modal response of cercarial density to snail control, becauseR� itself is a unimodal function of host background deathrates. The equilibrium density of cercariae, C�, is maximised

Figure 2 Resource-dependent life history and infection dynamics in an

experiment manipulating resource supply rate (colours) and infection status

(columns) for individual hosts. Prediction lines and shaded envelopes

correspond to the mean and 99% posterior distribution of the mean dynamics

of the bioenergetic model. For clarity, data points correspond to treatment

means � SE, although the model was fit to the individual observations.

Growth (a) and cumulative reproduction (c) of uninfected hosts increased

substantially over the 24-fold resource supply gradient, with c. 3- and 6000-

fold increases respectively. Host survival increased with resource supply (e),

and infection increased host mortality in all but the lowest resource supply

treatments (f). Infected host growth, reproduction and parasite production

also increased substantially over the resource gradient, by approximately 2.5-

fold, from 0 to 120 offspring, and 60-fold, respectively (b, d, g). The model

explains these dynamics extremely well, with all rc = 0.75–0.98, and

AUC = 0.75–0.81; however, it predicted more rapid mortality of infected

hosts than we observed, especially for low resource supply treatments (F).

© 2018 John Wiley & Sons Ltd/CNRS

696 D. J. Civitello et al. Letter

at an intermediate background death rate, d� (Fig. 4) whichcannot be calculated explicitly.

DISCUSSION

Resource acquisition drives tremendous variation in life his-tory and infection dynamics. In the resource supply

experiment, lifetime production of human-infectious cercariaeby infected snails increased approximately 60-fold over the 24-fold gradient. The fitted bioenergetic model explained muchof the variation in these dynamic multivariate (length, repro-duction, parasite production and survival) responses (Fig. 2).The positive resource–parasite production pattern observedhere and the strong explanatory power of the model suggest

Figure 3 Host density- and resource-dependent infection dynamics in an experiment manipulating uninfected competitor density (colours) and resource

supply rates (columns). Prediction lines and envelopes correspond to the mean and 99% posterior distribution of the mean dynamics based on the fitting of

the bioenergetic model to this experiment using the posterior distributions of the parameters from the resource gradient experiment as priors. For clarity,

data points correspond to treatment means � SE, although the model was fit to the individual observations. Growth of infected focal hosts (a–c), parasiteproduction by focal hosts (d–f), growth of competitors (g–i) and reproduction by all hosts (j–l) all increased with resource supply but decreased with

competitor density. The survival of focal infected hosts (m–o) was similar across the resource and competitor density gradients. The parameterised model

predicted growth, parasite production and survival extremely well (all rc ≥ 0.89, AUC = 0.89). The model predicted total reproduction slightly less

successfully (j–l), especially at the lowest resource supply (J), but still agreed well with the observed dynamics (rc = 0.68).

© 2018 John Wiley & Sons Ltd/CNRS

Letter Bioenergetic theory for infection dynamics 697

that resources, rather than the deployment of costly immunedefence (which is not explicitly included in this model, andoften generates negative resource-parasite production relation-ships; Cressler et al. 2014), primarily drive variation in para-site success. Indeed, successful S. mansoni infections evadehaemocyte responses of snails that are induced by other para-sites (Loker & Adema 1995; Zahoor et al. 2008). In other sys-tems, resource-dependent immune defences may play a criticalrole in infection dynamics across resource, size or ontogeneticgradients (Cressler et al. 2014).Explicitly adding induced immunity to bioenergetic models

could help understand infection dynamics in systems demon-strating potent and costly host defences, but the consistencyof our model with observations demonstrates that this seemsunnecessary for the specific combination of B. glabrata and S.mansoni used in this study. However, these strains have beenmaintained for > 50 years and may have been selected forhigh parasite productivity. Other snail genotypes or speciesmight exhibit greater constitutive or induced resistance toinfection by local schistosomes. If snails in natural popula-tions can induce costly and effective immune defences, thenincorporating the energetics of immunity would be importantfor predictions in field settings because it can qualitativelychange the relationship between resource supply and cercarial

production. There is genetic variation among snails in theability to rapidly encapsulate and kill invading schistosomemiracidia with haemocytes, primary immune effector cells(Lockyer et al. 2012). However, in another B. glabarata strain(Salvador), starvation increases hemocyte concentrations anddoes not reduce resistance (Nelson et al. 2016). Additionally,the ability to evade or suppress the induction of snail cellularand humoral defences is a common feature of successfultrematode parasites (Coustau et al. 2015), which suggests thatvariation in snail immunity may be more important in deter-mining the probability of infection, but not infection dynam-ics. It could also explain why parasite production increaseswith resource supply in many natural snail–trematode combi-nations (Keas & Esch 1997; Sandland & Minchella 2003;Sepp€al€a et al. 2008). Nonetheless, genetic variation in bioener-getic parameters could identify physiological strategiesexploited by coevolving schistosomes and snails (Ibikounl�eet al. 2012).Flatworms such as schistosomes can cause gigantism, cas-

tration and death of their snail hosts (Lafferty & Kuris 2009).This bioenergetic model suggests that these effects emergefrom parasite strategies of consumption, manipulation andreproduction. Here, we focus on the parameter estimatesderived from fitting both experiments, because these estimatesincorporate all accumulated data. Schistosomes consume c.34% of their biomass in reserve per day, efficiently build andmaintain biomass (YPE � 0.88 and mP � 0.017 d�1), and cer-carial release harms hosts (Θ � 2160; Fig. S1, Table S2). Theparasite appears to produce cercariae inefficiently, cRP � 0.05,but this parameter relates cumulative predictions to cumula-tive counts observed during 2-hour ‘shedding’ intervals eachweek. Therefore, this parameter underestimates true efficiencyof parasite reproduction. Consumption of host reserves byparasites can eliminate host reproduction, and it should con-sistently reduce host growth (Hall et al. 2007). However, thetemporary gigantism of infected hosts is consistent with aninfection-induced shift in the host’s allocation strategytowards somatic processes and away from reproduction,which facilitates a brief period of increased host growthbefore the parasite slows host growth by significantly deplet-ing host reserves (see Supplement for additional details onboth parameter sets).We validated the bioenergetic model by challenging it to

predict the results of a second experiment (i.e. predict dynam-ics to which the model had not been fitted) in which we facto-rially manipulated resource availability and the density ofuninfected conspecifics. Resource competition among hostsdecreases per capita consumption by hosts and thereforeshould predictably reduce growth, reproduction and parasiteproduction. To test this, we first simulated infections in focalsnails that shared the same pool of food resources with anincreasing number of uninfected conspecifics using parametersets drawn from the posterior distribution generated from thefirst (resource supply) experiment. This generated quantitativea priori predictions from the model that we could then com-pare to observed data from this second (resource competition)experiment where we manipulated host density and resourcesupply rates and quantified host traits and parasite produc-tion. Strong predictive ability of the model would indicate

Figure 4 Equilibrium density of human-infectious cercariae, C*, in a

general epidemiological model for human schistosome infections in

aquatic snail populations under two models of cercarial production by

infected snails: constant production (black) and resource-dependent

production (blue). Under the constant-production model, C* always

decreases as snail death rates increase. However, under the resource-

dependent production model, C* responds unimodally to increases in

snail death rates, and it peaks again at an intermediate death rate, d*. If

background death rates are high enough, C* approaches zero because

snail populations go extinct. Parameter values used for plotting both

models: r = 1, K = 1, f = 1, e = 0.5, M = 1, v = 0.04, b = 0.01, q = 0.1

and m = 1. To better match per snail rates of cercarial production and

the scale of plotted values between the two models, we set r = 20 for the

constant-production model and r = 300 for the resource-dependent

production model.

© 2018 John Wiley & Sons Ltd/CNRS

698 D. J. Civitello et al. Letter

that it captures the mechanistic drivers of host density depen-dence. Conversely, poor model performance would indicatethat resource competition among hosts is relatively unimpor-tant or that physiological rates depend on host density inother ways that are not included in our current model,thereby precluding its use for scaling up to the populationlevel or extrapolating across ecological contexts.The parameterised model predicted the growth of infected

and competing hosts very well (all rc ≥ 0.87). The model alsopredicted variation in cercarial production (rc = 0.76) andhost survival (AUC = 0.78; Fig. S3) moderately well. Thus,there was a very good match between the model and theobserved data, especially given that these are a priori predic-tions, not model fitting, to a novel ecological context. Asexpected, directly fitting the model simultaneously to theresults of both experiments improved the match to the multi-variate dynamics for infected and uninfected snails (Fig. 3),while retaining an extremely strong fit to the resource supplyexperiment (Fig. S5). These results indicate that exploitativeresource competition is a dominant driver of infection dynam-ics across host density gradients because it reduces per capitaresource acquisition rates of hosts. The relative importance ofother aspects of competition, for example interference compe-tition, size asymmetry, degradation of environmental qualityor ‘crowding stress’, could also be assessed with extensions ofthis model or supplementary experiments (see Supplement).This within-host model could be fused with a transmissionmodel to generate a fully dynamic model for the aquatic ecol-ogy of schistosomes. Snail infection depends on contact withmiracidia and per-miracidia susceptibility (Civitello & Rohr2014). Intrinsic and extrinsic factors, for example genotype,host size/age, exposure time and temperature shape both ofthese processes (Anderson et al. 2009; Th�eron et al. 2014).Therefore, a stochastic transmission model, in which transmis-sion depends on intrinsic or extrinsic factors, could extend thisbioenergetic model by specifying the probability of parasitebiomass ‘arriving’ in an individual.Infection outcomes that depend on resource and host den-

sity could have important consequences for epidemiologicaldynamics and human risk of parasite exposure, which canenhance predictions and management of disease. There can betremendous variation in resource and host densities acrossspace (Civitello et al. 2015) and parasites themselves candepress host densities and alter resource flow and abundance(Hudson et al. 1998; Sato et al. 2011). Thus, resource-depen-dent traits could drive epidemiological dynamics and humanrisk in otherwise unanticipated ways. The density and infectiv-ity of schistosome cercariae in the aquatic environment drivesecological risk for human exposure to schistosomes (Prentice& Ouma 1984). In practice, however, it can be logisticallychallenging and prohibitively expensive to assess the densityof infectious cercariae under field conditions at relevant scales(Ouma et al. 1989; Hung & Remais 2008). Instead, manage-ment strategies and epidemiological models often assume thatcercarial production per snail is constant, and thereforehuman risk is positively correlated with the density of infectedsnails (Mangal et al. 2008; Sokolow et al. 2015). However,densities of cercariae and infected snails can be poorly corre-lated (Ouma et al. 1989; Muhoho et al. 1997) and the

proportion of infected snails actively releasing cercariae isextremely variable (Hamburger et al. 2004), compromisingfield estimation and model prediction of human risk.This bioenergetic perspective suggests variation in resource

availability and competition could mechanistically explainpart of this mismatch and enhance risk assessment. In particu-lar, total cercarial production by snail populations (and there-fore ecological risk of human exposure) could be low whensnail densities are low (because there are few infected snails)or when snail densities are high (if competition limits per cap-ita parasite production). This potential unimodal relationshipbetween snail density and human risk of exposure could drivethe success or failure of current and proposed methods ofschistosome control, which depend on reducing the density ofsnail vectors through molluscicides or predatory biocontrol(Kariuki et al. 2013; Sokolow et al. 2015). If resource compe-tition in natural snail populations is strong enough, then snailreduction programmes could potentially backfire becausedecreases in intermediate host density could release remaininghosts from resource competition, boosting per host rates ofparasite production (Fig. 4). This effect echoes overcompensa-tion in age-structured models, where increased mortality ratescan counterintuitively raise the densities of specific life stagesor the total population (Schr€oder et al. 2014). In stage-struc-tured models, overcompensation can occur because increaseddeath rates reduce competition for a shared resource, boostingthe resource-dependent reproductive rates of surviving individ-uals. Overcompensatory effects have been observed in plantand animal systems, and they may explain why efforts to con-trol pest species can backfire (Zipkin et al. 2009). Resource-dependent production of cercariae by snail hosts raises thepossibility of similar complications for the control of humanschistosomes. However, this potential failure of controldepends on the intensity of snail control. If snail controlincreases death rates sufficiently, then it can reduce cercarialdensities or even extirpate snail populations, thereby reducingecological risk of human exposure (Fig. 4).More quantitative data on resource availability, snail densi-

ties and sizes, and cercarial production rates by infected snailsin natural transmission sites are still needed to assess the impor-tance of resource competition among snail hosts for control ofhuman risk of exposure to schistosomes. Therefore, we encour-age snail monitoring and elimination programmes to estimateper capita schistosome release rates or the starvation times offield-collected snails whenever possible. We also call for popula-tion-level models, experiments and field surveys to assess theimportance of these ecological feedbacks for epidemiologicaldynamics and human risk of exposure to schistosomes at thepopulation level and across disease systems more broadly.

ACKNOWLEDGEMENTS

Savannah Poor and Karena Nguyen assisted with the datacollection. David Lewis and Bert Anderson conducted the ele-mental analyses on snail food. Snails and schistosomes wereobtained through BEI Resources, NIAID, NIH. DJC wassupported by an NIH NRSA postdoctoral fellowshipF32AI112255. RMN was supported by US EPA STAR grant835797. LRJ was supported by NSF PLR 1341649.

© 2018 John Wiley & Sons Ltd/CNRS

Letter Bioenergetic theory for infection dynamics 699

AUTHORSHIP

DJC, RMN and JRR conceived the study, DJC and HF con-ducted the experiments, DJC, LRJ, RMN and JRR developedthe analysis, DJC wrote the paper, and all authors edited it.

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SUPPORTING INFORMATION

Additional Supporting Information may be found online inthe supporting information tab for this article.

Editor, Frida Ben-AmiManuscript received 29 June 2017First decision made 4 August 2017Second decision made 3 November 2017Third decision made 12 February 2018Manuscript accepted 13 February 2018

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Letter Bioenergetic theory for infection dynamics 701