A Metabolic and Body-Size Scaling Framework for Parasite Within

vol. 182, no. 2 the american naturalist august 2013

A Metabolic and Body-Size Scaling Framework for Parasite

Within-Host Abundance, Biomass, and Energy Flux

Ryan F. Hechinger*

Marine Science Institute and the Department of Ecology, Evolution, and Marine Biology, University of California, Santa Barbara,California 93106

Submitted October 24, 2012; Accepted March 8, 2013; Electronically published June 21, 2013

Dryad data: http://dx.doi.org/10.5061/dryad.14nn1.

abstract: Energetics may provide a useful currency for studyingthe ecology of parasite assemblages within individual hosts. Parasiteassemblages may also provide powerful models to study general prin-ciples of ecological energetics. Yet there has been little ecologicalresearch on parasite-host energetics, probably due to methodologicaldifficulties. However, the scaling relationships of individual metabolicrate with body or cell size and temperature may permit us to tacklethe energetics of parasite assemblages in hosts. This article offers thefoundations and initial testing of a metabolic theory of ecology(MTE) framework for parasites in hosts. I first provide equations toestimate energetic flux through observed parasite assemblages. I thendevelop metabolic scaling theory for parasite abundance, energetics,and biomass in individual hosts. In contrast to previous efforts, thetheory factors in both host and parasite metabolic scaling, how par-asites use host space, and whether energy or space dictates carryingcapacity. Empirical tests indicate that host energetic flux can setparasite carrying capacity, which decreases as predicted consideringthe scaling of host and parasite metabolic rates. The theory and resultsalso highlight that the phenomenon of “energetic equivalence” is notan assumption of MTE but a possible outcome contingent on howspecies partition resources. Hence, applying MTE to parasites canlend mechanistic, quantitative, predictive insight into the nature ofparasitism and can inform general ecological theory.

Keywords: metabolic theory of ecology, parasite communities, infra-population, infracommunity, pathology, virulence.

Introduction

When we get sick—particularly with infectious agents—we frequently invoke language concerning the energeticimpacts of infection. For instance, we speak of having our“energy drained.” This common language underscores thatenergy may provide a useful currency to investigate theimpacts of infectious agents, or parasites, on their hosts.In fact, an energetics perspective may apply more broadlyto the ecology of parasites within hosts. Although this was

* E-mail: [email protected].

Am. Nat. 2013. Vol. 182, pp. 234–248. � 2013 by The University of Chicago.

0003-0147/2013/18202-54211$15.00. All rights reserved.

DOI: 10.1086/670820

recognized decades ago (Noble 1974), very little researchhas examined the energetics of both parasites and hosts(e.g., Walkey and Meakins 1970; Bailey 1975; Munger andKarasov 1994). The lack of such research almost certainlyreflects the difficult nature of precise, detailed studies ofenergetics of both parasites and their hosts, particularlywhen dealing with multiple parasite species. This articleoffers a possible solution. I present and provide initialtesting of a framework that may readily permit us to studyand predict the energetics, biomass, and abundance ofparasites within hosts. The framework is quantitative, im-mediately implementable, and testable, and it uses the scal-ing relationships of metabolic rate with body size andtemperature.

What has become known as the metabolic theory ofecology (MTE) is a formulation of metabolic ecology(Brown et al. 2004; Brown et al. 2012). Metabolic ecologyseeks to use individual metabolism—the transformationand use of energy and materials by individual organisms—as the foundation for a theoretical unification of ecology.This is sensible, because we can readily express many eco-logical interactions in terms of the processing and ex-change of energy and materials. For instance, metabolicrate directly reflects energy use and, consequently, demandon resources (Peters 1983; Brown et al. 2004). MTE putsmetabolic ecology to practice by capitalizing on the scalingrelationships of individual metabolic rate with body tem-perature and body size (pcell size for single-celled or-ganisms; e.g., Robinson et al. 1983; Gillooly et al. 2001;Makarieva et al. 2008; DeLong et al. 2010). Temperatureand body size are readily available variables. Therefore,MTE is particularly implementable at broad scales, sayentire assemblages and communities, as we can estimatemetabolic rates for even poorly studied species. In additionto reflecting energy use, metabolic rate also appears to setthe pace of other ecologically important biological rates(e.g., growth, reproduction, and mortality). These ratesalso scale with body size and temperature (Peters 1983;

http://dx.doi.org/10.5061/dryad.14nn1

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Parasite Abundance, Biomass, Energetics 235

16g

A1g

16g

B

16g

Numbers: 17 vs 2 8xBiomass: 32 vs 32 1xEnergy Flux: 21 vs 10 2x

1g1g

1g

1g

1g

1g

1g1g

1g

1g

1g

1g

1g1g

1g

Figure 1: Different currencies and their implications for depicting parasite assemblages within hosts, focusing on impacts on hosts. Thereare two host individuals (A and B) and two parasite species, one with individuals weighing 16 g and the other with individuals weighing1 g. The parasites otherwise similarly use their hosts. Numbers are clearly insufficient for depicting parasite impacts on hosts; no one wouldthink that the parasites affect host A eight times more than they do host B. Despite having different parasite numbers, the two hosts bothharbor equivalent parasite biomass. However, in host A, half of the biomass is composed of small-bodied parasites. Given metabolic scaling,smaller-bodied parasites burn more calories per gram of tissue (they have higher mass-specific metabolic rates). Hence, using equations(2) and (3) indicates that the energy fluxed through parasites in host A is two times the amount fluxed through host B. Clearly, currencychoice can substantially affect our depiction of parasites within hosts.

Calder 1984; Schmidt-Nielsen 1984; Sibly et al. 2012).Hence, by building on the scaling relationships of indi-vidual metabolic rate, MTE has promise of facilitatingquantitative, mechanistic, and predictive research exam-ining broad patterns and processes characterizing popu-lations, communities, and ecosystems (Brown et al. 2004;Marquet et al. 2005; Sibly et al. 2012).

Parasites form assemblages within individual hosts. Agroup of conspecifics within a single host is termed an“infrapopulation,” distinguishing them from the broaderparasite population occurring in the surrounding ecosys-tem (Bush et al. 1997). Similarly, mixed-species groups arecalled “infracommunities.” These parasite assemblages in-teract with their hosts, sometimes causing disease. Themembers of infracommunities also interact with eachother through a suite of direct and indirect interactions(reviewed in Dobson 1985; Esch et al. 1990; Poulin 1998).Can we apply MTE to parasite infrapopulations and in-fracommunities to gain insight on the ecology of infectiousdisease and parasites?

We should expect that MTE might benefit parasitologybecause metabolism and body size are intensely inter-twined with parasitism. Hosts provide food and space toparasite infrapopulations and infracommunities. There-fore, host metabolic rate and body size should directlyinfluence parasites in terms of providing energy or spaceresources. At the same time, parasites also have bodies andmetabolic rates, and their energetic demands should affecttheir hosts and competing parasites. Because free-livingspecies and parasites both appear to follow general met-

abolic scaling relationships (but see Hechinger et al. 2012for issues concerning available data for parasites), there isa clear possibility of using the scaling of host and parasitemetabolism to inform parasitology.

Another advantage of MTE for parasitology is that ituses energy as a currency. Parasitology typically focuseson the number of parasite individuals per host. However,focusing on numbers limits generalizing to other species,and it can be meaningless when dealing with parasite spe-cies that differ in body size (fig. 1). Biomass or biovolumehas been considered as an alternative currency to numbersfor parasite infrapopulations and infracommunities(Rohde et al. 1994; George-Nascimento et al. 2004; Munozand Cribb 2005; Munoz and George-Nascimento 2008).Although using biomass is a good step, it may not performwell if energetics is important and the community underinvestigation is composed of parasites that vary in bodysize and mass-specific metabolic rates (fig. 1). In thesecases, equal biomasses will process different amounts ofenergy. Therefore, energy flux (e.g., J s�1) may best reflectthe interactions of parasite with their hosts and with eachother. I hasten to add that emphasizing energy does notrequire abandoning the traditional currencies of numbersor biomass. In fact, by focusing on the relationship be-tween individual body size and metabolic rate, MTE di-rectly links energy to numbers and biomass (Brown et al.2004; Gillooly et al. 2006).

Previous, pioneering studies have examined the body-size scaling of parasite infrapopulation or infracommunityabundance or biomass. For instance, Arneberg et al. (1998)

236 The American Naturalist

and Morand and Poulin (2002) examined the empiricalscaling of nematode parasite population abundance inhosts. However, they did not have the goal of constructingabundance scaling theory and did not consider how hostmetabolic rates could provide resources to parasites.George-Nascimento et al. (2004) and Poulin and George-Nascimento (2007) developed metabolic scaling theory forhow parasite infracommunity biomass would scale withhost body size. However, that theory assumes that parasitesmetabolize at the same mass-specific rates characterizingtheir hosts. That is, the theory assumes that parasite met-abolic rates do not scale with their own bodies, which isinconsistent with available, albeit limited, data (Hechingeret al. 2012). Those two studies also took a conceptualmisstep in applying a prediction for biomass productionto standing-stock biomass (discussed later in this article).

Here, I offer the foundations and initial testing of amore fully specified metabolic, body-size scaling frame-work for parasite infrapopulations and infracommunities.The next section first covers the basics of individual met-abolic rate (energy flux) scaling with body size. I thenpresent equations that estimate energetic flux through ob-served infrapopulations and infracommunities. Theseequations provide a new way to depict parasite infrapop-ulations and infracommunities, including impacts onhosts, as the energy flowing through parasites was takenfrom their hosts. After that, I develop an MTE-based the-ory to predict within-host maximal or carrying-capacityparasite abundance, energy flux, and biomass. Contraryto previous work, the theory factors in both parasite andhost metabolic scaling and the way that parasites use hostspace. Paralleling standard MTE abundance theory, partof the framework applies to situations where energy con-strains parasite infrapopulations and infracommunities.However, I also provide equations for the alternative sit-uation where space, not energy, constrains parasites. Un-derstanding whether energy or space or both influencesparasites is of clear importance for understanding the na-ture of parasitism and bears on efforts to use parasiteinfracommunities as model systems. Finally, I provide re-sults of initial empirical testing of several aspects of thetheory. The results support the promise of the MTE frame-work for parasites within hosts and indicates that, for theexamined parasites, abundance follows the energy-con-straints framework better than the space-constraintsframework.

Theory

Metabolic Rate Scaling

Whole-organism metabolic rate, I, scales allometricallywith body size, M, and varies with temperature, T, as

aI p iM f(T). (1)

In equation (1), i is a normalization constant that variesfor organisms of different physiological types (e.g., plants,endothermic vertebrates, or invertebrates; Brown et al.2004; Marquet et al. 2004; Sibly et al. 2012). The M rep-resents body size in mass units. It is possible to apply theequation to intraspecific body-size variation (Glazier2005). However, in cross-species or cross-population work,M can be taken as the mean body size characterizing aspecies or local population, and this is the conceptuali-zation on which this article focuses. Interspecifically, acrossa wide range of multicellular species, the scaling exponent,a, is often ∼3/4 (e.g., Kleiber 1932; Hemmingsen 1960;Peters 1983; Savage et al. 2004; Glazier 2005). Recent workindicates that a different value characterizes a for unicel-lular organisms, unicellular eukaryote metabolic rates ap-pear to scale with body (cell) size with an exponent of 1,and bacteria scale with an exponent larger than 1 (Mak-arieva et al. 2008; DeLong et al. 2010). The f (T) functionrepresents the influence of temperature on metabolic rate.MTE has primarily used e�E/kT, where E is the activationenergy for enzymatic reactions (∼0.63 eV on average foroxidative respiration), k is Boltzmann’s constant( ), and T is the average operating�5 �18.62 # 10 eV 7 Ktemperature in degrees Kelvin (Gillooly et al. 2001; Brownet al. 2004). This term is a formulation of the Arrheniusequation, which can capture the kinetic influence of a widerange of temperatures on metabolic rate (Gillooly et al.2001; Brown et al. 2004; White et al. 2012). For simplicity,in this article I will use e�E/kT when temperature depen-dence is included in the equations. However, readersshould note that any appropriate temperature-dependencefunction could be incorporated as f (T), including thosethat depict a unimodal response of metabolic rates withtemperatures (e.g., Schoolfield et al. 1981; Molnar et al.2013). The operational criterion is that the term be a di-mensionless, multiplicative modifier.

Energetic Flux of Observed ParasiteInfrapopulations/Communities

By applying metabolic scaling (eq. [1]) to parasites, onecan use observed abundance and body-size informationof parasites to predict the total energy flow through as-semblages of parasites. The energy flux, Fp, characterizinga parasite infrapopulation p, will be the mean individualmetabolic rate Ip (eq. [1]) times the infrapopulation size,Np, so that , orF p I Np p p

a �E/kTpF p (iM e )N . (2)p p p

Total infracommunity energy flux, Ftot, is simply the sum


of constituent infrapopulation fluxes, Fp (eq. [2]), so that, or

s sF p � F p � I Ntot p p ppp1 pp1

s

a �E/kTpF ∝ (iM e )N , (3)�tot p ppp1

where s is the total number of parasite species in a singlehost or in the particular parasite assemblage under inves-tigation (e.g., ectoparasitic lice or gut-dwelling helminths).My first empirical test will employ these equations to es-timate total energy flux in single- and mixed-species par-asite infracommunities.

Scaling of Parasite Abundance, Energy Flux,and Biomass within Hosts

Next I introduce basic MTE abundance theory. I thendiscuss appropriate density units for parasite infrapopu-lations and communities. Following this I present the scal-ing theory for parasite abundance, energy flux, and bio-mass at carrying capacity imposed by either energetic orspace constraints.

Basic MTE Abundance Theory. Standard MTE predictssteady state, maximum population abundance (carryingcapacity) by using the scaling of whole-organism metabolicrate and by factoring in resource supply (Brown et al. 2004;Marquet et al. 2004). At carrying capacity, abundance Ndeclines with body size because a given resource supply,R, supports fewer larger-bodied individuals than smaller-bodied individuals. Individual resource requirements par-allel whole-body metabolic rates, which scale with (eq.aM[1]). Hence, abundance will decrease with body size as

. To simplify notation, I use “∝” to refer to�aN ∝ RMgeneral scaling, dropping specific coefficients, normaliza-tion constants, and temperature effects on metabolic rate.To increase clarity, I will maintain this practice when de-veloping the theory below. However, for precise and ab-solute predictions, temperature effects, coefficients, andnormalization constants are needed (also note the nec-essary addition of a coefficient for resource-supply con-version efficiency). With these issues in mind, we can askhow we can apply MTE abundance theory to parasiteabundance within individual hosts.

What Are the Appropriate Density Units for Parasites inHosts? Parasitology has traditionally focused on the hostindividual as the “quadrat” unit (“intensity” for numbersper infected host, “abundance” when uninfected hosts areincluded; Bush et al. 1997). By itself, this will not serveas a useful measure of density for MTE, particularly ifhosts vary in body size. One should divide parasite num-bers by the aspect of the host that reflects how the parasites

use host space. For instance, host mass, Mh, (or host vol-ume, Vh) makes sense as density unit for parasites thatuse host space in a volumetric way, such as many tissue-or cavity-dwelling parasites. In these cases, density unitswould be N/Mh or N/Vh. However, many parasites use hostsurface areas (e.g., skin-dwelling parasites). Here, for ex-ample, because host external body surfaces often scale withhost body size to the 2/3 power (Calder 1984), for theseparasites the appropriate density units could be . I2/3N/Mh

will use these two exponents (1 and 2/3) as examplesthroughout the text, but one should use whatever scalingexponent is most appropriate for the hosts and parasitesunder investigation. Further, when available, one coulduse more specific information concerning how much of ahost the parasites use. For instance, one could multiplythe host body-size term by a coefficient that represents theproportion of the host mass or surface area used by theparasites under investigation (e.g., in humans, some liceuse only the scalp, malaria uses only the liver and theblood, tapeworms use only a portion of the intestine, etc.).Below, I will use “abundance” for the total number ofparasites per host individual (corresponding to the stan-dard ecological parasitology term) and “density” whenabundance is divided by an aspect of the host (and I willuse host mass, not volume).

Theoretical Assumptions. The scaling theory presented be-low assumes that parasite metabolic rate is related to par-asite body size and temperature. The theory does not as-sume specific values for scaling exponents or temperaturedependence. However, implementing the framework en-tails using whatever values appear best using available the-oretical or empirical information for hosts and parasitesfor either intra- or interspecific applications (e.g., consultGillooly et al. 2001; Glazier 2005; DeLong et al. 2010;Hechinger et al. 2012). Further, the theory assumes bot-tom-up limitation (energy or space) and a “zero-sumgame” for parasite assemblages; it therefore most preciselydepicts parasite assemblages at carrying capacity wheretotal resources are partitioned among species. However,as discussed in the second empirical test section, with anadditional assumption, it can also directly apply to situ-ations where parasites are below carrying capacity.

Theory for Parasite Infrapopulation Carrying-CapacityAbundance. Consider hypothetical parasite infrapopula-tions wherein individuals recruit to, grow, or reproducewithin hosts so that limiting resources reduce populationproduction rates to equal loss rates. I will refer to suchmaximal steady-state abundance as carrying capacity. Ifparasites consume host metabolic products in a volumetricway, hosts will provide resources at a rate parallel to hostmass-specific metabolic rates, which decrease with host


body size as . I will use �g to representa 1 a �1h hM /M p Mh h h

the scaling exponent associated with mass-specific meta-bolic rates (e.g., with 3/4 scaling of whole-body metabolicrate, ). This leads to the pre-�g p a � 1 p �1 p �1/4diction that parasite infrapopulation density at carryingcapacity scales with both host and parasite body size as

j �g �ah h pN/M ∝ M M , (4a)h h p

where is the appropriate spatial density term (e.g., 1jh

for parasites that use host volume and 2/3 for parasitesthat use host external surfaces). Because host mass is thedensity unit, we can rearrange to get total parasite abun-dance at carrying capacity,

j �g �ah h pN ∝ M M . (4b)p h p

Hence, the equation predicts that parasite infrapopula-tion carrying capacity will decrease with increasing par-asite body size, but increase with host body size to the∼3/4 power for parasites that use host volume, and tothe ∼5/12 power for those that use host external surfaces.

If space, not host metabolic rate, limits parasite infra-populations, we drop the host resource-supply term anduse a coefficient to represent the aspect of parasite bodiesthat reflects their spatial packing (e.g., 1 for volume).Hence, under spatial constraints, parasite infrapopulationdensity at carrying capacity decreases with parasite bodysize as

j �jh pN/M ∝ M . (5a)h p

Rearranging predicts that parasite abundance at carryingcapacity increases directly with increasing host space (vol-ume or surface area) used, as

j �jh pN ∝ M M . (5b)p h p

Hence, considering energy or space constraints (eqq. [4]and [5]) results in different predictions for how parasiteabundance should scale with host and parasite body size.My second empirical test will test which equations are mostconsistent with data on nematode abundance in mam-malian hosts. In subsequent theory, I will present only theabundance forms of the equations.

Theory for Parasite Infrapopulation Energy Flux andBiomass. Equation (2) describes the total energy flux ofan observed infrapopulation as . ForapF p I N ∝ M Np p p p p

parasites at energetically determined carrying capacity, wecan predict how energy flux will scale with host body sizebecause we can assume the carrying-capacity abundancescaling described by equation (4b) as .j �g �ah h pN ∝ M Mp h p

Substituting this for Np in the observed infrapopulationflux equation provides a j �g �ap h h pF ∝ M (M M ) ∝p p h p

, orj �g 0h hM Mh p

j �gh hF ∝ M . (6)p h

Thus, equation (6) predicts that the maximum energy fluxthrough a parasite infrapopulation (i.e., one at carryingcapacity) is invariant of parasite body size but scales withhost mass depending on host mass-specific metabolic ratesand how the parasites use host space.

An analogous scaling relationship should occur for max-imum total biomass production rates (amount of biomassproduced via growth and reproduction per unit time) be-cause individual rates of production parallel metabolic ratefor a wide range of free-living species (Ernest et al. 2003).

With space constraints, the maximum energy fluxthrough a parasite infrapopulation will vary with howmany parasites can fill host space as (carryingj jh pM /Mh p

capacity Np (eq. [5b]) multiplied by individual parasitemetabolic rate , givingaI ∝ Mp p

j a �jh p pF ∝ M M . (7)p h p

What is the biomass of a parasite infrapopulation at en-ergy-determined carrying capacity? Parallel to derivingenergy flux, we substitute steady-state infrapopulationabundance (eq. [4b]) into an observed biomass equationto predict that maximum standing-stock biomass of aparasite infrapopulation will be W p M N ∝p p p

, orj �g �ah h pM (M M )p h p

j �g 1�a .h h pW ∝ M M (8)p h p

Thus, in contrast to energy flux and biomass productionbut similarly to individual abundance, equation (8) pre-dicts that both host and parasite body sizes influence themaximum standing-stock biomass of parasite infrapopu-lations under energetic constraints.

We can easily contrast the prediction of the carrying-capacity biomass of a parasite infrapopulation under en-ergetic limitation to one experiencing space limitation.Here, the biomass at carrying capacity will be invariant ofparasite body size and be a simple fraction of host space,such that

jhW ∝ M , (9)p h

where j represents the scaling term from the appropriate(host body) density units for the parasite infrapopulation.

Theory for Parasite Infracommunity Energy Flux andBiomass. If host metabolism constrains the total energyflux of parasites, carrying-capacity flux of a combined par-asite infracommunity, Ftot, must scale the same as the pre-diction for infrapopulations operating under energy lim-itations (eq. [6]), so that

j �gh hF ∝ M . (10)tot h

In multispecies assemblages at carrying capacity, each par-


ticular species will, or course, process a lower level ofenergy than that predicted by the single-species (infra-population) equations given above (eqq. [4]–[9]).

Under space constraints, infracommunity carrying-capacity biomass will be a set proportion of the host (seebelow), but the total energy flux will vary with the relativeabundance of species with different metabolic rates andbody sizes. Without information on parasite species abun-dances, we can make headway by assuming that parasitespecies of different sizes and metabolic rates use, on av-erage, equal portions of host space. In this case, each par-asite species will increase in abundance with host bodysize and decrease with parasite body size as N ∝p

. Hence, energetic flux at spatially determined car-j �jh pM Mh p

rying capacity, , ors s a j �jp h pF p � I N ∝ � M (M M )tot p p p h ppp1 pp1

s

j a �jh p pF ∝ M M . (11)�tot h ppp1

With energetic constraints, the parasite infracommunitystanding-stock biomass, Wtot, supported by a host will alsovary with the relative abundance of species in the infra-community. This is because parasite species process dif-ferent amounts of energy per unit biomass depending ontheir metabolic rates and therefore their body size. Similarto infracommunity carrying-capacity biomass under spaceconstraints, we can progress by assuming that parasite spe-cies of different sizes have, on average, equal access to hostresources. In this case, we can predict infracommunitybiomass at carrying capacity will scale as ,

sW ∝ � Wtot ppp1

or

s

j �g 1�ah h pW ∝ M M . (12)�tot h ppp1

The carrying-capacity biomass of a parasite infracom-munity should therefore increase with host body size (e.g.,to the 3/4 or 5/12 power) and also depend on the metabolicscaling of each parasite species.

We can contrast energetic and space constraints for thecarrying-capacity biomass of parasite infracommunities. Ifparasites are restricted to a certain proportion of hostspace, carrying-capacity biomass will be independent ofthe body sizes of constituent parasite species. Hence, underspace constraints, carrying-capacity biomass will scale as

jhW ∝ M . (13)tot h

Thus, in contrast to energetic constraints, biomass will notdepend on parasite body sizes or metabolic scaling.

The above infracommunity equations (eqq. [10]–[13])most directly apply to parasite infracommunities com-posed of species that use the same space and resourceswithin or among host species. If parasites vary in use ofhosts space or resources within any host species, then con-

sideration of the degree these differences would permitappropriate inflation of carrying capacity (niche overlapindices [Krebs 1999] would be helpful here). If parasitesvary in the use of host resources among host species, thencareful consideration of coefficients and the spatial ex-ponents will explain additional variability. Model 1 pro-vides a summary of the equations presented above and alist of terms with definitions.

Empirical Testing

Does Energy or Biomass Best Reflect InfracommunityCarrying Capacity?

Holmes (1961, 1962) provides classic research representingone of the earliest experimental documentations of inter-specific competition. Holmes studied two gut-dwelling,parasitic worm species that belonged to different phyla,the rat tapeworm and an acanthocephalan. The rat tape-worm is well known to experience an intraspecific “crowd-ing effect” that is at least partly explained by competitionfor glucose (reviewed by Roberts 2000). These worms alsohave near-indeterminant growth, whereby a few worms oreven a single worm may reach carrying capacity in a rat.Holmes experimentally constructed replicate infracom-munities composed of either species by themselves and ofboth species simultaneously. Holmes quantified individualbody sizes and survivorship within the three communitytypes for 8 weeks. A major result from his work is thatinterspecific competition resulted in smaller individualbody sizes, mainly for the tapeworms. To my knowledge,no one has examined whether and how this competitionaffected attributes of the entire infracommunities. How-ever, the data in the articles do permit estimation, usingequations (2) and (3), of the total biomass and energyflux characterizing the three infracommunity types overthe study period.

Figure 2 shows the total standing-stock biomass andestimated energy flux for the two single-species and themixed-species infracommunities. Tapeworm-only infra-communities reached maximum biomass (via individualgrowth) within 3 weeks. This biomass remained the same,or slightly decreased, over the subsequent 5 weeks. Acan-thocephalan-only infracommunities did not reach steady-state biomass but continued to increase over the entire 8-week period (never reaching tapeworm-only infra-community levels). However, when tapeworms weregrown with acanthocephalans, the maximum biomass at-tained was not additive but about one-third lower thanthat achieved by the tapeworms when alone. The energetic-constraints framework predicts the lower carrying-capacitybiomass, given the smaller body sizes and higher mass-specific metabolic rates characterizing the tapeworms in


Model 1: Summary of main models for parasite energy flux, abundance, and biomass in hosts and term definitions

Main modelsObserved parasite assemblages

Infrapopulation energy flux[2] a �E/kTpF p I N p (iM e )Np p p p p

Infracommunity energy flux

[3]s s s

a �E/kTpF p � F p � I N p � (iM e )Ntot p p p p ppp1 pp1 pp1

Predicted maximum steady-state parasite abundance, energy flux, biomassa

InfrapopulationsEnergy constraints Space/biomass constraints

[4] j �g �ah h pN ∝ M Mp h p [5] j �jh pN ∝ M Mp h p

[6] j �gh hF ∝ Mp h [7] j a �jh p pF ∝ M Mp h p

[8] j �g 1�ah h pW ∝ M Mp h p [9] jhW ∝ Mp h

InfracommunitiesEnergy constraints Space/biomass constraints

[10]s

j �gh hF ∝ M �tot hpp1

[11]s

j a �jh p pF ∝ M � Mtot h ppp1

[12]s

j �g 1�ah h pW ∝ M � Mtot h ppp1

[13]s

jhW ∝ M �tot hpp1

Term definitionse�E/kT Arrhenius temperature-dependence term. Can be swapped for any appropriate temperature-dependence term.F Energy flux of infrapopulation or infracommunity.h Subscript denoting a particular host species.I Individual whole-organism metabolic rate.M Individual body size, host or parasite.N Infrapopulation abundance (total number of individuals infecting a host).p, p Subscript denoting a particular parasite species/population.s Number of parasite species in a particular assemblage.tot Subscript denoting aggregate value for entire infracommunity.W Aggregate biomass of infrapopulation or infracommunity.a Exponent for body-size scaling of whole-organism metabolic rate (e.g., ∼3/4 across multicellular species).�g Exponent for mass-specific metabolic rate scaling (e.g., ∼�1/4 across multicellular species).j Spatial exponent for body size of host or parasite (e.g., 1 when volume or 2/3 when surface area is important).

a This figure presents only the abundance forms of the equations. Obtain density by dividing both sides by , the term for host space used by thejhMh

parasites. Density can also use host volumetric or surface area units. However, any statistical analysis using density instead of abundance must contend with

possible “spurious correlations,” given the potential interdependence of response with predictor variables (see appendix).

the mixed-species infracommunities. In fact, estimated to-tal energy flux appeared to not only reach a maximum at3 weeks but reach the same maximum for both saturatedsingle- and mixed-species infracommunities. Hence, thereis evidence for parasitic worm infracommunities reachinga steady state, maximum abundance condition and thatenergy flux reflects this better than does standing-stockbiomass.

Does Energy or Space Better Explain InfrapopulationAbundance Scaling?

Poulin and Morand (2000) assembled data on body sizeand abundance of gut-dwelling nematode parasites ofmammals. Because they also provide host body sizes, wecan use their data to test the predictions of the energetic-

versus space-constraints frameworks (eqq. [4] vs. eqq. [5]).The data are of mean infrapopulation abundances for dif-ferent parasite-host species pairs. Mean abundances willbe less than maximum abundances, to which the scalingtheory most precisely applies. However, assuming thatmean abundance is associated with maximum abundanceand that the proportional degree of unsaturation is notassociated with host or parasite body size, we can use thesedata to test the theoretical scaling exponents and not con-cern ourselves with exact values of the coefficients or nor-malization factors.

Using appropriate values for exponents for these par-asites and hosts, equation (4) predicts thatcarrying-capacity density will allometrically decrease withboth host and parasite body sizes as 1N /M ∝p h

, where represents the decreasing re-�1/4 �3/4 �1/4M M Mh p h


Figure 2: Energy flux better reflects steady state than does standing-stock biomass for experimental parasite infracommunities composedof one or two gut-dwelling worm species. A, Steady-state biomassdecreases under the conditions of interspecific competition that char-acterize the mixed-species infracommunities, while in B steady-stateenergy flux remains the same. Data derived by applying the metabolicscaling equation from Gillooly et al. (2001) for invertebrates at 39�Cto body mass and abundance information from Holmes (1961, 1962).Numbers of worms indicated in the labels represent the number ofinitial recruits, but data use the average amount of worms recoveredfor each species, which was constant among treatments. Error barsrepresent 95% confidence limits, derived by propagating (Taylor1982) the reported standard errors in mean body sizes and using 5df (4–10 infracommunity replicates for each treatment at each week).Data underlying figure 2 are deposited in the Dryad Digital Repos-itory: http://dx.doi.org/10.5061/dryad.14nn1; Hechinger (2013).

source supply rate (host mass-specific metabolic rate)while reflects dividing that resource supply by the�3/4M p

metabolic demands of an individual parasite. We can per-form a similar exercise for space constraints using equation(5), which predicts that parasite density does not vary withhost body size but does scale, isometrically (perfectly in-versely), with parasite body size as .1 �1N /M ∝ Mp h p

We can use a general linear model (GLM) to test whichof the two models the data best support by using a loggedform of the density equation where host and parasite bodysizes are inputted as predictor variables: 1log (N /M ) pp h

. Here, the b variables representb � b log M � b log M0 1 h 2 p

the familiar parameters (intercept and slopes) estimatedby a GLM. Antilogging the equation provides 1N /M pp h

, which clarifies two things. First, the intercept,b0 b1 b210 M Mh p

b0, in the GLM is the log of the compound coefficientmissing in the equations expressed with the ∝ sign. Sec-ond, the slopes estimated by the GLM permit testing thepredictions of both energetic constraints ( ,b p �1/41

) and space constraints models ( ,b p �3/4 b p 0 b p2 1 2

).�1The nematode data are most consistent with energetic

constraints (fig. 3). Both host and parasite body sizes weresignificant predictors of nematode density. The point es-timate for the slope with parasite body size lines up exactlywith the metabolic prediction of �3/4 scaling. However,the estimate has broad confidence limits that also overlap�1, the space constraints prediction. On the other hand,parasite density also decreased with host body size (evenwhile statistically holding parasite body size constant). Thisis inconsistent with space constraints but predicted underenergetic constraints. In fact, dropping the host body-sizeterm resulted in a model that explained only 14% of thevariance, compared to the 30% explained using both hostbody size (reflecting resource supply) and parasite bodysize (reflecting energetic requirements). Therefore, thisanalysis favors the energetic limitation hypothesis and in-dicates the promise of further testing the MTE frameworkfor parasite abundance.

General Discussion

The empirical tests indicate the promise of further testing,implementation, and developing of both aspects of thepresented framework for parasite infrapopulations and in-fracommunities. The analysis of the parasitic worms inrats indicates that parasite infracommunities can reach asaturation point and that energetics, indicated by body-size scaling, best reflect that condition. The nematode spe-cies abundance analysis provides further support for theidea that scaling equations can provide the foundations ofan individual-energetics-based but broad theory for theabundance of parasites in hosts, a theory that factors inboth host and parasite body-size and metabolic scaling.

Observed Energy Flux of ParasiteInfrapopulations/Communities

The first major aspect to this study is the set of equations(eqq. [2] and [3]) to estimate energetic flux of observed



Figure 3: The scaling of parasite density with host and parasite body size (g wet weight) for 76 species of gut-dwelling nematode parasitesin mammalian hosts (data derived from Morand and Poulin 2000). A, Parasite infrapopulation density decreases with increasing host bodysize. Confidence limits for the slope with host body size overlap the �1/4 predicted if host mass-specific metabolic rates constrain parasitedensity and exclude the 0 slope predicted under space constraints. B, Parasite infrapopulation density decreases with parasite body size.The slope estimate is exactly consistent with the �3/4 scaling predicted if parasite metabolic requirements constrain parasite density, butthe confidence limits overlap the �1 slope predicted under space constraints. Data in A and B represent results from a general linear model,holding the other predictor variable to its average (Sall 1990; Quinn and Keough 2002). Ordinary least squares is appropriate because theerror in body-size estimates is certainly much smaller than error in abundances. I used randomization tests to generate the null distribution(10,000 permutations) to calculate P values and proportion of variance explained ( ). The overall general linear equation was2R p 0.30

. See appendix for issues to consider when analyzing the “density” forms of the equationslog (N /M ) p �3.2 � 0.35 log M � 0.75 log Mp h h p

and for several solutions to any issues. Data underlying figure 3 are deposited in the Dryad Digital Repository: http://dx.doi.org/10.5061/dryad.14nn1; Hechinger (2013).

parasite infrapopulations and infracommunities. Theseequations are particularly useful for multispecies studiespartly because they are readily implementable, requiringprimarily inputs of parasite body (or cell) size and tem-perature. The equations are applicable to all taxa of uni-or multicellular parasite and can be used in at least twomajor ways.

The equations permit us to use estimated energy fluxin standard ecological parasitology focused on infrapo-pulations and infracommunities. For instance, energy fluxcan serve as a complementary currency to numbers orbiomass to investigate competitive interactions amongparasites or other aspects of infracommunity structure andfunction, as suggested by the analysis of rat parasitic worminfracommunities.

We can also use equations (2) and (3) to estimate im-pacts on hosts. In fact, host pathology experiments canprovide useful tests of the equations and whether parasiteenergy flux can serve as a useful currency. Such experi-ments should vary numbers and body sizes of parasites ininfracommunities to maximize differences predicted bycurrencies of numbers, biomass, and energy flux. Whichcurrency best reflects pathology? Does energy flux permit

precise and predictive generalization of parasite impactson hosts?

It is important to remark that parasites impact hosts inways beyond the direct energy consumption indicated byequations (2) and (3). Other potentially considerable en-ergetic costs to the host involve repair and defense (in-cluding pathological overresponse; e.g., Lochmiller andDeerenberg 2000). When such information is available, itshould be relatively straightforward to incorporate it intothe equations. Many of these factors will likely also scalewith either parasite or host body size or energy flux. Fur-ther, using equations (2) and (3) to estimate baseline en-ergetic demands of parasites may help interpret the in-consistent ways that hosts metabolically respond toinfection across systems (e.g., Robar et al. 2011). Finally,in some cases, pathology on hosts may be best reflectedby something other than energy. For instance, parasitesmay deprive hosts of a key nutrient (e.g., iron with hookworms; Crompton and Whitehead 1993), release toxins(as with malaria; Pichyangkul et al. 1994), or modify hostbehavior to reduce fitness (e.g., Lafferty and Morris 1996).However, such effects may frequently parallel parasite en-ergetic demands and could be readily incorporated into




the equations. In short, enhancing the equations with non-consumptive impacts of parasites may increase the abilityof MTE to provide a novel perspective for not only eco-logical parasitology but also medical and veterinaryparasitology.

Theory for Scaling of Infrapopulation/CommunityAbundance and Energetics

The second major section of this article is the predictiveand explanatory theory for the scaling of parasite abun-dance, energetics, and biomass (eqq. [4]–[13]). The en-ergetic constraints theory and the analysis of nematodeabundance within hosts indicate that the amount of par-asites within a host is better explained by simultaneouslyconsidering the scaling of host metabolic rate (reflectingresource supply to parasites) and parasite metabolic rate(reflecting energetic requirements of parasites). Hence, itwill be worthwhile to revisit data from the previous ex-aminations of body-size scaling of parasite infrapopula-tion/community abundance, which did not factor in bothhost and parasite metabolic rate scaling (Arneberg et al.1998; Morand and Poulin 2002; George-Nascimento et al.2004; Poulin and George-Nascimento 2007). Contrary tothe empirical findings in this article, there may be con-ditions where space, not energy, will be the limiting re-source for parasites in hosts. However, in such cases, par-asites would have to not use all the energy a host providesto the space occupied by parasites. Given the broad overlapcharacterizing the mass-specific metabolic rates of varioustypes of life forms (Makarieva et al. 2008; DeLong et al.2010), it is difficult to make strong predictions as to whenthis may occur based on metabolic scaling constraints.However, some parasites are relatively inactive (e.g., sometrophically transmitted cyst stages that are waiting for theirhost to be eaten by the next host in the life cycle). Perhapsfor these parasites space, not energy, will be limiting. Theframework provided here can help test this and other ideasconcerning whether energy or space constrains parasiteswithin hosts. The equations make specific and contrastingpredictions that should be particularly testable with par-asitological data that spans a wide range of host and par-asite body sizes where broad patterns among species aremost readily observable and therefore distinguishable.

The predictive scaling equations should apply to alltypes of parasite infracommunities, even if we restrict con-sideration to its ability to make accurate predictions aboutwithin-host carrying capacities. This is because the theorycan apply both directly and indirectly to observed infra-communities. The theory directly applies to those infra-communities that reach carrying capacity. Therefore, itmay generally apply to parasites with closed recruitment—those that primarily build up from reproduction within

the infected host—such as pathogens (sensu Kuris andLafferty 2000; Lafferty and Kuris 2002). These parasitesmay readily saturate habitats within hosts, particularly atpeak levels of infection. The theory should also directlyapply to infracommunities characterized by open recruit-ment—where infectious propagules originate from outsidethe host—if recruitment rates are high or individual par-asites grow a lot. In the later cases, greater individualgrowth can counteract low recruitment rates, resulting insaturated habitats. The first empirical test dealt with sucha system. There are other, natural systems with open re-cruitment where saturation also frequently occurs (e.g.,Bush and Holmes 1986; Stock and Holmes 1988; Munozand George-Nascimento 2008) and to which the scalingtheory should directly apply. Parasitoids will be very in-teresting to consider, as they regularly approach and exceedcarrying capacity. These parasites consume most of theirhost and emerge from dead or dying hosts as part of theirdevelopment. Parasitoids should therefore regularly exceedcarrying capacity but only late in their development.Hence, the scaling theory may therefore provide precisepredictions concerning abundance, energy flux, and bio-mass regularly achieved by several types of parasite.

However, many parasites reach saturation in only asmall percentage of hosts (Holmes and Price 1986; Shawand Dobson 1995; Rohde 2005). This often occurs forsome parasites with open recruitment and lower amountsof individual growth, such as many adult trematode, acan-thocephalan, and copepod parasites. As discussed and evi-denced in the second empirical test section, part of thetheory (scaling exponents) can apply to these parasites ifthe relative degree of unsaturation is not associated withhost or parasite body size. However, we can go furtherand test precise predictions concerning carrying capacityfor such parasites by using data on maximum abundances,as pointed out by Poulin and George-Nascimento (2007).Additionally, we will likely find more direct applicationsby focusing on parasite infracommunities, versus infra-populations, as infracommunities will more frequentlyreach saturation than constituent infrapopulations. Em-phasizing infracommunities is further warranted becausebeing infected by more than a single parasite species islikely the general rule in nature (Petney and Andrews 1998;Cox 2001). However, in any case, for parasites that fre-quently do not saturate within-host habitats, the theorymakes the most precise abundance predictions for only asmall subset of real infracommunities. Therefore, for theseparasites, carrying capacity theory may find its greatest useby examining how observed infracommunities deviatefrom theoretical expectations for carrying capacity.

Because one can now predict carrying capacity, one canquantify the differences between carrying capacity and ob-served—or realized—abundance, energy flux, and bio-


mass. There are several examples where these differencesmay provide insight into processes structuring parasite in-fracommunities, general impacts on hosts, or different par-asite trophic strategies. First, for infracommunities withopen recruitment, the difference between observed abun-dances and carrying capacity may provide an index ofparasite recruitment (transmission) limitation. Second, asmany of us can attest, hosts can maintain infrapopulationswell below carrying capacity by providing “top-down”control of parasite abundance or growth. This is mostlikely for pathogens, which reproduce and recruit withinindividual hosts and would reach carrying capacity if notlimited by host defense (e.g., grooming and immune sys-tems). For these parasites, differences between observedabundances and carrying capacity may reflect variation inhost defense. Third, host mortality likely increases as par-asites approach carrying capacity. Hence, deviations be-tween observed abundance and carrying capacity may re-flect the degree to which infracommunities are at risk ofbeing lost through host mortality. This loss is a majorfactor for host and parasite population dynamics (Ander-son and May 1978; May and Anderson 1979). In short,similar to the way null models can be informative in com-parison to reality (Gotelli and Graves 1996), theory forparasite carrying capacity may be shed light on severalaspects of parasitism to the degree that its expectationsdiffer from observed abundances.

Future enhancement of the scaling framework can focuson directly incorporating the factors that influence thedegree of unsaturation in parasite infracommunities. It willbe interesting if host immune defensive capabilities scalewith body size (e.g., Wiegel and Perelson 2004), but ourunderstanding here is in its infancy. It is also possible thatparasites stimulate host immune systems to a degree thatparallels their metabolic rates. It is also particularly worth-while to examine whether the degree of unsaturation isassociated with epidemiological factors that may scale withhost or parasite body size (e.g., recruitment rates drivenby host feeding rates, host density, parasite productionrates, or parasite longevity). A possible route of investi-gation would be to examine host-parasite dynamical mod-els that are parameterized by body size and temperaturescaling equations (e.g., building upon those presented inDe Leo and Dobson 1996; Kuris and Lafferty 2000; Mor-and and Poulin 2002; Molnar et al. 2013). One can thenask whether dynamical models can also derive broaderscaling patterns, as DeLong and Vasseur (2011, 2012) re-cently showed for abundance scaling of mammals andprotists. Thus, enhancements to the theory may increaseits predictive ability for parasite abundances below car-rying capacity.

Parasite Metabolic Scaling

Obtaining more information on parasite metabolic scalingwill strengthen the use of MTE in parasitology, particularlyby increasing our ability to make precise predictions.Hechinger et al. (2012) noted that parasitic animals andprotists appear to scale similarly to the rest of life but thatthere are problems with interpreting the available data.The authors suggested that until better information provesotherwise, a sensible approach is to use standard, generalempirical and theoretical scaling relationships for parasites,tempering conclusions as necessary for the particularstudy.

The way parasites metabolize also bears on the infra-community scaling theory presented by George-Nasci-mento and colleagues (George-Nascimento et al. 2004;Poulin and George-Nascimento 2007). As mentioned inthe “Introduction,” that theory assumes that parasites me-tabolize at the same mass-specific rates as their hosts. Par-asite infracommunities are then assumed to take a fractionof host whole-body metabolic rate, which scales as .3/4Mh

However, the study mistakenly extended the prediction forinfracommunity energy flux, or biomass production, tostanding-stock biomass, predicting that it would scale with

, instead of , which would be appropriate under3/4 1M Mh h

the assumption that parasites metabolize at host tissuerates (see Hechinger et al. 2012 for details). In contrast,the framework presented here predicts that infracom-munity biomass depends on both host and parasite met-abolic scaling, in addition to how parasites use host space(eqq. [8] and [12]). Parasite carrying-capacity biomass inmulticellular hosts should generally scale with, for ex-ample, or , not , but this may only be ap-3/4 5/12 1M M Mh h h

parent after factoring in parasite body size. However, scal-ing with is consistent with the space constraints models1Mh

when parasites use host volumes (eqq. [9] and [13]), in-dicating the utility of knowing how parasites metabolizeto permit distinguishing space constraints and parasitemetabolic scaling from parasites metabolizing at host rates.If it turns out that parasites do metabolize at the samerates as host tissues, investigations could distinguish be-tween energetic constraints and space constraints by vary-ing host body size and metabolic rates, for instance, bypicking hosts providing equal space, but different meta-bolic rates, and vice versa.

Parasite Infracommunities as Model Communities

Most of this article uses MTE to inform parasitology. How-ever, parasitology may inform general MTE. One reasonfor this is that parasite infracommunities can serve asunique model communities for ecological research (seeparticularly Holmes and Price 1986; Price 1990). Hosts


provide neat, naturally defined, tractable units of repli-cation for parasite infracommunities. Consequently, care-ful consideration of and capitalizing on novel aspects ofparasite infracommunities may provide unique insight andtests of both MTE and the nature of ecological commu-nities in general.

For example, the results from the analysis of nematodeparasite abundance in mammals bears on the general scal-ing issue in community ecology referred to as “energeticequivalence” (Damuth 1981, 1987; Nee et al. 1991; Isaacet al. 2012). Energetic equivalence is simply the invariantscaling of population energy flux, F, with species bodysize. Energetic equivalence can occur across species ofvarying body size when abundance decreases as .�3/4MBecause F is individual metabolic rate multiplied by abun-dance, F scales as . In the analysis of nem-3/4 �3/4 0M M p Matode infrapopulations, N exhibited scaling. But this�3/4Mwas clear only after controlling for resource supply as re-flected by host body size and mass-specific metabolic rate.If we drop the resource supply term, nematode densityscales with (�1.39, �0.37, 95% confidence limits).�0.87MThis indicates that in absolute terms, energetic equivalencemay not occur among these parasite infrapopulations:larger-bodied nematode infrapopulations may process lessenergy than smaller nematodes. The revealing of �3/4Mabundance scaling only after factoring in resource supplyfor parasite infrapopulations is parallel to results from pre-vious studies on carnivoran mammals (Carbone and Git-tleman 2002) and parasitic and free-living species in es-tuarine food webs (Hechinger et al. 2011). Hence, usingparasite infrapopulations helps solidify that energeticequivalence is not an assumption of MTE abundance the-ory but is an outcome that may arise if resource supplyis evenly distributed among body sizes of physiologicallysimilar organisms.

Coda

Almost 40 years have passed since the parasitologist ElmerNoble propounded that energetics should provide a major,fecund avenue of research in parasitology (Noble 1974).MTE may permit us finally to begin to extensively tacklethe energetic aspects of parasitism, particularly at multi-species scales that are otherwise intractable. Recently, en-hanced MTE abundance theory permitted inclusion ofparasites alongside free-living consumers in species-richfood webs (Hechinger et al. 2011). Considering parasitesthere helped refine MTE and also shed light on the roleof parasitism in ecosystems. The MTE framework offeredin this article focuses on parasites within host bodies. Thisis where parasites directly impact their host resources andinteract with each other. Consequently, further MTE-basedparasitological research may continue to lend empirical

and theoretical insight into the nature of parasitism. Thisincludes how parasitism relates to host and parasite size,temperature, and host physiological type (e.g., endothermyvs. ectothermy). It also includes how those factors influ-ence the ecology and evolution of parasites themselves.Research on parasites may also enhance and inform gen-eral MTE. I hope that my colleagues will use, criticallyevaluate, and enhance the framework presented here.

Acknowledgments

I thank A. Kuris, K. Lafferty, the peer reviewers (M.George-Nascimento and one anonymous), and the editors(T. Day and J. Elser) for critical and constructive com-ments. This article benefited from support from a NationalScience Foundation Ecology of Infectious Diseases grant(OCE-1115965) and a California Sea Grant (R/OPCENV-01).

APPENDIX

Analyzing “Density” and “Abundance” Versionsof the Scaling Equations

A useful feature of analyzing the “density” forms of theequations (those with an aspect of host body size as thedensity unit), is that they permit direct testing and inter-pretation of the host body-size exponent that should cor-respond solely to mass-specific metabolic rate (parasiteresource supply). However, an analytical issue can arisewhen testing density forms of the equations. For instance,concerning the analysis in “Does Energy or Space BetterExplain Infrapopulation Abundance Scaling?,” having anaspect of host body size in the response variable ( )jhN/Mh

and as a predictor variable ( ) can cause “spurious�ghMh

correlations” (see Pearson 1897; Jackson and Somers1991). With spurious correlations, the null of the statisticalrelationship is not a zero slope. Randomization tests pro-vide a solution to this problem by generating the nulldistribution of the relationship inherent to the data (Jack-son and Somers 1991). Although such tests are readilyimplementable (and are how I tested the relationship—using the freely available PopTools add-in for Excel), theyare not nearly as familiar as standard linear models are.We can preclude this potential analytical difficulty by usingforms of the equations that put all related terms into thesame side. For instance, for the analysis in “Does Energyor Space Better Explain Infrapopulation Abundance Scal-ing?,” we could use the “abundance” forms of the equa-tions: for energetic constraints or1�1/4 �3/4N ∝ M Mp h p


for space constraints. Again, logging the1 �1N ∝ M Mp h p

equations provides a model suitable for testing with a gen-eral linear model with host and parasite body sizes aspredictor variables. Alternatively, if we use theoretical orempirically justified estimates for the host body-size ex-ponent reflecting resource supply, we can also put all hostbody-size terms on the left side of the equation to have a“resource-supply corrected parasite density” for the MTEequation, , or simple parasite density1�1/4 �3/4N /M ∝ Mp h p

under space constraints, . Logging these1 �1N /M ∝ Mp h p

equations permits testing with simple regression, but onlyof the parasite body-size exponent. Choice of the form ofthe equations to analyze may also be influenced by howwell the different versions meet standard statistical as-sumptions concerning error distributions and a lack ofstrong collinearity among predictor variables. In any case,empirical tests on the nematode parasite data using thesealternative forms of the equation yielded estimates com-pletely congruent with expectations from the density anal-ysis (statistics not presented), further substantiating thepossible utility of an MTE framework for parasite abun-dance in hosts.

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Associate Editor: James ElserEditor: Troy Day

How many parasitic worms can fit in a host? Data involving the rat tapeworm, Hymenolepis diminuta, competing with other parasitesliving in rats, was used to test new theory about parasite abundance and energetics inside of hosts. Photo credit: Todd C. Huspeni andRyan F. Hechinger.

A Metabolic and Body-Size Scaling Framework for Parasite Within

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