A Metabolic and Body-Size Scaling Framework for Parasite Within-Host Abundance, Biomass, and Energy Flux

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1 vol. 182, no. 2 the american naturalit augut 2013 A Metabolic and Body-Size Scaling Framework for Paraite Within-Hot Abundance, Bioma, and Energy Flux Ryan F. Hechinger* Marine Science Intitute and the Department of Ecology, Evolution, and Marine Biology, Univerity of California, Santa Barbara, California Submitted October 24, 2012; Accepted March 8, 2013; Electronically publihed June 21, 2013 Dryad data: abtract: Energetic may provide a ueful currency for tudying the ecology of paraite aemblage within individual hot. Paraite aemblage may alo provide powerful model to tudy general principle of ecological energetic. Yet there ha been little ecological reearch on paraite-hot energetic, probably due to methodological difficultie. However, the caling relationhip of individual metabolic rate with body or cell ize and temperature may permit u to tackle the energetic of paraite aemblage in hot. Thi article offer the foundation and initial teting of a metabolic theory of ecology (MTE) framework for paraite in hot. I firt provide equation to etimate energetic flux through oberved paraite aemblage. I then develop metabolic caling theory for paraite abundance, energetic, and bioma in individual hot. In contrat to previou effort, the theory factor in both hot and paraite metabolic caling, how paraite ue hot pace, and whether energy or pace dictate carrying capacity. Empirical tet indicate that hot energetic flux can et paraite carrying capacity, which decreae a predicted conidering the caling of hot and paraite metabolic rate. The theory and reult alo highlight that the phenomenon of energetic equivalence i not an aumption of MTE but a poible outcome contingent on how pecie partition reource. Hence, applying MTE to paraite can lend mechanitic, quantitative, predictive inight into the nature of paraitim and can inform general ecological theory. Keyword: metabolic theory of ecology, paraite communitie, infrapopulation, infracommunity, pathology, virulence. Introduction When we get ick particularly with infectiou agent we frequently invoke language concerning the energetic impact of infection. For intance, we peak of having our energy drained. Thi common language undercore that energy may provide a ueful currency to invetigate the impact of infectiou agent, or paraite, on their hot. In fact, an energetic perpective may apply more broadly to the ecology of paraite within hot. Although thi wa * hechinger@lifeci.ucb.edu. Am. Nat Vol. 182, pp by The Univerity of Chicago /2013/ $ All right reerved. DOI: / recognized decade ago (Noble 1974), very little reearch ha examined the energetic of both paraite and hot (e.g., Walkey and Meakin 1970; Bailey 1975; Munger and Karaov 1994). The lack of uch reearch almot certainly reflect the difficult nature of precie, detailed tudie of energetic of both paraite and their hot, particularly when dealing with multiple paraite pecie. Thi article offer a poible olution. I preent and provide initial teting of a framework that may readily permit u to tudy and predict the energetic, bioma, and abundance of paraite within hot. The framework i quantitative, immediately implementable, and tetable, and it ue the caling relationhip of metabolic rate with body ize and temperature. What ha become known a the metabolic theory of ecology (MTE) i a formulation of metabolic ecology (Brown et al. 2004; Brown et al. 2012). Metabolic ecology eek to ue individual metabolim the tranformation and ue of energy and material by individual organim a the foundation for a theoretical unification of ecology. Thi i enible, becaue we can readily expre many ecological interaction in term of the proceing and exchange of energy and material. For intance, metabolic rate directly reflect energy ue and, conequently, demand on reource (Peter 1983; Brown et al. 2004). MTE put metabolic ecology to practice by capitalizing on the caling relationhip of individual metabolic rate with body temperature and body ize (pcell ize for ingle-celled organim; e.g., Robinon et al. 1983; Gillooly et al. 2001; Makarieva et al. 2008; DeLong et al. 2010). Temperature and body ize are readily available variable. Therefore, MTE i particularly implementable at broad cale, ay entire aemblage and communitie, a we can etimate metabolic rate for even poorly tudied pecie. In addition to reflecting energy ue, metabolic rate alo appear to et the pace of other ecologically important biological rate (e.g., growth, reproduction, and mortality). Thee rate alo cale with body ize and temperature (Peter 1983;

2 Paraite Abundance, Bioma, Energetic g A 16g B 16g Number: 17 v 2 8x Bioma: 32 v 32 1x Energy Flux: 21 v 10 2x Figure 1: Different currencie and their implication for depicting paraite aemblage within hot, focuing on impact on hot. There are two hot individual (A and B) and two paraite pecie, one with individual weighing 16 g and the other with individual weighing 1 g. The paraite otherwie imilarly ue their hot. Number are clearly inufficient for depicting paraite impact on hot; no one would think that the paraite affect hot A eight time more than they do hot B. Depite having different paraite number, the two hot both harbor equivalent paraite bioma. However, in hot A, half of the bioma i compoed of mall-bodied paraite. Given metabolic caling, maller-bodied paraite burn more calorie per gram of tiue (they have higher ma-pecific metabolic rate). Hence, uing equation (2) and (3) indicate that the energy fluxed through paraite in hot A i two time the amount fluxed through hot B. Clearly, currency choice can ubtantially affect our depiction of paraite within hot. Calder 1984; Schmidt-Nielen 1984; Sibly et al. 2012). Hence, by building on the caling relationhip of individual metabolic rate, MTE ha promie of facilitating quantitative, mechanitic, and predictive reearch examining broad pattern and procee characterizing population, communitie, and ecoytem (Brown et al. 2004; Marquet et al. 2005; Sibly et al. 2012). Paraite form aemblage within individual hot. A group of conpecific within a ingle hot i termed an infrapopulation, ditinguihing them from the broader paraite population occurring in the urrounding ecoytem (Buh et al. 1997). Similarly, mixed-pecie group are called infracommunitie. Thee paraite aemblage interact with their hot, ometime cauing dieae. The member of infracommunitie alo interact with each other through a uite of direct and indirect interaction (reviewed in Dobon 1985; Ech et al. 1990; Poulin 1998). Can we apply MTE to paraite infrapopulation and infracommunitie to gain inight on the ecology of infectiou dieae and paraite? We hould expect that MTE might benefit paraitology becaue metabolim and body ize are intenely intertwined with paraitim. Hot provide food and pace to paraite infrapopulation and infracommunitie. Therefore, hot metabolic rate and body ize hould directly influence paraite in term of providing energy or pace reource. At the ame time, paraite alo have bodie and metabolic rate, and their energetic demand hould affect their hot and competing paraite. Becaue free-living pecie and paraite both appear to follow general metabolic caling relationhip (but ee Hechinger et al for iue concerning available data for paraite), there i a clear poibility of uing the caling of hot and paraite metabolim to inform paraitology. Another advantage of MTE for paraitology i that it ue energy a a currency. Paraitology typically focue on the number of paraite individual per hot. However, focuing on number limit generalizing to other pecie, and it can be meaningle when dealing with paraite pecie that differ in body ize (fig. 1). Bioma or biovolume ha been conidered a an alternative currency to number for paraite infrapopulation and infracommunitie (Rohde et al. 1994; George-Nacimento et al. 2004; Muñoz and Cribb 2005; Munoz and George-Nacimento 2008). Although uing bioma i a good tep, it may not perform well if energetic i important and the community under invetigation i compoed of paraite that vary in body ize and ma-pecific metabolic rate (fig. 1). In thee cae, equal biomae will proce different amount of energy. Therefore, energy flux (e.g., J 1 ) may bet reflect the interaction of paraite with their hot and with each other. I haten to add that emphaizing energy doe not require abandoning the traditional currencie of number or bioma. In fact, by focuing on the relationhip between individual body ize and metabolic rate, MTE directly link energy to number and bioma (Brown et al. 2004; Gillooly et al. 2006). Previou, pioneering tudie have examined the bodyize caling of paraite infrapopulation or infracommunity abundance or bioma. For intance, Arneberg et al. (1998)

3 236 The American Naturalit and Morand and Poulin (2002) examined the empirical caling of nematode paraite population abundance in hot. However, they did not have the goal of contructing abundance caling theory and did not conider how hot metabolic rate could provide reource to paraite. George-Nacimento et al. (2004) and Poulin and George- Nacimento (2007) developed metabolic caling theory for how paraite infracommunity bioma would cale with hot body ize. However, that theory aume that paraite metabolize at the ame ma-pecific rate characterizing their hot. That i, the theory aume that paraite metabolic rate do not cale with their own bodie, which i inconitent with available, albeit limited, data (Hechinger et al. 2012). Thoe two tudie alo took a conceptual mitep in applying a prediction for bioma production to tanding-tock bioma (dicued later in thi article). Here, I offer the foundation and initial teting of a more fully pecified metabolic, body-ize caling framework for paraite infrapopulation and infracommunitie. The next ection firt cover the baic of individual metabolic rate (energy flux) caling with body ize. I then preent equation that etimate energetic flux through oberved infrapopulation and infracommunitie. Thee equation provide a new way to depict paraite infrapopulation and infracommunitie, including impact on hot, a the energy flowing through paraite wa taken from their hot. After that, I develop an MTE-baed theory to predict within-hot maximal or carrying-capacity paraite abundance, energy flux, and bioma. Contrary to previou work, the theory factor in both paraite and hot metabolic caling and the way that paraite ue hot pace. Paralleling tandard MTE abundance theory, part of the framework applie to ituation where energy contrain paraite infrapopulation and infracommunitie. However, I alo provide equation for the alternative ituation where pace, not energy, contrain paraite. Undertanding whether energy or pace or both influence paraite i of clear importance for undertanding the nature of paraitim and bear on effort to ue paraite infracommunitie a model ytem. Finally, I provide reult of initial empirical teting of everal apect of the theory. The reult upport the promie of the MTE framework for paraite within hot and indicate that, for the examined paraite, abundance follow the energy-contraint framework better than the pace-contraint framework. Theory Metabolic Rate Scaling Whole-organim metabolic rate, I, cale allometrically with body ize, M, and varie with temperature, T, a a I p im f(t). (1) In equation (1), i i a normalization contant that varie for organim of different phyiological type (e.g., plant, endothermic vertebrate, or invertebrate; Brown et al. 2004; Marquet et al. 2004; Sibly et al. 2012). The M repreent body ize in ma unit. It i poible to apply the equation to intrapecific body-ize variation (Glazier 2005). However, in cro-pecie or cro-population work, M can be taken a the mean body ize characterizing a pecie or local population, and thi i the conceptualization on which thi article focue. Interpecifically, acro a wide range of multicellular pecie, the caling exponent, a, i often 3/4 (e.g., Kleiber 1932; Hemmingen 1960; Peter 1983; Savage et al. 2004; Glazier 2005). Recent work indicate that a different value characterize a for unicellular organim, unicellular eukaryote metabolic rate appear to cale with body (cell) ize with an exponent of 1, and bacteria cale with an exponent larger than 1 (Makarieva et al. 2008; DeLong et al. 2010). The f (T) function repreent the influence of temperature on metabolic rate. MTE ha primarily ued e E/kT, where E i the activation energy for enzymatic reaction ( 0.63 ev on average for oxidative repiration), k i Boltzmann contant 5 1 ( 8.62 # 10 ev 7 K ), and T i the average operating temperature in degree Kelvin (Gillooly et al. 2001; Brown et al. 2004). Thi term i a formulation of the Arrheniu equation, which can capture the kinetic influence of a wide range of temperature on metabolic rate (Gillooly et al. 2001; Brown et al. 2004; White et al. 2012). For implicity, in thi article I will ue e E/kT when temperature dependence i included in the equation. However, reader hould note that any appropriate temperature-dependence function could be incorporated a f (T), including thoe that depict a unimodal repone of metabolic rate with temperature (e.g., Schoolfield et al. 1981; Molnár et al. 2013). The operational criterion i that the term be a dimenionle, multiplicative modifier. Energetic Flux of Oberved Paraite Infrapopulation/Communitie By applying metabolic caling (eq. [1]) to paraite, one can ue oberved abundance and body-ize information of paraite to predict the total energy flow through aemblage of paraite. The energy flux, F p, characterizing a paraite infrapopulation p, will be the mean individual metabolic rate I p (eq. [1]) time the infrapopulation ize, N p,othat F p IN,or p p p ap E/kT Fp p (im p e )N p. (2) Total infracommunity energy flux, F tot, i imply the um

4 Paraite Abundance, Bioma, Energetic 237 of contituent infrapopulation fluxe, F p (eq. [2]), o that F p F p IN,or tot pp1 p pp1 p p ap E/kT Ftot (imp e )N p, (3) pp1 where i the total number of paraite pecie in a ingle hot or in the particular paraite aemblage under invetigation (e.g., ectoparaitic lice or gut-dwelling helminth). My firt empirical tet will employ thee equation to etimate total energy flux in ingle- and mixed-pecie paraite infracommunitie. Scaling of Paraite Abundance, Energy Flux, and Bioma within Hot Next I introduce baic MTE abundance theory. I then dicu appropriate denity unit for paraite infrapopulation and communitie. Following thi I preent the caling theory for paraite abundance, energy flux, and bioma at carrying capacity impoed by either energetic or pace contraint. Baic MTE Abundance Theory. Standard MTE predict teady tate, maximum population abundance (carrying capacity) by uing the caling of whole-organim metabolic rate and by factoring in reource upply (Brown et al. 2004; Marquet et al. 2004). At carrying capacity, abundance N decline with body ize becaue a given reource upply, R, upport fewer larger-bodied individual than mallerbodied individual. Individual reource requirement parallel whole-body metabolic rate, which cale with M a (eq. [1]). Hence, abundance will decreae with body ize a N RM a. To implify notation, I ue to refer to general caling, dropping pecific coefficient, normalization contant, and temperature effect on metabolic rate. To increae clarity, I will maintain thi practice when developing the theory below. However, for precie and abolute prediction, temperature effect, coefficient, and normalization contant are needed (alo note the neceary addition of a coefficient for reource-upply converion efficiency). With thee iue in mind, we can ak how we can apply MTE abundance theory to paraite abundance within individual hot. What Are the Appropriate Denity Unit for Paraite in Hot? Paraitology ha traditionally focued on the hot individual a the quadrat unit ( intenity for number per infected hot, abundance when uninfected hot are included; Buh et al. 1997). By itelf, thi will not erve a a ueful meaure of denity for MTE, particularly if hot vary in body ize. One hould divide paraite number by the apect of the hot that reflect how the paraite ue hot pace. For intance, hot ma, M h, (or hot volume, V h ) make ene a denity unit for paraite that ue hot pace in a volumetric way, uch a many tiueor cavity-dwelling paraite. In thee cae, denity unit would be N/M h or N/V h. However, many paraite ue hot urface area (e.g., kin-dwelling paraite). Here, for example, becaue hot external body urface often cale with hot body ize to the 2/3 power (Calder 1984), for thee 2/3 paraite the appropriate denity unit could be N/M h. I will ue thee two exponent (1 and 2/3) a example throughout the text, but one hould ue whatever caling exponent i mot appropriate for the hot and paraite under invetigation. Further, when available, one could ue more pecific information concerning how much of a hot the paraite ue. For intance, one could multiply the hot body-ize term by a coefficient that repreent the proportion of the hot ma or urface area ued by the paraite under invetigation (e.g., in human, ome lice ue only the calp, malaria ue only the liver and the blood, tapeworm ue only a portion of the intetine, etc.). Below, I will ue abundance for the total number of paraite per hot individual (correponding to the tandard ecological paraitology term) and denity when abundance i divided by an apect of the hot (and I will ue hot ma, not volume). Theoretical Aumption. The caling theory preented below aume that paraite metabolic rate i related to paraite body ize and temperature. The theory doe not aume pecific value for caling exponent or temperature dependence. However, implementing the framework entail uing whatever value appear bet uing available theoretical or empirical information for hot and paraite for either intra- or interpecific application (e.g., conult Gillooly et al. 2001; Glazier 2005; DeLong et al. 2010; Hechinger et al. 2012). Further, the theory aume bottom-up limitation (energy or pace) and a zero-um game for paraite aemblage; it therefore mot preciely depict paraite aemblage at carrying capacity where total reource are partitioned among pecie. However, a dicued in the econd empirical tet ection, with an additional aumption, it can alo directly apply to ituation where paraite are below carrying capacity. Theory for Paraite Infrapopulation Carrying-Capacity Abundance. Conider hypothetical paraite infrapopulation wherein individual recruit to, grow, or reproduce within hot o that limiting reource reduce population production rate to equal lo rate. I will refer to uch maximal teady-tate abundance a carrying capacity. If paraite conume hot metabolic product in a volumetric way, hot will provide reource at a rate parallel to hot ma-pecific metabolic rate, which decreae with hot

5 238 The American Naturalit ah 1 ah 1 body ize a M h /M h p Mh. I will ue g to repreent the caling exponent aociated with ma-pecific metabolic rate (e.g., with 3/4 caling of whole-body metabolic rate, g p a 1 p 1 p 1/4). Thi lead to the prediction that paraite infrapopulation denity at carrying capacity cale with both hot and paraite body ize a jh gh ap N/M h Mh M p, (4a) where j h i the appropriate patial denity term (e.g., 1 for paraite that ue hot volume and 2/3 for paraite that ue hot external urface). Becaue hot ma i the denity unit, we can rearrange to get total paraite abundance at carrying capacity, jh gh ap Np Mh M p. (4b) Hence, the equation predict that paraite infrapopulation carrying capacity will decreae with increaing paraite body ize, but increae with hot body ize to the 3/4 power for paraite that ue hot volume, and to the 5/12 power for thoe that ue hot external urface. If pace, not hot metabolic rate, limit paraite infrapopulation, we drop the hot reource-upply term and ue a coefficient to repreent the apect of paraite bodie that reflect their patial packing (e.g., 1 for volume). Hence, under patial contraint, paraite infrapopulation denity at carrying capacity decreae with paraite body ize a jh jp N/M h M p. (5a) Rearranging predict that paraite abundance at carrying capacity increae directly with increaing hot pace (volume or urface area) ued, a jh jp Np Mh M p. (5b) Hence, conidering energy or pace contraint (eqq. [4] and [5]) reult in different prediction for how paraite abundance hould cale with hot and paraite body ize. My econd empirical tet will tet which equation are mot conitent with data on nematode abundance in mammalian hot. In ubequent theory, I will preent only the abundance form of the equation. Theory for Paraite Infrapopulation Energy Flux and Bioma. Equation (2) decribe the total energy flux of a an oberved infrapopulation a F p p p IN p p Mp Np. For paraite at energetically determined carrying capacity, we can predict how energy flux will cale with hot body ize becaue we can aume the carrying-capacity abundance jh gh ap caling decribed by equation (4b) a Np Mh Mp. Subtituting thi for N p in the oberved infrapopulation ap jh gh ap flux equation provide Fp M p (Mh M p ) jh gh 0 M M,or h p j h gh Fp M h. (6) Thu, equation (6) predict that the maximum energy flux through a paraite infrapopulation (i.e., one at carrying capacity) i invariant of paraite body ize but cale with hot ma depending on hot ma-pecific metabolic rate and how the paraite ue hot pace. An analogou caling relationhip hould occur for maximum total bioma production rate (amount of bioma produced via growth and reproduction per unit time) becaue individual rate of production parallel metabolic rate for a wide range of free-living pecie (Ernet et al. 2003). With pace contraint, the maximum energy flux through a paraite infrapopulation will vary with how jh jp many paraite can fill hot pace a M h /M p (carrying capacity N p (eq. [5b]) multiplied by individual paraite metabolic rate I M a, giving p p jh ap jp Fp Mh M p. (7) What i the bioma of a paraite infrapopulation at energy-determined carrying capacity? Parallel to deriving energy flux, we ubtitute teady-tate infrapopulation abundance (eq. [4b]) into an oberved bioma equation to predict that maximum tanding-tock bioma of a paraite infrapopulation will be Wp p MN p p jh gh ap M (M M ),or p h p jh gh 1 a p. Wp Mh M p (8) Thu, in contrat to energy flux and bioma production but imilarly to individual abundance, equation (8) predict that both hot and paraite body ize influence the maximum tanding-tock bioma of paraite infrapopulation under energetic contraint. We can eaily contrat the prediction of the carryingcapacity bioma of a paraite infrapopulation under energetic limitation to one experiencing pace limitation. Here, the bioma at carrying capacity will be invariant of paraite body ize and be a imple fraction of hot pace, uch that j W M h p h, (9) where j repreent the caling term from the appropriate (hot body) denity unit for the paraite infrapopulation. Theory for Paraite Infracommunity Energy Flux and Bioma. If hot metabolim contrain the total energy flux of paraite, carrying-capacity flux of a combined paraite infracommunity, F tot, mut cale the ame a the prediction for infrapopulation operating under energy limitation (eq. [6]), o that j h gh Ftot M h. (10) In multipecie aemblage at carrying capacity, each par-

6 Paraite Abundance, Bioma, Energetic 239 ticular pecie will, or coure, proce a lower level of energy than that predicted by the ingle-pecie (infrapopulation) equation given above (eqq. [4] [9]). Under pace contraint, infracommunity carryingcapacity bioma will be a et proportion of the hot (ee below), but the total energy flux will vary with the relative abundance of pecie with different metabolic rate and body ize. Without information on paraite pecie abundance, we can make headway by auming that paraite pecie of different ize and metabolic rate ue, on average, equal portion of hot pace. In thi cae, each paraite pecie will increae in abundance with hot body ize and decreae with paraite body ize a N p jh jp M h M p. Hence, energetic flux at patially determined car- ap jh jp rying capacity, F p IN M (M M ), or tot pp1 p p pp1 p h p jh ap jp tot h p pp1 F M M. (11) With energetic contraint, the paraite infracommunity tanding-tock bioma, W tot, upported by a hot will alo vary with the relative abundance of pecie in the infracommunity. Thi i becaue paraite pecie proce different amount of energy per unit bioma depending on their metabolic rate and therefore their body ize. Similar to infracommunity carrying-capacity bioma under pace contraint, we can progre by auming that paraite pecie of different ize have, on average, equal acce to hot reource. In thi cae, we can predict infracommunity bioma at carrying capacity will cale a Wtot pp1 Wp, or jh gh 1 ap tot h p pp1 W M M. (12) The carrying-capacity bioma of a paraite infracommunity hould therefore increae with hot body ize (e.g., to the 3/4 or 5/12 power) and alo depend on the metabolic caling of each paraite pecie. We can contrat energetic and pace contraint for the carrying-capacity bioma of paraite infracommunitie. If paraite are retricted to a certain proportion of hot pace, carrying-capacity bioma will be independent of the body ize of contituent paraite pecie. Hence, under pace contraint, carrying-capacity bioma will cale a j W M h tot h. (13) Thu, in contrat to energetic contraint, bioma will not depend on paraite body ize or metabolic caling. The above infracommunity equation (eqq. [10] [13]) mot directly apply to paraite infracommunitie compoed of pecie that ue the ame pace and reource within or among hot pecie. If paraite vary in ue of hot pace or reource within any hot pecie, then conideration of the degree thee difference would permit appropriate inflation of carrying capacity (niche overlap indice [Kreb 1999] would be helpful here). If paraite vary in the ue of hot reource among hot pecie, then careful conideration of coefficient and the patial exponent will explain additional variability. Model 1 provide a ummary of the equation preented above and a lit of term with definition. Empirical Teting Doe Energy or Bioma Bet Reflect Infracommunity Carrying Capacity? Holme (1961, 1962) provide claic reearch repreenting one of the earliet experimental documentation of interpecific competition. Holme tudied two gut-dwelling, paraitic worm pecie that belonged to different phyla, the rat tapeworm and an acanthocephalan. The rat tapeworm i well known to experience an intrapecific crowding effect that i at leat partly explained by competition for glucoe (reviewed by Robert 2000). Thee worm alo have near-indeterminant growth, whereby a few worm or even a ingle worm may reach carrying capacity in a rat. Holme experimentally contructed replicate infracommunitie compoed of either pecie by themelve and of both pecie imultaneouly. Holme quantified individual body ize and urvivorhip within the three community type for 8 week. A major reult from hi work i that interpecific competition reulted in maller individual body ize, mainly for the tapeworm. To my knowledge, no one ha examined whether and how thi competition affected attribute of the entire infracommunitie. However, the data in the article do permit etimation, uing equation (2) and (3), of the total bioma and energy flux characterizing the three infracommunity type over the tudy period. Figure 2 how the total tanding-tock bioma and etimated energy flux for the two ingle-pecie and the mixed-pecie infracommunitie. Tapeworm-only infracommunitie reached maximum bioma (via individual growth) within 3 week. Thi bioma remained the ame, or lightly decreaed, over the ubequent 5 week. Acanthocephalan-only infracommunitie did not reach teadytate bioma but continued to increae over the entire 8- week period (never reaching tapeworm-only infracommunity level). However, when tapeworm were grown with acanthocephalan, the maximum bioma attained wa not additive but about one-third lower than that achieved by the tapeworm when alone. The energeticcontraint framework predict the lower carrying-capacity bioma, given the maller body ize and higher mapecific metabolic rate characterizing the tapeworm in

7 240 The American Naturalit Model 1: Summary of main model for paraite energy flux, abundance, and bioma in hot and term definition Main model Oberved paraite aemblage Infrapopulation energy flux ap E/kT [2] F p IN p (im e )N Infracommunity energy flux p p p p p ap E/kT [3] Ftot p Fpp IN p pp (imp e )Np pp1 pp1 pp1 Predicted maximum teady-tate paraite abundance, energy flux, bioma a Infrapopulation Energy contraint Space/bioma contraint j g a [4] Np Mh h h Mp p jh jp [5] Np MhMp j g [6] Fp Mh h h jh ap jp [7] Fp MhMp jh gh 1 ap [8] Wp Mh Mp [9] W M jh p h Infracommunitie Energy contraint Space/bioma contraint j g [10] h h j Ftot Mh [11] Ftot Mh Mp pp1 pp1 jh gh 1 ap j [12] Wtot Mh Mp [13] W M h tot pp1 h ap jp Term definition e E/kT Arrheniu temperature-dependence term. Can be wapped for any appropriate temperature-dependence term. F Energy flux of infrapopulation or infracommunity. h Subcript denoting a particular hot pecie. I Individual whole-organim metabolic rate. M Individual body ize, hot or paraite. N Infrapopulation abundance (total number of individual infecting a hot). p, p Subcript denoting a particular paraite pecie/population. Number of paraite pecie in a particular aemblage. tot Subcript denoting aggregate value for entire infracommunity. W Aggregate bioma of infrapopulation or infracommunity. a Exponent for body-ize caling of whole-organim metabolic rate (e.g., 3/4 acro multicellular pecie). g Exponent for ma-pecific metabolic rate caling (e.g., 1/4 acro multicellular pecie). j Spatial exponent for body ize of hot or paraite (e.g., 1 when volume or 2/3 when urface area i important). a jh Thi figure preent only the abundance form of the equation. Obtain denity by dividing both ide by M h, the term for hot pace ued by the paraite. Denity can alo ue hot volumetric or urface area unit. However, any tatitical analyi uing denity intead of abundance mut contend with poible puriou correlation, given the potential interdependence of repone with predictor variable (ee appendix). h pp1 the mixed-pecie infracommunitie. In fact, etimated total energy flux appeared to not only reach a maximum at 3 week but reach the ame maximum for both aturated ingle- and mixed-pecie infracommunitie. Hence, there i evidence for paraitic worm infracommunitie reaching a teady tate, maximum abundance condition and that energy flux reflect thi better than doe tanding-tock bioma. Doe Energy or Space Better Explain Infrapopulation Abundance Scaling? Poulin and Morand (2000) aembled data on body ize and abundance of gut-dwelling nematode paraite of mammal. Becaue they alo provide hot body ize, we can ue their data to tet the prediction of the energeticveru pace-contraint framework (eqq. [4] v. eqq. [5]). The data are of mean infrapopulation abundance for different paraite-hot pecie pair. Mean abundance will be le than maximum abundance, to which the caling theory mot preciely applie. However, auming that mean abundance i aociated with maximum abundance and that the proportional degree of unaturation i not aociated with hot or paraite body ize, we can ue thee data to tet the theoretical caling exponent and not concern ourelve with exact value of the coefficient or normalization factor. Uing appropriate value for exponent for thee paraite and hot, equation (4) predict that carrying-capacity denity will allometrically decreae with 1 both hot and paraite body ize a N p/m h 1/4 3/4 1/4 M M, where M repreent the decreaing re- h p h

8 Paraite Abundance, Bioma, Energetic 241 Figure 2: Energy flux better reflect teady tate than doe tandingtock bioma for experimental paraite infracommunitie compoed of one or two gut-dwelling worm pecie. A, Steady-tate bioma decreae under the condition of interpecific competition that characterize the mixed-pecie infracommunitie, while in B teady-tate energy flux remain the ame. Data derived by applying the metabolic caling equation from Gillooly et al. (2001) for invertebrate at 39 C to body ma and abundance information from Holme (1961, 1962). Number of worm indicated in the label repreent the number of initial recruit, but data ue the average amount of worm recovered for each pecie, which wa contant among treatment. Error bar repreent 95% confidence limit, derived by propagating (Taylor 1982) the reported tandard error in mean body ize and uing 5 df (4 10 infracommunity replicate for each treatment at each week). Data underlying figure 2 are depoited in the Dryad Digital Repoitory: Hechinger (2013). ource upply rate (hot ma-pecific metabolic rate) 3/4 while M p reflect dividing that reource upply by the metabolic demand of an individual paraite. We can perform a imilar exercie for pace contraint uing equation (5), which predict that paraite denity doe not vary with hot body ize but doe cale, iometrically (perfectly inverely), with paraite body ize a N /M M 1 1. p h p We can ue a general linear model (GLM) to tet which of the two model the data bet upport by uing a logged form of the denity equation where hot and paraite body 1 ize are inputted a predictor variable: log (N p/m h) p b0 b1log Mh b2log M p. Here, the b variable repreent the familiar parameter (intercept and lope) etimated 1 by a GLM. Antilogging the equation provide N p/m h p b0 b1 b2 10 M h M p, which clarifie two thing. Firt, the intercept, b 0, in the GLM i the log of the compound coefficient miing in the equation expreed with the ign. Second, the lope etimated by the GLM permit teting the prediction of both energetic contraint ( b p 1/4, b2 p 3/4) and pace contraint model ( b1 p 0, b2 p 1). The nematode data are mot conitent with energetic contraint (fig. 3). Both hot and paraite body ize were ignificant predictor of nematode denity. The point etimate for the lope with paraite body ize line up exactly with the metabolic prediction of 3/4 caling. However, the etimate ha broad confidence limit that alo overlap 1, the pace contraint prediction. On the other hand, paraite denity alo decreaed with hot body ize (even while tatitically holding paraite body ize contant). Thi i inconitent with pace contraint but predicted under energetic contraint. In fact, dropping the hot body-ize term reulted in a model that explained only 14% of the variance, compared to the 30% explained uing both hot body ize (reflecting reource upply) and paraite body ize (reflecting energetic requirement). Therefore, thi analyi favor the energetic limitation hypothei and indicate the promie of further teting the MTE framework for paraite abundance. General Dicuion The empirical tet indicate the promie of further teting, implementation, and developing of both apect of the preented framework for paraite infrapopulation and infracommunitie. The analyi of the paraitic worm in rat indicate that paraite infracommunitie can reach a aturation point and that energetic, indicated by bodyize caling, bet reflect that condition. The nematode pecie abundance analyi provide further upport for the idea that caling equation can provide the foundation of an individual-energetic-baed but broad theory for the abundance of paraite in hot, a theory that factor in both hot and paraite body-ize and metabolic caling. Oberved Energy Flux of Paraite Infrapopulation/Communitie The firt major apect to thi tudy i the et of equation (eqq. [2] and [3]) to etimate energetic flux of oberved 1

9 242 The American Naturalit Figure 3: The caling of paraite denity with hot and paraite body ize (g wet weight) for 76 pecie of gut-dwelling nematode paraite in mammalian hot (data derived from Morand and Poulin 2000). A, Paraite infrapopulation denity decreae with increaing hot body ize. Confidence limit for the lope with hot body ize overlap the 1/4 predicted if hot ma-pecific metabolic rate contrain paraite denity and exclude the 0 lope predicted under pace contraint. B, Paraite infrapopulation denity decreae with paraite body ize. The lope etimate i exactly conitent with the 3/4 caling predicted if paraite metabolic requirement contrain paraite denity, but the confidence limit overlap the 1 lope predicted under pace contraint. Data in A and B repreent reult from a general linear model, holding the other predictor variable to it average (Sall 1990; Quinn and Keough 2002). Ordinary leat quare i appropriate becaue the error in body-ize etimate i certainly much maller than error in abundance. I ued randomization tet to generate the null ditribution 2 (10,000 permutation) to calculate P value and proportion of variance explained ( R p 0.30). The overall general linear equation wa log (N p/m h) p logmh 0.75 logm p. See appendix for iue to conider when analyzing the denity form of the equation and for everal olution to any iue. Data underlying figure 3 are depoited in the Dryad Digital Repoitory: /dryad.14nn1; Hechinger (2013). paraite infrapopulation and infracommunitie. Thee equation are particularly ueful for multipecie tudie partly becaue they are readily implementable, requiring primarily input of paraite body (or cell) ize and temperature. The equation are applicable to all taxa of unior multicellular paraite and can be ued in at leat two major way. The equation permit u to ue etimated energy flux in tandard ecological paraitology focued on infrapopulation and infracommunitie. For intance, energy flux can erve a a complementary currency to number or bioma to invetigate competitive interaction among paraite or other apect of infracommunity tructure and function, a uggeted by the analyi of rat paraitic worm infracommunitie. We can alo ue equation (2) and (3) to etimate impact on hot. In fact, hot pathology experiment can provide ueful tet of the equation and whether paraite energy flux can erve a a ueful currency. Such experiment hould vary number and body ize of paraite in infracommunitie to maximize difference predicted by currencie of number, bioma, and energy flux. Which currency bet reflect pathology? Doe energy flux permit precie and predictive generalization of paraite impact on hot? It i important to remark that paraite impact hot in way beyond the direct energy conumption indicated by equation (2) and (3). Other potentially coniderable energetic cot to the hot involve repair and defene (including pathological overrepone; e.g., Lochmiller and Deerenberg 2000). When uch information i available, it hould be relatively traightforward to incorporate it into the equation. Many of thee factor will likely alo cale with either paraite or hot body ize or energy flux. Further, uing equation (2) and (3) to etimate baeline energetic demand of paraite may help interpret the inconitent way that hot metabolically repond to infection acro ytem (e.g., Robar et al. 2011). Finally, in ome cae, pathology on hot may be bet reflected by omething other than energy. For intance, paraite may deprive hot of a key nutrient (e.g., iron with hook worm; Crompton and Whitehead 1993), releae toxin (a with malaria; Pichyangkul et al. 1994), or modify hot behavior to reduce fitne (e.g., Lafferty and Morri 1996). However, uch effect may frequently parallel paraite energetic demand and could be readily incorporated into

10 Paraite Abundance, Bioma, Energetic 243 the equation. In hort, enhancing the equation with nonconumptive impact of paraite may increae the ability of MTE to provide a novel perpective for not only ecological paraitology but alo medical and veterinary paraitology. Theory for Scaling of Infrapopulation/Community Abundance and Energetic The econd major ection of thi article i the predictive and explanatory theory for the caling of paraite abundance, energetic, and bioma (eqq. [4] [13]). The energetic contraint theory and the analyi of nematode abundance within hot indicate that the amount of paraite within a hot i better explained by imultaneouly conidering the caling of hot metabolic rate (reflecting reource upply to paraite) and paraite metabolic rate (reflecting energetic requirement of paraite). Hence, it will be worthwhile to reviit data from the previou examination of body-ize caling of paraite infrapopulation/community abundance, which did not factor in both hot and paraite metabolic rate caling (Arneberg et al. 1998; Morand and Poulin 2002; George-Nacimento et al. 2004; Poulin and George-Nacimento 2007). Contrary to the empirical finding in thi article, there may be condition where pace, not energy, will be the limiting reource for paraite in hot. However, in uch cae, paraite would have to not ue all the energy a hot provide to the pace occupied by paraite. Given the broad overlap characterizing the ma-pecific metabolic rate of variou type of life form (Makarieva et al. 2008; DeLong et al. 2010), it i difficult to make trong prediction a to when thi may occur baed on metabolic caling contraint. However, ome paraite are relatively inactive (e.g., ome trophically tranmitted cyt tage that are waiting for their hot to be eaten by the next hot in the life cycle). Perhap for thee paraite pace, not energy, will be limiting. The framework provided here can help tet thi and other idea concerning whether energy or pace contrain paraite within hot. The equation make pecific and contrating prediction that hould be particularly tetable with paraitological data that pan a wide range of hot and paraite body ize where broad pattern among pecie are mot readily obervable and therefore ditinguihable. The predictive caling equation hould apply to all type of paraite infracommunitie, even if we retrict conideration to it ability to make accurate prediction about within-hot carrying capacitie. Thi i becaue the theory can apply both directly and indirectly to oberved infracommunitie. The theory directly applie to thoe infracommunitie that reach carrying capacity. Therefore, it may generally apply to paraite with cloed recruitment thoe that primarily build up from reproduction within the infected hot uch a pathogen (enu Kuri and Lafferty 2000; Lafferty and Kuri 2002). Thee paraite may readily aturate habitat within hot, particularly at peak level of infection. The theory hould alo directly apply to infracommunitie characterized by open recruitment where infectiou propagule originate from outide the hot if recruitment rate are high or individual paraite grow a lot. In the later cae, greater individual growth can counteract low recruitment rate, reulting in aturated habitat. The firt empirical tet dealt with uch a ytem. There are other, natural ytem with open recruitment where aturation alo frequently occur (e.g., Buh and Holme 1986; Stock and Holme 1988; Munoz and George-Nacimento 2008) and to which the caling theory hould directly apply. Paraitoid will be very intereting to conider, a they regularly approach and exceed carrying capacity. Thee paraite conume mot of their hot and emerge from dead or dying hot a part of their development. Paraitoid hould therefore regularly exceed carrying capacity but only late in their development. Hence, the caling theory may therefore provide precie prediction concerning abundance, energy flux, and bioma regularly achieved by everal type of paraite. However, many paraite reach aturation in only a mall percentage of hot (Holme and Price 1986; Shaw and Dobon 1995; Rohde 2005). Thi often occur for ome paraite with open recruitment and lower amount of individual growth, uch a many adult trematode, acanthocephalan, and copepod paraite. A dicued and evidenced in the econd empirical tet ection, part of the theory (caling exponent) can apply to thee paraite if the relative degree of unaturation i not aociated with hot or paraite body ize. However, we can go further and tet precie prediction concerning carrying capacity for uch paraite by uing data on maximum abundance, a pointed out by Poulin and George-Nacimento (2007). Additionally, we will likely find more direct application by focuing on paraite infracommunitie, veru infrapopulation, a infracommunitie will more frequently reach aturation than contituent infrapopulation. Emphaizing infracommunitie i further warranted becaue being infected by more than a ingle paraite pecie i likely the general rule in nature (Petney and Andrew 1998; Cox 2001). However, in any cae, for paraite that frequently do not aturate within-hot habitat, the theory make the mot precie abundance prediction for only a mall ubet of real infracommunitie. Therefore, for thee paraite, carrying capacity theory may find it greatet ue by examining how oberved infracommunitie deviate from theoretical expectation for carrying capacity. Becaue one can now predict carrying capacity, one can quantify the difference between carrying capacity and oberved or realized abundance, energy flux, and bio-

11 244 The American Naturalit ma. There are everal example where thee difference may provide inight into procee tructuring paraite infracommunitie, general impact on hot, or different paraite trophic trategie. Firt, for infracommunitie with open recruitment, the difference between oberved abundance and carrying capacity may provide an index of paraite recruitment (tranmiion) limitation. Second, a many of u can attet, hot can maintain infrapopulation well below carrying capacity by providing top-down control of paraite abundance or growth. Thi i mot likely for pathogen, which reproduce and recruit within individual hot and would reach carrying capacity if not limited by hot defene (e.g., grooming and immune ytem). For thee paraite, difference between oberved abundance and carrying capacity may reflect variation in hot defene. Third, hot mortality likely increae a paraite approach carrying capacity. Hence, deviation between oberved abundance and carrying capacity may reflect the degree to which infracommunitie are at rik of being lot through hot mortality. Thi lo i a major factor for hot and paraite population dynamic (Anderon and May 1978; May and Anderon 1979). In hort, imilar to the way null model can be informative in comparion to reality (Gotelli and Grave 1996), theory for paraite carrying capacity may be hed light on everal apect of paraitim to the degree that it expectation differ from oberved abundance. Future enhancement of the caling framework can focu on directly incorporating the factor that influence the degree of unaturation in paraite infracommunitie. It will be intereting if hot immune defenive capabilitie cale with body ize (e.g., Wiegel and Perelon 2004), but our undertanding here i in it infancy. It i alo poible that paraite timulate hot immune ytem to a degree that parallel their metabolic rate. It i alo particularly worthwhile to examine whether the degree of unaturation i aociated with epidemiological factor that may cale with hot or paraite body ize (e.g., recruitment rate driven by hot feeding rate, hot denity, paraite production rate, or paraite longevity). A poible route of invetigation would be to examine hot-paraite dynamical model that are parameterized by body ize and temperature caling equation (e.g., building upon thoe preented in De Leo and Dobon 1996; Kuri and Lafferty 2000; Morand and Poulin 2002; Molnár et al. 2013). One can then ak whether dynamical model can alo derive broader caling pattern, a DeLong and Vaeur (2011, 2012) recently howed for abundance caling of mammal and protit. Thu, enhancement to the theory may increae it predictive ability for paraite abundance below carrying capacity. Paraite Metabolic Scaling Obtaining more information on paraite metabolic caling will trengthen the ue of MTE in paraitology, particularly by increaing our ability to make precie prediction. Hechinger et al. (2012) noted that paraitic animal and protit appear to cale imilarly to the ret of life but that there are problem with interpreting the available data. The author uggeted that until better information prove otherwie, a enible approach i to ue tandard, general empirical and theoretical caling relationhip for paraite, tempering concluion a neceary for the particular tudy. The way paraite metabolize alo bear on the infracommunity caling theory preented by George-Nacimento and colleague (George-Nacimento et al. 2004; Poulin and George-Nacimento 2007). A mentioned in the Introduction, that theory aume that paraite metabolize at the ame ma-pecific rate a their hot. Paraite infracommunitie are then aumed to take a fraction 3/4 of hot whole-body metabolic rate, which cale a M h. However, the tudy mitakenly extended the prediction for infracommunity energy flux, or bioma production, to tanding-tock bioma, predicting that it would cale with 3/4 1 Mh, intead of Mh, which would be appropriate under the aumption that paraite metabolize at hot tiue rate (ee Hechinger et al for detail). In contrat, the framework preented here predict that infracommunity bioma depend on both hot and paraite metabolic caling, in addition to how paraite ue hot pace (eqq. [8] and [12]). Paraite carrying-capacity bioma in multicellular hot hould generally cale with, for example, Mh or Mh, not Mh, but thi may only be ap- 3/4 5/12 1 parent after factoring in paraite body ize. However, cal- 1 M h ing with i conitent with the pace contraint model when paraite ue hot volume (eqq. [9] and [13]), indicating the utility of knowing how paraite metabolize to permit ditinguihing pace contraint and paraite metabolic caling from paraite metabolizing at hot rate. If it turn out that paraite do metabolize at the ame rate a hot tiue, invetigation could ditinguih between energetic contraint and pace contraint by varying hot body ize and metabolic rate, for intance, by picking hot providing equal pace, but different metabolic rate, and vice vera. Paraite Infracommunitie a Model Communitie Mot of thi article ue MTE to inform paraitology. However, paraitology may inform general MTE. One reaon for thi i that paraite infracommunitie can erve a unique model communitie for ecological reearch (ee particularly Holme and Price 1986; Price 1990). Hot

12 Paraite Abundance, Bioma, Energetic 245 provide neat, naturally defined, tractable unit of replication for paraite infracommunitie. Conequently, careful conideration of and capitalizing on novel apect of paraite infracommunitie may provide unique inight and tet of both MTE and the nature of ecological communitie in general. For example, the reult from the analyi of nematode paraite abundance in mammal bear on the general caling iue in community ecology referred to a energetic equivalence (Damuth 1981, 1987; Nee et al. 1991; Iaac et al. 2012). Energetic equivalence i imply the invariant caling of population energy flux, F, with pecie body ize. Energetic equivalence can occur acro pecie of varying body ize when abundance decreae a M 3/4. Becaue F i individual metabolic rate multiplied by abundance, F cale a M M p M. In the analyi of nem- 3/4 3/4 0 3/4 atode infrapopulation, N exhibited M caling. But thi wa clear only after controlling for reource upply a reflected by hot body ize and ma-pecific metabolic rate. If we drop the reource upply term, nematode denity 0.87 cale with M ( 1.39, 0.37, 95% confidence limit). Thi indicate that in abolute term, energetic equivalence may not occur among thee paraite infrapopulation: larger-bodied nematode infrapopulation may proce le 3/4 energy than maller nematode. The revealing of M abundance caling only after factoring in reource upply for paraite infrapopulation i parallel to reult from previou tudie on carnivoran mammal (Carbone and Gittleman 2002) and paraitic and free-living pecie in etuarine food web (Hechinger et al. 2011). Hence, uing paraite infrapopulation help olidify that energetic equivalence i not an aumption of MTE abundance theory but i an outcome that may arie if reource upply i evenly ditributed among body ize of phyiologically imilar organim. Coda Almot 40 year have paed ince the paraitologit Elmer Noble propounded that energetic hould provide a major, fecund avenue of reearch in paraitology (Noble 1974). MTE may permit u finally to begin to extenively tackle the energetic apect of paraitim, particularly at multipecie cale that are otherwie intractable. Recently, enhanced MTE abundance theory permitted incluion of paraite alongide free-living conumer in pecie-rich food web (Hechinger et al. 2011). Conidering paraite there helped refine MTE and alo hed light on the role of paraitim in ecoytem. The MTE framework offered in thi article focue on paraite within hot bodie. Thi i where paraite directly impact their hot reource and interact with each other. Conequently, further MTE-baed paraitological reearch may continue to lend empirical and theoretical inight into the nature of paraitim. Thi include how paraitim relate to hot and paraite ize, temperature, and hot phyiological type (e.g., endothermy v. ectothermy). It alo include how thoe factor influence the ecology and evolution of paraite themelve. Reearch on paraite may alo enhance and inform general MTE. I hope that my colleague will ue, critically evaluate, and enhance the framework preented here. Acknowledgment I thank A. Kuri, K. Lafferty, the peer reviewer (M. George-Nacimento and one anonymou), and the editor (T. Day and J. Eler) for critical and contructive comment. Thi article benefited from upport from a National Science Foundation Ecology of Infectiou Dieae grant (OCE ) and a California Sea Grant (R/OPCENV- 01). APPENDIX Analyzing Denity and Abundance Verion of the Scaling Equation A ueful feature of analyzing the denity form of the equation (thoe with an apect of hot body ize a the denity unit), i that they permit direct teting and interpretation of the hot body-ize exponent that hould correpond olely to ma-pecific metabolic rate (paraite reource upply). However, an analytical iue can arie when teting denity form of the equation. For intance, concerning the analyi in Doe Energy or Space Better Explain Infrapopulation Abundance Scaling?, having an j apect of hot body ize in the repone variable ( N/M h h ) g and a a predictor variable ( M h h ) can caue puriou correlation (ee Pearon 1897; Jackon and Somer 1991). With puriou correlation, the null of the tatitical relationhip i not a zero lope. Randomization tet provide a olution to thi problem by generating the null ditribution of the relationhip inherent to the data (Jackon and Somer 1991). Although uch tet are readily implementable (and are how I teted the relationhip uing the freely available PopTool add-in for Excel), they are not nearly a familiar a tandard linear model are. We can preclude thi potential analytical difficulty by uing form of the equation that put all related term into the ame ide. For intance, for the analyi in Doe Energy or Space Better Explain Infrapopulation Abundance Scaling?, we could ue the abundance form of the equation: N M M for energetic contraint 1 1/4 3/4 or p h p

13 246 The American Naturalit 1 1 Np MM h p for pace contraint. Again, logging the equation provide a model uitable for teting with a general linear model with hot and paraite body ize a predictor variable. Alternatively, if we ue theoretical or empirically jutified etimate for the hot body-ize exponent reflecting reource upply, we can alo put all hot body-ize term on the left ide of the equation to have a reource-upply corrected paraite denity for the MTE 1 1/4 3/4 equation, N p/m h M p, or imple paraite denity 1 1 under pace contraint, N p/m h M p. Logging thee equation permit teting with imple regreion, but only of the paraite body-ize exponent. Choice of the form of the equation to analyze may alo be influenced by how well the different verion meet tandard tatitical aumption concerning error ditribution and a lack of trong collinearity among predictor variable. 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15 248 The American Naturalit microhabitat ditribution of enteric helminth of grebe (Podicipedidae): the evidence for interactive communitie. Journal of Paraitology 74: Taylor, J. R An introduction to error analyi: the tudy of uncertaintie in phyical meaurement. Univerity Science, Mill Valley, CA. Walkey, M., and R. H. Meakin An attempt to balance the energy budget of a hot-paraite ytem. Journal of Fih Biology 2: White, E. P., X. Xiao, N. J. B. Iaac, and R. M. Sibly Methodological tool. Page 7 20 in R. M. Sibly, J. H. Brown, and A. Kodric-Brown, ed. Metabolic ecology: a caling approach. Wiley- Blackwell, Chicheter. Wiegel, F. W., and A. S. Perelon Some caling principle for the immune ytem. Immunology and Cell Biology 82: Aociate Editor: Jame Eler Editor: Troy Day How many paraitic worm can fit in a hot? Data involving the rat tapeworm, Hymenolepi diminuta, competing with other paraite living in rat, wa ued to tet new theory about paraite abundance and energetic inide of hot. Photo credit: Todd C. Hupeni and Ryan F. Hechinger.