Coexistence of Predator and Prey in Intraguild Predation Systems with Ontogenetic NicheShifts.Author(s): Vincent Hin, Tim Schellekens, Lennart Persson, André M. de RoosReviewed work(s):Source: The American Naturalist, Vol. 178, No. 6 (December 2011), pp. 701-714Published by: The University of Chicago Press for The American Society of NaturalistsStable URL: http://www.jstor.org/stable/10.1086/662676 .Accessed: 22/02/2012 16:34

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vol. 178, no. 6 the american naturalist december 2011

Coexistence of Predator and Prey in Intraguild Predation

Systems with Ontogenetic Niche Shifts

Vincent Hin,1 Tim Schellekens,2,* Lennart Persson,2 and Andre M. de Roos1,†

1. Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, P.O. Box 94284, 1090 GE Amsterdam, The Netherlands;2. Department of Ecology and Environmental Science, Umea University, SE-90187 Umea, Sweden

Submitted November 12, 2010; Accepted July 27, 2011; Electronically published October 31, 2011

Online enhancement: appendix.

abstract: In basic intraguild predation (IGP) systems, predatorsand prey also compete for a shared resource. Theory predicts thatpersistence of these systems is possible when intraguild prey is su-perior in competition and productivity is not too high. IGP oftenresults from ontogenetic niche shifts, in which the diet of intraguildpredators changes as a result of growth in body size (life-historyomnivory). As a juvenile, a life-history omnivore competes with thespecies that becomes its prey later in life. Competition can hencelimit growth of young predators, while adult predators can suppressconsumers and therewith neutralize negative effects of competition.We formulate and analyze a stage-structured model that capturesboth basic IGP and life-history omnivory. The model predicts in-creasing coexistence of predators and consumers when resource useof stage-structured predators becomes more stage specific. This co-existence depends on adult predators requiring consumer biomassfor reproduction and is less likely when consumers outcompete ju-venile predators, in contrast to basic IGP. Therefore, coexistenceoccurs when predation structures the community and competitionis negligible. Consequently, equilibrium patterns over productivityresemble those of three-species food chains. Life-history omnivorythus provides a mechanism that allows intraguild predators and preyto coexist over a wide range of resource productivity.

Keywords: intraguild predation, ontogenetic niche shifts, life-historyomnivory, stage-dependent interactions, alternative stable states, tri-trophic food chain.

Introduction

Omnivory is defined as the feeding on different trophiclevels (Pimm and Lawton 1978), which allows a species(an intraguild predator) to simultaneously prey on andcompete with another species (its intraguild prey), an in-teraction we refer to as basic intraguild predation (IGP;Polis et al. 1989; Holt and Polis 1997). IGP has received

* Present address: Wageningen Institute for Marine Resources and Ecosystem

Studies, P.O. Box 77, 4400 AB Yerseke, The Netherlands.†

Corresponding author; e-mail: a.m.deroos@uva.nl.

Am. Nat. 2011. Vol. 178, pp. 701–714. � 2011 by The University of Chicago.

0003-0147/2011/17806-52608$15.00. All rights reserved.

DOI: 10.1086/662676

considerable attention, since it is shown to be commonin natural communities (Polis 1991; Polis and Strong 1996;Arim and Marquet 2004). Theoretical predictions, how-ever, show limited scope for coexistence of intraguild pred-ators and intraguild prey (Holt and Polis 1997; Diehl andFeissel 2000; Mylius et al. 2001). Holt and Polis (1997)formulated two necessary conditions for coexistence inbasic IGP systems, namely, that the intraguild prey (orintermediate consumer) should be superior in resourcecompetition and that productivity levels should be inter-mediate. In systems with low productivity, resource com-petition plays the most dominant role, since consumerdensity is too low to be beneficial for the intraguild pred-ator, eventually leading to predator exclusion. In contrast,in highly productive systems, intraguild predators becometoo abundant and, hence, predation too intense for theconsumer to persist. Coexistence is therefore maintainedonly at intermediate productivity levels when competitionand predation are by and large balanced. Many subsequentstudies have focused on possible mechanisms that promotecoexistence of intraguild prey and predators, given thatIGP and omnivory are common in natural systems.Among the mechanisms originally proposed by Holt andPolis (1997) are age-restricted predation or prey life stagesinvulnerable to predation (Mylius et al. 2001; Borer 2002;Rudolf and Armstrong 2008), adaptive foraging behaviorby intraguild predators (Krivan 2000; Krivan and Diehl2005), spatial or temporal refugees for the intraguild prey(Finke and Denno 2006; Janssen et al. 2007; Amarasekare2008; Okuyama 2008), or additional resources for intra-guild prey (Holt and Huxel 2007). In theory, these mech-anisms may enhance coexistence of consumers and pred-ators by extending the conditions under whichcompetition and predation are balanced. This effect is,however, often rather marginal, as exemplified by the studyby Borer (2006), which showed that an empirically pa-rameterized IGP model is not likely to increase coexistencepossibilities. More commonly, these mechanisms increase

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coexistence by reducing the strength of the competitiveinteractions between intraguild predators and prey to anegligible level, which effectively marginalizes the IGP na-ture of the interaction (simultaneous predation and com-petition). In this sense, the frequent occurrence of IGPcan still only be understood by assuming that it is a rel-atively weak interaction (Janssen et al. 2006).

Omnivory often results from changes in body size overontogeny (Polis et al. 1989). Because many species growconsiderably in size during their life, ecological traits thatscale with body size—such as metabolic rate, risk to pre-dation, resource availability, and exploitation rate—changeover ontogeny (Peters 1983; Werner and Gilliam 1984).Species may therefore shift habitat or feed on differentresources in different life stages, a phenomenon referredto as ontogenetic niche shift (Werner and Hall 1979; Wer-ner and Gilliam 1984; Mittelbach 1988; Olson et al. 1995),or life-history omnivory (Pimm and Rice 1987). A speciesmay therefore be an omnivore when considered over itsentire life, while all its different life stages are specialistconsumers of their own single resource. Commonly, whenintraguild predation involves life-history omnivory, adultintraguild predators prey on consumers, while juvenileintraguild predators compete with consumers for a sharedresource. Feeding on different prey types during differentlife stages is generally associated with a trade-off in feedingefficiency, so that predators are inferior in resource com-petition to their specialist prey species (Werner and Gilliam1984; Persson 1988). Competing for a shared resource atan early life stage may therefore limit recruitment of ju-venile predators to later life stages and thus result in ajuvenile competitive bottleneck (Werner and Gilliam 1984;Neill 1988; Persson and Greenberg 1990; Bystrom et al.1998). Bystrom et al. (1998), for example, showed thatcompetition for zooplankton between juveniles of the life-history omnivore perch (Perca fluviatilis) and its prey spe-cies roach (Rutilus rutilus) negatively affected growth andcondition of perch. In systems where IGP is a consequenceof growth in body size, adult intraguild predators can sup-press the competitors of their offspring, in this way coun-teracting juvenile bottleneck effects (Persson 1988). Wal-ters and Kitchell (2001) dubbed this the cultivation effect,since dominant large species in this way cultivate a fa-vorable environment for their young. When species thatare dependent on cultivation for their persistence collapseand reach low abundances, a juvenile competitive bottle-neck can prevent recovery, although the species would beable to persist once present, owing to the cultivation byadult predators.

Although life-history omnivory and ontogenetic nicheshifts are widespread phenomena (Werner and Gilliam1984; Polis et al. 1989), their impact on the dynamics ofIGP is studied only to a limited extent (Mylius et al. 2001;

Van de Wolfshaar et al. 2006; Rudolf 2007). Studies thatexplicitly focus on stage- or size-dependent interactions inIGP systems model life-history omnivory more as an on-togenetic niche widening than as an ontogenetic niche shift(Van de Wolfshaar et al. 2006; Rudolf 2007). Such a nichewidening implies that additional resources become avail-able when intraguild predators grow in size. In that case,juvenile predators feed only on basic resource, while adultpredators are involved in IGP and hence prey on bothresource and consumers. Such a configuration still allowsthe intraguild predator to exclude the consumer, sinceadult predators can exclusively forage on resource biomasswhen productivity levels are high (Van de Wolfshaar et al.2006). However, a recent study (V. H. W. Rudolf and K.D. Lafferty, unpublished manuscript) has shown that theresource overlap between different predator stages is lim-ited even among nonmetamorphosing species, for whichthe ontogenetic niche shifts result from growth in bodysize. In the most extreme case, each life-history stage ofthe predator depends on its own exclusive and essentialresource type without any resource overlap between stagesat all. The study shows that such ontogenetic specialistscan alter the otherwise stabilizing effect that complexityhas on the stability of food webs (V. H. W. Rudolf and K.D. Lafferty, unpublished manuscript). Since ontogeneticspecialists have multiple essential resources, they face ahigh risk of secondary extinction resulting from the lossof such an essential resource (V. H. W. Rudolf and K. D.Lafferty, unpublished manuscript). To address the questionof how such a complete diet shift, in which resource useof juvenile and adult predators is nonoverlapping, affectsthe dynamics of IGP, we formulate and analyze a stage-structured IGP model. In this model, the interaction ofpredators with consumers can be varied from basic IGP,as considered in classical IGP models (Holt and Polis 1997;Diehl and Feissel 2000; Mylius et al. 2001), to completelife-history omnivory. First, we address how the parameterregion of coexistence of intraguild predators and preychanges as a function of the resource overlap betweenjuvenile and adult intraguild predators. Furthermore, weaddress to what extent the two conditions that are crucialfor coexistence in basic IGP (superior dominance of con-sumers and intermediate productivity) are required forcoexistence in systems where intraguild predation is a re-sult of an ontogenetic niche shift. The model predicts in-creasing coexistence possibilities when interactions are in-creasingly stage specific. A balance between competitionand predation can indeed lead to equilibrium coexistenceover a large range of productivities when the intraguildpredator is a life-history omnivore, but this equilibriumis generically unstable. Stable coexistence occurs only whencommunity dynamics are shaped primarily by predation,with competitive interactions playing only a marginal role.

Stage-Structured IGP 703

Table 1: Model equations

Dynamic equation Description

dR R (1 � F)R FRp d(R � R) � M C � M P � M Pmax c p j p adt H � R H � (1 � F)R � FC H � FR � (1 � F)Cc p p Resource biomass

dC FC (1 � F)Cp n (R)C � m C � M P � M Pc c p j p adt H � (1 � F)R � FC H � FR � (1 � F)Cp p Consumer biomass

dPj p n (R, C)P � n (R, C)P � g(n (R, C))P � m Pa a j j j j p jdt Juvenile predator biomassdPa p g(n (R, C))P � m Pj j p adt Adult predator biomass

As a result, changes in equilibrium density with increasingproductivity in the stable coexistence state largely resemblethose of a three-species linear food chain. In contrast,community dynamics may also be governed by strongcompetition between consumers and juvenile predators,leading to an alternative stable state, in which intraguildprey outcompete predators by imposing a juvenile bottle-neck. As a consequence, the assumption that intermediateconsumers are superior in the competition for basic re-source, which is crucial for coexistence in basic IGP sys-tems, can in fact hinder coexistence in IGP systems withlife-history omnivory. Finally, we also show that these re-sults remain valid when consumers are also stage struc-tured and intraguild predators have different feeding pref-erences for the different life stages of consumers.

Model Formulation

The ontogenetic changes in feeding habits of an intraguildpredator are modeled using the bioenergetics approach ofYodzis and Innes (1992), with a stage-structured extensionas formulated by de Roos et al. (2007). Four ordinarydifferential equations keep track of biomass changes ofresource R, intraguild prey or intermediate consumer C,juvenile intraguild predator Pj, and adult intraguild pred-ator Pa (table 1). For reasons provided by Mylius et al.(2001) and to allow comparison with the results of thatstudy, resource follows semi-chemostat dynamics( ) in the absence of consumers anddR/dt p d (R � R)max

intraguild predators, with turnover rate d and maximumresource density Rmax. Resource decreases through feedingby consumers and intraguild predators. Resource feedingby consumers increases their net biomass production,

, which equals the balance between biomass produc-n (R)c

tion through mass-specific ingestion and biomass lossthrough mass-specific maintenance rate Tc. Ingestion fol-lows a Type II functional response, with half-saturationconstant Hc, maximum ingestion rate Mc, and conversionefficiency j. Hence,

Rn (R) p jM � T . (1)c c cH � Rc

Consumer biomass decreases through predation by intra-guild predators and through background mortality mc (ta-ble 1).

The intraguild predator is structured into a juvenile andan adult stage and feeds on both consumer and resourcebiomass. Juvenile net biomass production, , is usedn (R, C)j

for growth of juveniles and maturation, which is repre-sented by the mass-specific rate . Net biomassg(n (R, C))j

production of adults, , is used only for productionn (R, C)a

of juveniles, so intraguild predators do not grow any fur-ther after entering the adult stage. Both adult and juvenilebiomass decrease through background mortality, mp, whichis assumed to be equal for both stages.

The mass-specific maturation rate is derived from deRoos et al. (2007) and given by

n (R, C) � mj pg(n (R, C)) p . (2)j 1�m /n (R, C)p j1 � z

This function expresses that the maturation rate increaseswith net biomass production of juveniles, , andn (R, C)j

decreases with predator background mortality mp as wellas with an increasing ratio between the predator body sizeat birth and at maturation, represented by the parameterz (de Roos et al. 2007). The maturation function is derivedfrom a structured population model in terms of partialdifferential equations, which accounts for a class of non-growing, equally sized adult predators and a continuoussize distribution of juvenile predators between their sizeat birth and their size at maturation. The derivation ofthis function is based on an assumption that at any par-ticular time the size distribution of juveniles between theirbirth and maturation size has the same shape as the equi-librium size distribution pertaining to the current mass-specific net production rate and mortality rate mpn (R, C)j

of juveniles. This equilibrium assumption applies only tothe relative juvenile biomass distribution and not theirtotal biomass. It is also equivalent to the assumption thatthe dynamics of the relative within-stage size distribution

704 The American Naturalist

of juveniles takes place on a faster timescale than thechanges in resource and absolute juvenile and adult bio-mass density. In addition, this is the only choice for thematuration function, which ensures that all equilibria oc-curing in the stage-structured biomass model are one-to-one identical to the equilibria occurring in the underlyingsize-structured model (de Roos et al. 2008). Despite itsformulation in only two ordinary differential equations,the model thus consistently translates the assumptionabout individual life history that forms the basis of theunderlying size-structured model to the population level.Under nonequilibrium conditions, dynamics of the stage-structured biomass model have also been shown to bequalitatively similar to the dynamics of a underlying size-structured model, except when the latter exhibits single-cohort or single-generation oscillations, in which not allsize classes of individuals are continuously present in thepopulation, but the population is dominated by individ-uals with body sizes within a restricted range (de Roos etal. 2008; Guill 2009).

Mass-specific net biomass production of juveniles andadults, denoted by and , respectively,n (R, C) n (R, C)j a

equals the difference between mass-specific ingestion andmass-specific maintenance Tp. Ingestion follows a Type IIfunctional response with maximum ingestion Mp, half-saturation constant Hp, and conversion efficiency j. Be-cause all model variables represent biomass densities, themaximum ingestion rate and half-saturation constant areassumed independent of whether predator individuals feedon resource or on consumers. Hence, andn (R, C)j

become:n (R, C)a

(1 � F)R � FCn (R, C) p jM � T , (3)j p pH � (1 � F)R � FCp

FR � (1 � F)Cn (R, C) p jM � T . (4)a p pH � FR � (1 � F)Cp

The total rates with which predators forage on resourceand consumers can be derived from the sum of the for-aging rates of juveniles and adults, given by

(1 � F)R FRM P � M P , (5)p j p aH � (1 � F)R � FC H � FR � (1 � F)Cp p

FC (1 � F)CM P � M P . (6)p j p aH � (1 � F)R � FC H � FR � (1 � F)Cp p

Parameter F models the extent of ontogenetic diet shiftbetween juveniles and adults. Although F represents dif-ferences in feeding habits rather phenomenologically, itcan be interpreted as the relative time spent feeding on aparticular prey species. For simplicity, we do not vary thediet composition of juvenile and adult predators indepen-dently, but restrict the model formulation and analysis to

the situation where feeding preferences of both predatorylife stages are symmetric and therefore use a single pa-rameter to model feeding habits of juvenile and adult pred-ators. At F p 0.5, no diet shift occurs and both predatorystages equally divide feeding time between resource andconsumers. In this case, net biomass production is equalfor both stages, since and simplify ton (R, C) n (R, C)j a

0.5R � 0.5Cn (R, C) p jM � T . (7)p p pH � 0.5R � 0.5Cp

The structured model in table 1 in this case reduces to anunstructured population model in which the intraguildpredator is not divided into different life stages (P �j

) and can be described with a single ordinary dif-P p Pa

ferential equation:

dPp n (R, C)P � m P. (8)p pdt

In this case, the model simplifies to the IGP model ana-lyzed by Mylius et al. (2001). If , the stage-struc-F ( 0.5tured model in table 1 rather than equation (8) describespredator dynamics. Decreasing F increases adult prefer-ence for consumers and simultaneously increases juvenilepreference for resource. At , adults prey solely onF p 0consumers, and juveniles forage only on the resource, rep-resenting a complete diet shift during development of theintraguild predator. Analyzing the dynamical conse-quences of changing F thus provides a method to studythe effect of various intensities of life-history omnivoryon an intraguild predation system.

Model Parameterization

Default model parameters are summarized in table 2. Max-imum ingestion (M) and maintenance (T) are both mass-specific rates (expressed in unit biomass per unit biomassper unit time), whereas the mortality parameter (m) rep-resents a per capita rate. Default values for these rates aretaken inversely proportional to the quarter power of adultbody size, with proportionality constants of 0.01 for main-tenance (Peters 1983; Yodzis and Innes 1992) and 0.001for background mortality (Gillooly et al. 2001). Maximumingestion rate is assumed equal to 10 times the mainte-nance rate (Peters 1983; Yodzis and Innes 1992). The de-pendence on adult body size can be simplified by adoptingthe mass-specific maintenance rate of consumers, Tc, toscale the time variable and hence set . Given thisT p 1c

scaling of time, maximum ingestion rate and mortalityrate become 10 and 0.1, respectively.

Adult predators are assumed to be 100 times larger thanconsumers (Yodzis and Innes 1992). The quarter powerscaling relations then dictate , , andM p 3 T p 0.3p p

Stage-Structured IGP 705

Table 2: Default model parameters

Parameter Resource Consumer Predator Description

Rmax Varied Resource maximum biomass densityd 1 Resource turnover ratej .5 .5 Assimilation efficiencyM 10 2.5 Maximum ingestion rate (mass specific)T 1 .3 Maintenance rate (mass specific)m .1 .03 Background mortality rateH 1 1 Half-saturation constantF .5–.0 Ontogenetic diet shiftz .01 Newborn-adult predator size ratio

Note: All figures are made with default parameters, unless indicated otherwise.

, given the scaling of the time variable with Tc.m p 0.03p

However, theory on IGP stipulates that coexistence is pos-sible only when consumers are superior in resource com-petition (Holt and Polis 1997). At , juvenile pred-F p 0ators and consumers are engaged in full resourcecompetition. Minimum resource requirements that allowfor biomass growth of consumers and juvenile predatorscan then be obtained by solving anddC/dt p 0

, respectively, while setting and :dP /dt p 0 P p 0 C p 0j a

H (T � m )c c c∗R p , (9)cjM � T � mc c c

H (T � m )p p p∗R p . (10)Pj jM � T � mp p p

The parameter setting as described above results in, which is not in line with the assumption of∗ ∗R p Rc Pj

competitive dominance of consumers (i.e., ). We∗ ∗R ! Rc Pj

therefore assume the default maximum ingestion rate ofintraguild predators to equal 2.5 instead of 3.0, repre-senting a reduction in feeding efficiency resulting from thedifferent prey types that an omnivore has to cope withduring ontogeny (Werner and Gilliam 1984). We, however,also study the case where juvenile predators have lowerminimum resource requirements than consumers (i.e.,

), by setting .∗ ∗R 1 R M p 3.5c P pj

In this study, the Type II functional responses are mod-eled using a maximum ingestion rate (M) and a half-saturation density (H). They can, however, easily be turnedinto the alternative formulation using attack (or clearance)rate in combination with handling time, which would re-veal that the maximum ingestion is identical to the inverseof the handling time and that the half-saturation densityH equals the ratio of maximum ingestion and attack rate.This latter identity suggests that the half-saturation densityis in fact independent of body size, since it equals the ratiobetween two per capita rates that both tend to scale withadult body size to the three-quarters power (Brown et al.

2004). Data on diverse groups of zooplankton confirmthis expectation (Hansen et al. 1997). The maximum re-source density Rmax and both half-saturation densities Hc

and Hp are expressed as gram biomass per unit volumeand are therefore the only parameters containing the unitof volume. Given that Hc and Hp are equal, they can henceboth be set to 1 without loss of generality, since this merelyimplies a scaling of the unit of the total system volume.Maximum resource density Rmax is then expressed as mul-tiples of the half-saturation density. Similarly, because ofthe scaling of time, the resource turnover rate d is ex-pressed as multiples of maintenance rate Tc. We adopt thedefault value such that resource turnover takes placed p 1at the same rate as consumer biomass turnover throughmetabolism. The ratio between newborn and adult pred-ator body size (z) is set to 0.01, so that newborn body sizeequals consumer body size. A conversion efficiency of 0.5is used for conversion of both resource and consumerbiomass (Peters 1983).

Model predictions are analyzed for different values ofRmax and F. Maximum resource densities Rmax correspondto different productivity levels, which equal dRmax. We willhence use maximum resource density and resource pro-ductivity as synonyms. We used Content, a numerical bi-furcation software package (Kuznetsov et al. 1996), to cal-culate equilibrium densities as a function of Rmax and F

and to assess equilibrium stability.

Results

For , predator dynamics are described by equationF p 0.5(8), and the model simplifies to a basic IGP system, inwhich juvenile and adult intraguild predator to the sameextent compete with and prey on intermediate consumers.While qualitative similar dynamics have been described byMylius et al. (2001), we will shortly summarize them herefor completeness and the introduction of symbols. In thebasic IGP system, four equilibrium types occur: (1) aresource-only equilibrium; (2) a consumer-resource equi-

706 The American Naturalist

Figure 1: Resource, consumer, and intraguild predator equilibrium biomass densities as a function of Rmax for (left) andF p 0.5 F p(right), with default values for all other parameters (table 2). Solid lines represent stable equilibria and dotted lines unstable equilibria.0.3

In the top row, juvenile predator biomass is indicated with gray lines and adult predator biomass with black lines. Dashed lines markdifferent productivity thresholds, at which a qualitative change in possible equilibria occurs. The threshold at which predators invade theconsumer-resource equilibrium leading to coexistence is the predator invasion point (Ip), the threshold where a stable predator-resourceequilibrium becomes possible is the consumer invasion point (Ic), and the threshold where consumers are excluded from the coexistencestate is the consumer exclusion point (Ec).

librium; (3) a coexistence equilibrium with resource,consumers, and intraguild predators; and (4) a predator-resource equilibrium (fig. 1, left). The resource-only equi-librium is stable as long as the population growth rates ofconsumers and predators are negative at the particularequilibrium resource density. Since consumers have lowerresource requirements than predators (i.e., ), con-∗ ∗R ! Rc p

sumers can invade the resource-only equilibrium whenpredator growth rate is still negative. At the consumer-resource equilibrium, resource density stays constant at

while consumer density increases with increasing Rmax.∗R c

Invasion of predators in the consumer-resource equilib-rium can occur when net biomass production of predatorsbecomes high enough to overcome their background mor-tality ( ). This productivity threshold is de-∗ ∗n (R , C ) p mp p

noted as the predator invasion point (Ip; fig. 1, left). In-

creasing productivity in the coexistence equilibriumincreases predator and resource biomass and decreasesconsumer biomass. At a particular resource productivity,a stable predator-resource equilibrium becomes possible.This productivity level is denoted as the consumer invasionpoint (Ic), since it is the highest Rmax value for which con-sumers can invade the predator-resource equilibrium (fig.1, left). In the absence of consumers, a predator-resourceequilibrium is feasible as soon as Rmax is above the min-imum resource density that predators need for persistence.This occurs already for Rmax values below Ic (at ,F p 0.5predators can in fact persist on resource alone at R ≈max

). However, as long as , consumers can in-0.717 R ! Imax c

vade the predator-resource equilibrium, which makes thelatter equilibrium unstable. Above the productivity thresh-old Ic, this invasion is no longer possible because of too

Stage-Structured IGP 707

Figure 2: Location of the productivity thresholds dependent on Rmax

and F, with all other parameters having default values. Black dashedline, predator invasion point (Ip). Black solid line, consumer invasionpoint (Ic). Gray dashed line, predator exclusion point (Ep). Gray solidline, consumer exclusion point (Ec).

high predation pressure, causing the predator-resourceequilibrium to become stable (Mylius et al. 2001). In-creasing productivity in the coexistence state eventuallyleads to exclusion of consumers, as predation pressurebecomes too high for their persistence. This threshold isreferred to as the consumer exclusion point (Ec; fig. 1, left).The two threshold levels of productivity Ic and Ec may notcoincide, resulting in bistability with the coexistence equi-librium and the predator-resource equilibrium as alter-native stable states. Here, consumers can persist when pre-sent but are unable to invade when absent because of highpredation pressure. Beyond Ec, the predator-resource equi-librium is the only stable state. For a more detailed de-scription of dynamics and equilibrium conditions of aclosely related basic IGP model, we refer to Mylius et al.(2001).

With decreasing F, juvenile predators increasingly de-pend on resource biomass and thus increasingly competewith consumers, while adult predators increasingly preyon consumers and thus become less resource dependent.These changing interactions alter the equilibrium prop-erties of the IGP system. Figure 2 shows how the pro-ductivity thresholds that separate parameter regions withdifferent types of equilibria shift to higher Rmax values whenF is decreased from 0.5. Because consumers are compet-itively superior and hence in consumer-resource equilib-rium impose a resource density that is insufficient forjuvenile predators to achieve positive biomass production,invasion of intraguild predators is successful only if ju-venile predators compensate their lower resource ingestionwith ingestion of consumer biomass. Lower values of F

imply that juveniles forage less on consumers and henceneed higher consumer densities to attain positive biomassproduction. Because higher consumer densities occur athigher productivity levels, the predator invasion thresholdIp shifts to higher Rmax values for lower values of F. Withdecreasing values of F, consumers hence increasingly im-pose a competitive bottleneck for juvenile predators, whichlimits invasion of the intraguild predator in the consumer-resource equilibrium.

The productivity threshold where the predator-resourceequilibrium becomes stable against invasion by consumers(Ic) also shifts to higher Rmax values with decreasing valuesof F. As shown by Mylius et al. (2001), this productivitythreshold is determined by the predation pressure imposedon consumers, preventing successful consumer invasion.Since adult predators feed less on the resource with de-creasing F, higher productivity levels are needed to sustainpredator densities that are sufficient to suppress the con-sumer’s growth rate below 0. Around , Ic mergesF p 0.35with Ec so that bistability between the predator-resourceand the coexistence equilibrium no longer occurs.

For lower F values, juvenile predators forage more and

more on resource and hence suffer increasingly from thecompetition by consumers. Predator persistence is thenpossible only if consumer densities are driven down bypredation to such an extent that resource density is suf-ficiently high for juvenile predator growth. Consequently,for low F values, predators may be able to persist at ahigh density but fail to invade the consumer-resource equi-librium when at low density. This also implies that thereare ranges of Rmax values, for which a coexistence equilib-rium occurs as an alternative stable state of a consumer-resource equilibrium that the predator cannot invade. Fig-ure 1 (right) shows for that invasion of predatorsF p 0.3occurs at slightly higher Rmax values than for andF p 0.5that all values of Rmax allowing for predator persistencealso allow for invasion of the consumer-resource equilib-rium by predators (see also the position of Ip along theRmax axis in fig. 2). For (fig. 3, left), however, thereF p 0.1are Rmax values where predators can persist at high density,while these Rmax values do not allow invasion of the con-sumer-resource equilibrium by a low density of predators.In figure 3 (left), this is apparent from the fact that thecurve representing coexistence equilibria starts out at thethreshold value Ip in the direction of lower Rmax values (fig.3, top left). This initial part of the equilibrium curve rep-resents unstable equilibria, separating the stable consumer-

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Figure 3: Resource, consumer, and predator equilibrium biomass densities as a function of Rmax for (left) and (right),F p 0.1 F p 0.0with other parameters as default. The lowest productivity for which coexistence is possible is indicated as the predator exclusion point Ep.All other lines are as in figure 1. Note the stable consumer-resource equilibrium next to the stable coexistence equilibrium for .F p 0

resource equilibrium from a stable coexistence state. At aproductivity threshold denoted by Ep, the predator equi-librium curve changes direction to higher Rmax values again(limit point or saddle node bifurcation) and continues asa curve representing stable coexistence equilibria. Thepoint Ep is the predator exclusion point and represents theminimal productivity level required for predators to persistin coexistence with consumers. The F value at which Ep

originates is shown in figure 2. For F values where thepersistence boundary Ep is positioned at lower productivitythan the invasion boundary Ip, bistability occurs betweenthe consumer-resource state and the coexistence state. Bi-ologically, this means that for productivity levels wherethese two states co-occur, predators cannot invade the con-sumer-resource state because of the negative effect of com-petition on juveniles, but predators can maintain them-selves when present at high density. This persistence is dueto the predation of adult predators on consumers, which

increases resource biomass for juvenile predators. For Rmax

values exceeding Ip, a wide range of resource productivitiesexist for which coexistence is the only stable state (fig. 3,left). At Rmax values exceeding the consumer invasionthreshold (Ic), consumers are excluded and a predator-resource equilibrium is the only stable state (fig. 3, left).The different combinations of equilibria are depicted infigure 2, in which the positions of the productivity thresh-olds along the Rmax axis for are plotted. As0.5 ≤ F ≤ 0.0shown in figure 2, decreasing the value of F toward 0shifts the positions of Ip and Ic toward higher Rmax values,while the productivity threshold Ep changes little over Rmax.Ultimately, this results in the equilibrium configuration asillustrated in figure 3 (right) for . Adults now preyF p 0solely on consumers, and juveniles forage only on theresource. Because of the competitive advantage of con-sumers, the predator invasion point disappeared, and theconsumer-resource equilibrium is stable for all Rmax values.

Stage-Structured IGP 709

Figure 4: Resource, consumer, and predator equilibrium biomassdensities as a function of Rmax for , , and otherF p 0.0 M p 3.5p

parameters as default. Lines as in figures 1 and 3.

As an alternative outcome of dynamics, a stable coexis-tence state exists. Since adults lack an alternative resourceat , consumers cannot be excluded from the co-F p 0existence state, which translates in the absence of the con-sumer invasion point (Ic). Therefore, for low F values, theonly productivity threshold present is Ep, marking thelower limit of Rmax for which the intraguild predator per-sists (fig. 2).

In the coexistence state at , equilibrium patternsF p 0.0with increasing productivity largely resemble those of athree-species linear food chain (Oksanen et al. 1981),where top predators regulate biomass of consumers andthus release the consumer’s control over resource biomass.Consumer densities therefore stay constant with changingvalues of Rmax, leading to bottom-up regulation of resourcebiomass in equilibrium, which increases with increasingRmax. Under these conditions, predation by adult predatorsacts as the main structuring force, and consumers are top-down regulated by adult predators, which nullifies the po-tentially strong competition between juvenile predatorsand consumers. This cultivation by adult predators in-creases food availability for juvenile predators and enablestheir coexistence with the consumer (Walters and Kitchell2001). In the alternative, consumer-resource equilibrium,strong competition for resources between juvenile pred-ators and consumers translates into a juvenile competitivebottleneck, which restricts maturation and thereby mar-ginalizes the predatory interactions between consumersand adults. Under such conditions interspecific competi-tion is the main structuring interaction in the communityleading to predator exclusion.

To allow for coexistence in basic IGP systems, consum-ers should be superior in resource consumption to offsetthe negative effects of predation (Holt and Polis 1997).When this assumption is not met, the intraguild predatorcan invade at lower resource densities compared with theconsumer and a predator-resource equilibrium is the ex-clusive outcome of system dynamics (Diehl and Feissel2000). In the case of life-history omnivory with a completeniche shift, however, adult predators require consumerbiomass to reproduce. This assumption ensures that in-vasion of the intraguild predator is possible only with con-sumers present and also prohibits consumer exclusion.Resource competition now takes place between juvenilepredators and consumers. When relaxing the assumptionof consumer competitive dominance, juvenile predatorsno longer suffer from competition, and the intraguildpredator can invade the consumer-resource equilibriumat . This results in the equilibrium patterns asF p 0.0shown in figure 4. Here, the maximum ingestion rate ofthe predator (Mp) is set to 3.5, which ensures that juvenilepredators can attain a positive growth rate at a lower Rmax

value than required by consumers. Compared with basic

IGP (fig. 1, left), there is a large scope for coexistencebetween consumers and intraguild predators. Similar towhen consumers are superior resource competitors (fig.3, right), equilibrium patterns in the coexistence equilib-rium resemble those of a three-species linear food chain.Whereas IGP clearly operates as juvenile predators feedexclusively on resource, the ontogenetic niche shift of theintraguild predator results in a type of dynamics thatclosely resemble the classical pattern of a linear food chain.

Discussion

We formulated and analyzed an intraguild predationmodel that allowed us to vary the degree of resource over-lap between juvenile and adult intraguild predators. In thisway, the dynamics as described for classical IGP models,with no stage structure for the intraguild predator (hereat ; Holt and Polis 1997; Mylius et al. 2001), canF p 0.5

710 The American Naturalist

be linked to the dynamics of a system in which IGP is aconsequence of a complete ontogenetic niche shift (hereat ). In the latter configuration, juvenile and adultF p 0.0predators have nonoverlapping resource use, and resourcesof both life stages are essential and nonsubstitutable. Holtand Polis (1997) originally proposed that nonoverlappingresource use of juveniles and adult intraguild predatorsmight reduce the likelihood of consumer exclusion andthereby enhance coexistence. Furthermore, Polis et al.(1989) conclude that IGP in many cases involves speciesthat change food type at metamorphosis or by ontogeneticniche shifts, which is especially common in aquatic sys-tems. In this study, we show that IGP as a result of suchontogenetic niche shifts can greatly alter the dynamics ofclassical IGP systems. Furthermore, it changes the con-ditions for which intraguild predator and prey can coexist,compared with IGP systems in which juvenile and adultpredators have the same resource use (Holt and Polis 1997;Mylius et al. 2001).

Originally, IGP can persist in case of a delicate balanceof competition and predation, which occurs when con-sumers are superior in resource competition to offset thenegative effects of predation and when environmental pro-ductivity is intermediate (Polis et al. 1989; Holt and Polis1997; Mylius et al. 2001; Amarasekare 2008). In low-pro-ductivity environments, resource competition dominates,allowing the superior consumer to outcompete the intra-guild predator, while at high productivity, predation pres-sure becomes too high for consumer persistence. We showthat a diet shift between juvenile and adult predators in-creases the scope of coexistence and totally prevents ex-clusion of the consumer at high productivity when theomnivorous feeding by the intraguild predator is com-pletely divided between the juvenile and adult life stages(here at ; fig. 3, right). The inclusion of a dietF p 0.0shift in the life history of the intraguild predator thereforegreatly increases the scope of coexistence between intra-guild predators and intraguild prey. Coexistence, however,crucially depends on the assumption that adult predatorsrequire consumer biomass for reproduction and cannotpersist on resource biomass alone. If consumers dominateresource competition, the coexistence state occurs next toa stable consumer-resource state, which cannot be invadedby predators (fig. 3, right). A competitively superior con-sumer is therefore able to prevent coexistence by imposinga bottleneck in the recruitment of the life-history omni-vore. This contrasts with early studies on IGP, which fora variety of models show that the consumers should besuperior resource competitors to allow for coexistence(Holt and Polis 1997; Borer et al. 2007). We furthermoreshow that this juvenile bottleneck does not occur whenjuvenile predators have a lower resource requirement thanconsumers (fig. 4). Note that this does not imply that the

predator population as a whole is competitively superiorto consumers, since adult predators are not involved incompetition with consumers at all.

Whether consumer species are superior in resourcecompetition compared with intraguild predators dependson the system considered. Vance-Chalcraft et al. (2007)showed in a meta-analysis that intraguild prey species aregenerally more effective at suppressing the shared resourcecompared with the intraguild predator, indicating thatconsumers are the dominant competitor. This effect, how-ever, varied among different ecosystems (Vance-Chalcraftet al. 2007). It may also be argued that the feeding of life-history omnivores on different prey types results in mor-phological and behavioral trade-offs, and omnivores aretherefore expected to be inferior resource feeders, com-pared with their specialist prey species (Werner and Gil-liam 1984; Persson 1988).

Negative effects of competition on growth of life-historyomnivores have been observed, especially in aquatic sys-tems. Piscivorous fish that in early life stages compete withtheir prey for zooplankton or macroinvertebrates havebeen shown to suffer from reduced growth and devel-opment (Neill 1988; Persson and Greenberg 1990; Olsonet al. 1995; Bystrom et al. 1998; Schroder et al. 2009).However, the effect of competition also depends on theamount of resource overlap, the time exposed to com-petition, and spatial factors such as habitat heterogeneity(Persson 1991). Considering this, young life-history om-nivores might escape negative effects of competition. Forexample, piscivorous adult European perch (Perca fluvia-tilis) induce a behavioral response in their prey, juvenileindividuals of roach (Rutilus rutilus), to spend more timein the littoral habitat as opposed to the pelagic zone of alake (Persson 1991). This reverses the outcome of com-petition between juveniles because perch dominates com-petition in the more complex littoral zone, whereas roachdominates in the pelagic zone.

In the perch-roach system, as in many especially aquaticIGP systems, consumers and predators both grow consid-erably in body size, and size-dependent interactions mayhence be important for both populations. For simplicity,we assumed that consumers do grow in body size but thatthe interactions of differently sized consumers are the sameper unit biomass. In the appendix (available online), wepresent an extension of the current model in which theconsumer population is also stage structured. This allowsfor different mass-specific feeding rates between juvenileand adult consumers and for predators to feed on eitherjuvenile or adult consumers. In the appendix, we showthat these extensions do not qualitatively change modelpredictions. Moreover, a consumer population in whichjuvenile and adult individuals have different feeding ratesallows for enlarged coexistence possibilities of consumers

Stage-Structured IGP 711

and intraguild predators as a consequence of overcom-pensation in stage-specific biomass that can occur with anincrease in consumer mortality (de Roos et al. 2007).

Rudolf (2007) studied an IGP model with a stage-struc-tured intraguild predator and showed that coexistence isalso possible in cases where intraguild predators are su-perior in resource competition, if the stage-structuredpredator is cannibalistic. While the condition that con-sumers should be superior competitors for the resourceseems to hold for IGP systems lacking size structure (Holtand Polis 1997; Borer et al. 2007), the results presentedhere and the study performed by Rudolf (2007) suggestthat this condition is not crucial for coexistence in systemswhere IGP is the result of an ontogenetic niche shift. Fur-thermore, a substantial degree of cannibalism in the pred-ator population prevents predator-mediated exclusion ofconsumers and so enables coexistence with intraguild preyat high productivity (Crumrine 2005, 2010; Rudolf 2007).While these dynamics are comparable to the dynamics ofthe model presented here at , the underlyingF p 0.0mechanisms differ. In the model of Rudolf (2007), co-existence depends on the assumed density-dependentmortality (cannibalism) of intraguild predators, whereasin our model it depends on the assumption that consumersare an essential and nonsubstitutable resource for adultintraguild predators.

Other studies focusing on size-specific interactionswithin IGP systems conclude that life-history omnivorylimits coexistence of predators and prey (Van de Wolfshaaret al. 2006) or increases coexistence only to a limited extent(Mylius et al. 2001). The manner in which size structureis implemented in those studies, however, differs from theway stage structure is incorporated here. Mylius et al.(2001) extended the basic IGP model with either a preystage invulnerable to IGP or a predatory stage incapableof IGP. While this quantitatively increased the parameterspace over which coexistence was possible, the generalresult of coexistence being limited to intermediate pro-ductivity levels remained valid (Mylius et al. 2001). Vande Wolfshaar et al. (2006) analyzed a physiologically struc-tured population model with a size-structured predatorand prey population. In that model, growth of both preyand predator was modeled food dependently, and foragingrates depended on the size of individuals. A positive feed-back loop between foraging success of a predator on theresource early in life, more rapid growth in size, and hencehigher foraging rates on consumers later in life resultedin rapid exclusion of consumers, especially at high resourceproductivities (Van de Wolfshaar et al. 2006). However,large adult intraguild predators in the model studied byVan de Wolfshaar et al. (2006) could still persist exclusivelyon resource biomass, which allowed the consumer to beexcluded.

In short, this study shows that coexistence is promotedwhen consumer biomass is an essential resource for adultpredators and when juveniles do not experience negativeeffects of competition. When all species coexist, equilib-rium patterns resemble those of a three-species linear foodchain where predator biomass is controlled bottom-upwhile consumer densities are top-down controlled by adultpredators, which are the abundant predatory life stage (fig.4). Furthermore, top-down control of consumers causesresource biomass to increase with productivity (fig. 3,right). Similar to classic IGP systems (here at ),F p 0.5the presence of a life-history omnivore in an IGP systemleads to higher resource density at equilibrium, comparedwith resource density in the consumer-resource state (fig.3, right).

The prediction of linear food chain dynamics in a stage-structured IGP system is supported by Persson et al.(1992), who found that biomass patterns of planktivorousand piscivorous fish in Scandinavian lakes agree with pre-dictions of linear food chain theory in low to moderatelyproductive lakes, even though these species are potentiallyinvolved in IGP interactions. While coexistence in basicIGP systems results from balanced competition/predation,our results show that in the case of life-history omnivory,such a balance leads to unstable coexistence. Potentially,both interactions might be equally strong; however, long-term dynamics converge to a state in which one of theinteractions is far stronger than the other. In coexistence,predation by adult predators acts as the main force struc-turing the community, preventing competition betweenjuveniles and consumers to occur. Coexistence is thereforea dynamical result that arises from the interaction betweenintraguild predators and prey, instead of resulting from apriori assumptions that weaken this interaction and, inthis way, increase the scope of coexistence between intra-guild predators and prey, for example, through spatial ortemporal heterogeneity (Finke and Denno 2006; Janssenet al. 2007; Amarasekare 2008; Okuyama 2008) or addi-tional resources for intraguild prey (Holt and Huxel 2007).As an alternative outcome of system dynamics, however,predators cannot persist because of the strong competitionbetween juveniles and consumers. Now, the communityis structured by interspecific competition, preventing pred-atory interactions between adults and consumers. So eventhough resource feeding by juvenile predators and pre-dation on consumers by adult predators takes place con-tinuously and simultaneously, only one of these two in-teractions determines community dynamics.

In classical models of IGP, the type of resource dynamicsand functional response, the relative competitive ability ofintraguild prey (consumer) versus intraguild predator, andthe relative efficiency of IGP (i.e., the energy transfer ef-ficiency of the direct link from resource to intraguild pred-

712 The American Naturalist

ator compared with the indirect link via consumers) de-termine whether and which type of alternative stable statesoccur (Takimoto et al. 2007; Verdy and Amarasekare 2010).With semi-chemostat resource dynamics, two differentscenarios are possible: either a consumer-resource equi-librium or a coexistence equilibrium occurs as an alter-native stable state next to a stable predator-resource equi-librium (Verdy and Amarasekare 2010). Accordingly, wefind a coexistence state next to a predator-resource statefor the classical IGP model (at ). However, forF p 0.5decreasing values of F, we find that the scenario changesfrom a coexistence and a predator-resource equilibriumto a coexistence and a consumer-resource equilibrium asalternative stable states. The latter combination can occuronly in classical IGP systems with logistic resource growthand Type II consumer functional responses (Verdy andAmarasekare 2010). The occurrence of a coexistence equi-librium as an alternative stable state to a consumer-resource equilibrium implies that persistence of the intra-guild predator is possible at lower productivity levels thanthe productivity that allows for predator invasion of theconsumer-resource equilibrium. Thus, intraguild preda-tors are subjected to an Allee effect, which in classical IGPmodels originates from the nonlinearities of the logisticresource growth and the Type II consumer functional re-sponse. In our system at , however, a completelyF p 0.0different mechanism is responsible for this Allee effect,since it represents a juvenile competitive bottleneck whoseoccurrence depends only on the assumption that consum-ers are superior resource competitors.

Our model prediction that an IGP system involving alife-history omnivore is, in coexistence, mainly structuredby predation—despite a potential for mixed competition/predation interactions—is supported by long-term studiesfocusing on the interactions between the life-history om-nivore perch (Perca fluviatilis) and its competing preyroach (Rutilus rutilus; L. Persson and A. M. de Roos, un-published manuscript). In this system, the potential formixed interactions appears to be of minor importance forexplaining long-term dynamics. Instead, interspecific pre-dation of perch on roach and intraspecific processes suchas competition and cannibalism are proposed to determinecoexistence (L. Persson and A. M. de Roos, unpublishedmanuscript). During transient dynamics, however, com-petition between roach and juvenile perch may be relevant,since roach can impose a bottleneck for perch recruitment(Bystrom et al. 1998). Similarly, the interaction betweenarctic char (Salvelinus alpinus) and brown trout (Salmotrutta) has generally been interpreted as driven by inter-specific competition (Nilsson 1965; Jansen et al. 2002),whereas long-term data now suggest that the system isstructured by predation only (Persson et al. 2007).

Results presented here also have implications for eco-

system management. In particular, strong predation byadult predators structuring a community may mask po-tentially strong competitive interactions between juvenilesand consumers. Therefore, communities with the potentialof mixed competition/predation interactions may seem-ingly respond to changes in productivity or exploitationas a linear food chain by, for example, revealing a trophiccascade with increasing exploitation of top predators. Neg-ative effects of competition may remain hidden and be-come apparent only after the collapse of the predator.Depending on the competitiveness of juvenile predators,the community may shift to an alternative state from whichpredator recovery is impossible. Overexploitations of pi-scivorous fish stocks provide good examples of this phe-nomenon (Frank et al. 2005; Persson et al. 2007; Van Leeu-wen et al. 2008; Casini et al. 2009). For example,overexploitation of cod in the Northwest Atlantic and Bal-tic Sea has led to an increase in prey fish densities and acommunity-wide regime shift. The recovery of the codpopulation may now be limited by the strong competitiveinteraction between prey fish and juvenile cod resultingfrom the community shift (Casini et al. 2009). For predatorexploitation and recovery, it is hence important to considerrealized as well as potential interactions between predatorsand their prey. From this ecosystem perspective, the strat-egy of culling prey to relax competition or increase adultfood availability (Persson et al. 2007), which at first sightseems counterintuitive, starts to make sense.

Acknowledgments

The excellence grant Lake Ecosystem Response to Envi-ronmental Change from the Swedish Research Council forEnvironment, Agricultural Sciences, and Spatial Planningto L. Persson supported T.S.

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