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Journal of Theoretical Biology 308 (2012) 36–44 Contents lists available at SciVerse ScienceDirect Journal of Theoretical Biology journal homepage: www.elsevier.com/locate/yjtbi Coexistence of two stage-structured intraguild predators Tim Schellekens a,n, Tobias van Kooten b a b IMARES, P.O. Box 77, 4400 AB Yerseke, The Netherlands IMARES, P.O. Box 68, 1976 CP Ijmuiden, The Netherlands H I G H L I G H T S c c c We model two stage-structured intraguild predator populations with life-history omnivory. We examine the consequences of distinct adult diets for coexistence of these predators. Coexistence is enabled because one is forced to act as a predator and the other to act as a consumer. a r t i c l e i n f o a b s t r a c t Article history: Received 16 January 2012 Received in revised form 26 April 2012 Accepted 14 May 2012 Available online 31 May 2012 An organism can be defined as omnivorous if it feeds on more than one trophic level. Omnivory is present in many ecosystems and multiple omnivorous species can coexist in the same ecosystem. How coexisting omnivores are able to avoid competitive exclusion is very much an open question. In this paper we analyze a model of a community consisting of two omnivorous predators and a basal resource. The population of both predators is explicitly structured into juveniles and adults, of which juveniles only feed on basal resource and adults feed on a varied proportion of basal resource and juveniles of the other population. We thereby separate the omnivorous roles (competitor for basal resource and predator of competitors) over life history. We show in this study that persistence of multiple omnivorous predators is possible when predators differ in adult diets. In this case, coexistence occurs because community dynamics force one of the model species to act as a predator and the other to act as a consumer. We conclude that separation of omnivorous roles over life history not only offers an explanation on why systems with omnivory can persist, but also how multiple omnivores can coexist at the same trophic levels of those systems. & 2012 Elsevier Ltd. All rights reserved. Keywords: Ontogenetic diet shifts Life-history omnivory Niche widening Tritrophic food chain Reciprocal predation 1. Introduction Pimm and Lawton (1978) defined omnivory as the feeding on different trophic levels, which allows an intraguild predator species to simultaneously prey on and compete with another species (named the intraguild prey). The basic form of this type of interaction is also referred to as intraguild predation (IGP: Holt and Polis, 1997; Polis et al., 1989). IGP is shown to be common in natural communities (Arim and Marquet, 2004; Polis, 1991; Polis et al., 1996). Theoretical models predict, however, limited possibilities for coexistence of intraguild predators and intraguild prey (Diehl and Feissel, 2000; Holt and Polis, 1997; Mylius et al., 2001). These models have led to two generic insights: reduced scope for coexistence compared to tritrophic food chains and the possibility of alternative stable states with community shifts along productivity n Corresponding author. Tel.: þ31317 480954; fax: þ 31317 487359. E-mail addresses: [email protected] (T. Schellekens), [email protected] (T. van Kooten). 0022-5193/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jtbi.2012.05.017 gradients (Holt and Polis, 1997, Diehl and Feissel, 2000, Mylius et al., 2001). Coexistence between intraguild predator and prey in models is only possible, according to Holt and Polis, 1997, if two essential conditions are met. Firstly, the intraguild prey should be superior in resource competition, and secondly, productivity levels should be intermediate. Given the commonness of omnivory in nature also beyond these essential conditions, studies have since focused on possible mechanisms that promote coexistence of intraguild prey and predators. Mechanisms that have been found to promote coexistence are age-restricted predation or prey life stages invulnerable to predation (Borer, 2002; Mylius et al., 2001; Rudolf and Armstrong, 2008), adaptive foraging behavior by intraguild predators (Krivan, 2000; Krivan and Diehl, 2005), spatial or temporal refuges for the intraguild prey (Amarasekare, 2008; Finke and Denno, 2006; Janssen et al., 2007; Okuyama, 2008), additional resources for intraguild prey (Holt and Huxel, 2007) and cannibalism (Rudolf, 2007). The mechanisms proposed may enhance coexistence of consumers and predators by extending the conditions under which competition and predation are balanced. Borer (2006) questioned that the effect of these mechanisms is actually present in T. Schellekens, T. van Kooten / Journal of Theoretical Biology 308 (2012) 36–44 nature, however, because it was marginal in an empirically parameterized IGP model. As species grow during their life, resource availability and exploitation rate change over ontogeny (Peters, 1983; Werner and Gilliam, 1984). Species may therefore feed on different resources in different life stages, a phenomenon referred to as life-history omnivory (Pimm and Rice, 1987). As a result, adult life history omnivores for instance prey on consumers, while juveniles compete with them for a shared resource. The impact of life-history omnivory on the dynamics of IGP has only been studied to a limited extent (Hin et al., 2011; Mylius et al., 2001; van de Wolfshaar et al., 2006). Nevertheless, Hin et al. (2011) showed that life-history omnivory is a form of intraguild predation that permits coexistence of predator and prey over more than just intermediate resource productivities and no longer requires the prey to be the better competitor for resource. This occurs because Hin et al., 2011 assumed that the adult intraguild predator feeds only on intraguild prey and hence cannot persist in its absence. Rudolf (2007) and van de Wolfshaar et al. (2006) modeled life-history omnivory as an ‘ontogenetic niche widening’ instead of an ontogenetic niche shift, which assumes that additional resources become available when intraguild predators grow in size. The intraguild predator that undergoes an ontogenetic niche widening is still able to exclude the intraguild prey at high resource productivity, when adult predators can exclusively forage on resource (van de Wolfshaar et al., 2006). Given the commonness of omnivory in nature, it is not surprising that several omnivorous species regularly coexist in the same habitat (Arim and Marquet, 2004; Polis, 1991; Polis et al., 1996). Woodward and Hildrew, 2002 assessed the importance of body size in relation to intraguild predation and niche overlap between predators in the food web of Broadstone Stream (UK) and found that mutual predation between intraguild predators was frequent. Decapods, for instance, appear capable of preying on heterospecific juveniles while feeding on the same basal resources as heterospecifics (League-Pike and Shulman, 2009; Ojeda and Dearborn, 1991; Ropes, 1969; Rossong et al., 2006; Williams et al., 2006). The same holds true for spider communities (Balfour et al., 2003; Rypstra and Samu, 2005). Interestingly, all these studies show that the occurrence of the intraguild predatory interaction is size-dependent; Small individuals of the intraguild predator compete for resources with the intraguild prey, whereas larger individuals feed on them. Although coexistence of multiple intraguild predators is commonly observed in nature, it is only studied to a limited extent using models. General consensus among these theoretical studies is that possibilities for coexistence of multiple omnivores on the same trophic level at the same time are limited. Feeding relationships in ecological communities are generally conceptualized as networks of nodes representing taxa linked by feeding interactions, the strength of which is based on assumptions about body size (Brose et al., 2006; Woodward et al., 2005). In these networks, trophic position of species is fixed. Size spectrum models, in contrast, describe the community as a continuous size distribution, and diets are determined by some criterion, often related to gape size. This means that as organisms grow, ontogenetic niche widening occurs and they move up the trophic hierarchy (e.g. Hartvig et al., 2011; Law et al., 2009; Williams and Martinez, 2000). As a result, size spectrum models generally predict food webs with a higher degree of omnivory at larger body size. Because species with a similar size-range will have similar diets and hence strong niche overlap, all but one of these species will generally be outcompeted in resulting food webs. According to size spectrum models, coexistence of multiple omnivores is therefore only possible between species which start off at and/or ultimately reach different body sizes and thus attain sufficient niche segregation. 37 Using a simple population dynamical model, HilleRisLambers and Dieckmann (2003) varied the diet of two unstructured intraguild populations by defining a trade-off between feeding on heterospecifics and resource. In their model, coexistence was only possible when omnivores were ‘punished’ with lower combined maximum intake rates compared to specialized predators or consumers. In essence, coexistence was only possible if both species were a priori set to be more efficient as either a predator or a consumer. When omnivores profited from feeding on more than one trophic level, or their combined intake did was not differ from the intake of specialized predators or consumers, coexistence was highly unlikely. The authors disregarded, however, the fact that omnivory results from changes in body size over ontogeny (Polis et al., 1989) and assumed unstructured populations. Thereby, they overlooked possible mechanisms for coexistence that may arise from population dynamical feedbacks of population structure as presented by Hin et al. (2011). In this paper, we include population structure and study the possibilities for coexistence of two intraguild predators with linear trade-offs between feeding on heterospecifics and resource. We assume, following studies on natural occurrences of coexisting omnivores, that predation only takes place when individuals get large enough (adult) and that juveniles feed on shared resource only. For one of the populations at a time, we vary the diet of adults in a linear trade-off. At one extreme this population only feeds on resource throughout its entire life and no predation on heterospecifics takes place. At the other extreme the adults exclusively prey on juvenile heterospecifics. We show, in contrast to predictions from size spectrum models (e.g. Hartvig et al., 2011; Law et al., 2009; Williams and Martinez, 2000) and HilleRisLambers and Dieckmann (2003), that coexistence of two intraguild predators is stable if either of these extremes in the varied population is approached. These two extremes result in two different community settings. In the first setting just one intraguild population preys on the other, resulting in community dynamics that resemble classic intraguild predation schemes in which coexistence is limited to intermediate resource productivities. In the second setting predation takes place between the two populations reciprocally, but community dynamics reflect that of a tritrophic food chain. This setting results in coexistence possibilities beyond intermediate resource productivities. 2. Materials and methods Dynamics are modeled using the bioenergetics approach of Yodzis and Innes (1992) with a stage-structured extension as formulated by De Roos et al. (2008) for the two intraguild predators. Five ordinary differential equations (ODEs) keep track of biomass changes of resource R, and two intraguild predators: P, the fixed population, and G, the varied population (juveniles Pj and Gj and adults Pa and Ga, see Table 1, subscripts j and a are used throughout the text to indicate juveniles and adults, respectively). Resource follows semi-chemostat dynamics in absence of P and G, with turnover rate d and maximum resource density Rmax. We have explicitly avoided the use of logistic growth of resource to avoid problems in mass-balance (Kooi et al., 1998). Resource biomass decreases through feeding by P and G. Both intraguild predators are structured into a juvenile and an adult stage which potentially feeds on juveniles of the other predator and/or resource biomass. Because much of the descriptions for both intraguild predators are the same, we will use subscript i in these descriptions to indicate either of the populations G or P. Juvenile predator biomass decreases through predation by intraguild predators and through background mortality mb (Table 1). Juvenile net biomass production, nij, is used for growth of juveniles and maturation, which is represented by the 38 T. Schellekens, T. van Kooten / Journal of Theoretical Biology 308 (2012) 36–44 mass-specific rate gi. Net biomass production of adults, nia, is only used for reproduction. Intraguild predators therefore do not grow after entering the adult stage. Adult biomass only decreases through background mortality, mb. The mass-specific maturation rate is derived in De Roos et al. (2007): gi ¼ nij mi will vary FG to investigate the consequences of this linear tradeoff between feeding on heterospecifics and resource. At first we assume adults of the fixed intraguild predator, Pa, always feed on both resource and juvenile competitors (Gj) equally (FP ¼0.5). Later on, we will fix FG and vary FP. Hence mass-specific net biomass production rates for both populations’ juvenile stages Pj and Gj become: ð1Þ 1z1mi =nij nij ðRÞ ¼ sMi Maturation depends on net biomass production of juveniles, nij, juvenile predator mortality mi and the ratio of predator body size at birth and at maturation, represented by the parameter z (De Roos et al., 2007). Eq. (1) captures the growth and survival of juvenile individuals from the size at birth to the size at maturation in such a way that the stage-structured biomass model in equilibrium is exactly identical to a physiologically structured population model (PSPM) accounting for a continuous sizedistribution of juvenile predators (De Roos, 2008). Mass-specific net biomass production of juveniles and adults, denoted by nij and nia, respectively, equals the difference between mass-specific ingestion and mass-specific maintenance Ti. Ingestion follows a type II functional response with maximum ingestion rate Mi, half-saturation constant Hi and conversion efficiency s. Parameter FG models the extent of ontogenetic diet shift between juveniles and adults of predator G. ^G can be interpreted as the relative time spent by adults feeding on a particular prey species and can be varied in a linear trade-off. At ^G ¼1, no diet shift occurs and both stages of G feed on the resource R. When FG o1, however, individuals broaden their diet after maturation and start feeding on juvenile heterospecifics (Pj). At FG ¼0.5, adults spend half their time feeding on resource and half on juvenile heterospecifics. At FG ¼0, the varied population G experiences a full diet shift over ontogeny: juveniles feed on the resource only and adults feed on juvenile heterospecifics only. We Table 1 Ordinary differential equations. dR R FP R ¼ dðRmax RÞM p P M p Pa dt HþR j H þ FP R þ ð1FP ÞGj R FG R G M g M g Ga HþR j H þ FG R þ ð1FG ÞPj dGj ¼ nga ðR,Gj ÞGa þ ngj ðRÞGj gg ðngj ðRÞÞGj mgj ðP a ÞGj dt dGa ¼ gg ðngj ðRÞÞGj mg Ga dt dP j ¼ npa ðR,Gj ÞP a þ npj ðRÞPj gp ðnpj ðRÞÞP j mpj ðGa ÞPj dt dP a ¼ gp ðnpj ðRÞÞP j mb P a dt R T i H þR The mass-specific net biomass production rates for adults Ga and Pa become: nga ðR,Pj Þ ¼ sMg FG Rþ ð1FG ÞPj T g H þ FG R þ ð1FG ÞPj npa ðR,Gj Þ ¼ sMp FP R þ ð1FP ÞGj T p H þ FP R þð1FP ÞGj With corresponding mortality rates for the juvenile stages: mpj ðGa Þ ¼ mb þ ð1FG ÞGa M p H þ FG R þð1FG ÞP j mgj ðPa Þ ¼ ma þ ð1FP ÞP a Mp H þ FP R þ ð1FP ÞGj 2.1. Model parameterization The model is parameterized to describe the dynamics of herring using similar rates as in Van Leeuwen et al. (2008). Furthermore, we assume that all parameters, except F are the same in both populations. This way we can isolate the effects of changing F on community dynamics from effects of other differences between populations. The stage-structured biomass model and its parameterization as used here, is such that the results presented in this report are more generally applicable to interactions between all sorts of organisms (for justification of this statement see De Roos et al., 2007; De Roos et al., 2008; Schellekens et al., 2010). Model parameters and their default values are summarized in Table 2. Maximum ingestion (M) and maintenance (T) are both massspecific rates (expressed in unit biomass per unit biomass per unit time), whereas the mortality parameter (m) represents a per capita rate. The maximum resource density Rmax and half-saturation density H are expressed as gram biomass per unit volume and therefore the only parameters containing the unit of volume. H can be set to 1 without loss of generality, as this merely implies a scaling of the unit of the total system volume. Maximum resource density Rmax is then expressed as multiples of the half-saturation density. A conversion efficiency of 0.5 is used for conversion of both resource and consumer biomass (Peters, 1983). Table 2 Parameters and parameter values. Parameter Resource Rmax Varied 0.1 d s M T mb H F z Predator G and P Description 0.5 0.23 0.032 0.001 1 Varied 0.035 Resource maximum biomass density Resource turn-over rate Assimilation efficiency Maximum ingestion rate (mass specific) Maintenance rate (mass specific) Background mortality rate Half-saturation constant Adult time spent feeding on either juvenile heterospecifics or R Newborn-adult predator size ratio T. Schellekens, T. van Kooten / Journal of Theoretical Biology 308 (2012) 36–44 39 Model predictions are analyzed for different values of Rmax and F. Productivity of a semi-chemostat system is given by d Rmax, so varying maximum resource density Rmax corresponds to varying the productivity, and we use maximum resource density and resource productivity as synonyms throughout the rest of this study. We used Content, a numerical bifurcation software package (Kuznetsov et al., 1996), to calculate equilibrium densities as a function of Rmax and FG and to assess equilibrium stability. 3. Results 3.1. FG ¼1, consumer and intraguild predator This configuration lets population G feed on resource R throughout its life (Fig. 1a). Therefore, the interaction between the varied and fixed population (G and P) is one that is similar to a classic intraguild predation scheme, like the one presented by Mylius et al. (2001). There, the intraguild predator (equivalent to the fixed population P) is an inferior resource competitor compared to the intraguild consumer (equivalent to the varied population G), but instead is able to feed on the consumer. However, like in van de Wolfshaar et al. (2006) the adults of the fixed population P have widened their niche compared to juveniles, feeding on both resource and juveniles of the varied population (Gj). Just like in the unstructured IGP system (Mylius et al., 2001), four equilibrium types at FG ¼1 occur: (1) a resource-only equilibrium; (2) a consumer-resource equilibrium; (3) a coexistence equilibrium with resource, consumers and intraguild predators and (4) a predator-resource equilibrium (Fig. 2, right panel). The resource-only equilibrium is stable when there is not enough basal resource to sustain either populations G and P. The varied population G has lower resource requirements than the fixed (i.e. Rng oRnp, see Tilman, 1982). Therefore the varied population G can invade the resource-only equilibrium when there is still too little basal resource for the fixed population P Fig. 2. Diet proportion of adults of population G (FG) over resource productivity Rmax. Changing positions of the productivity thresholds changing FG from 1 to 0.5 (G is better competitor, but weaker predator than P; Ga relies mostly on basal resource). Gray lines: single population invasion thresholds (solid: invasion threshold of G, dashed: invasion threshold of P). Black lines: coexistence thresholds (dashed: Eg, solid: Ip). to sustain. In the resulting stable G-resource equilibrium, resource density stays constant at Rng while biomass G increases with increasing Rmax. Invasion of the fixed population (P) in the G-resource equilibrium becomes possible when net biomass production of the fixed population becomes high enough to overcome their background mortality and the life time reproduction equals unity. This productivity threshold is denoted as the invasion point of the fixed population P (Ip; Fig. 3, right panel). Following (De Roos, 2008) we express this invasion threshold as: npa mpj =npj 1 z ¼1 mb ð2Þ Increasing productivity in the coexistence equilibrium (P þG þR) increases equilibrium biomass of predator P and resource biomass and decreases the biomass of G. Above a certain resource productivity (the G-exclusion point (Eg), in Fig. 3), the varied population is excluded by the fixed population and only the P-resource equilibrium is stable. 3.2. 0.5 o FG o1, two intraguild predators, G the most efficient competitor Fig. 1. (a) Community structure at FG ¼ 1 (population G is a consumer of basal resource only), (b): Community structure at FG ¼0.5 (adults of population G feed on resource and juvenile heterospecifics equally, similar to population P), (c): Community structure at FG ¼ 0.0 (adults of population G feed on juvenile heterospecifics only). Decreasing FG decreases the ability of population G to use the basal resource. It requires higher resource productivity in order to be able to persist in the system in absence of the fixed population P. In other words, the minimum resource productivity needed for the single population invasion threshold increases with decreasing FG (visible in Fig. 4 as the solid gray line). Until FG ¼0.5, however, the minimum resource requirements of G remain below that of P (Fig. 2). Decreasing FG simultaneously enables the adults of the varied population G to feed on heterospecific juveniles Pj. As a result, the fixed population P now suffers higher mortality. Furthermore, the invasion threshold of P (Ip, Eq. (2)) is only satisfied at higher Rmax when decreasing FG. Because of the increasing predation on Pj, P needs ever more resource productivity to compensate for those losses, even though the competitive difference between G and P for resource becomes smaller with decreasing FG. At a certain value of FG the invasion point of P (Ip) crosses the exclusion point of population G (Eg), resulting in a single threshold Ip. This makes invasion of the fixed population and therefore coexistence 40 T. Schellekens, T. van Kooten / Journal of Theoretical Biology 308 (2012) 36–44 Fig. 4. Diet proportion of adults of population G (FG) over resource productivity Rmax. Changing positions of the productivity thresholds changing FG from 0.5 to 0.0 (G is worse competitor, but stronger predator than P; Ga relies mostly on predation of Pj). Gray lines: single population invasion thresholds (solid: invasion threshold of G, dashed: invasion threshold of P). Black lines: coexistence thresholds (solid: Ig, dashed: Eg, dotted: start of limit cycles). parameter combination for which life-time reproduction in absence of predation equals 1 for varied population G: nga mgj =ngj 1 z ¼1 mb Fig. 3. Biomass equilibria of P, G and R over Rmax (from top to bottom panels reflecting trophic position) at two values of diet proportion; FG ¼ 0.8 at the left and FG ¼ 1 at the right panels (G is better competitor, but weaker predator than P; Ga relies mostly on basal resource). Dotted equilibria: unstable. Solid equilibria: stable (green: resource only equilibria, gray: single population equilibria, black: coexistence equilibria). Green vertical lines: single population invasion thresholds (solid: lowest threshold (G), dashed: highest threshold). Black vertical lines: coexistence thresholds (solid: Ip, dashed: Eg). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) unstable (Fig. 3, left panel dotted lines). As a consequence, from Ip onwards the fixed population P eliminates G through predation without the possibility for coexistence. If FG ¼0.5, as in Fig. 1b, both intraguild predator populations have equal feeding and production rates and hence all invasion thresholds collapse into a single higher-order bifurcation point (see Figs. 2 and 4). This represents a biologically unlikely situation which we do not discuss further. 3.3. FG o0.5, two intraguild predators, G the more efficient predator When FG o0.5, population G will be a more efficient predator but a poorer resource competitor than population P (Fig. 4, note the (trophic) position of P and G); when FG o0.5: Rng 4Rnp and population P becomes the more efficient resource consumer. At low resource productivity population P will be able to exclude population G by resource competition. Increasing productivity at low enough FG (below 0.34 in this case, Fig. 4) will enable population G to invade, because G will depend to a lesser extent on the resource, and instead feeds on Pj. Furthermore, this results in a new productivity threshold: Ig, which, like Eq. (2), is the ð3Þ When productivity is increased further, population G can exclude P, but an alternative stable state emerges. When FG is nearly zero, adults of population G require Pj to sustain, such that P can no longer be excluded. As shown in Fig. 4, decreasing the value of FG towards zero shifts the position of Ig toward higher Rmax values, while the productivity threshold from where coexistence is possible (Eg) changes less rapid over Rmax. Ultimately this results in the equilibrium configuration as illustrated in Fig. 5 (right panel) for FG ¼0. In coexistence the community at FG ¼0 consists of two distinct types of intraguild predators: a life history omnivore (G) and an ontogenetic niche widener (see Fig. 1c). Ga now solely feeds on juvenile heterospecifics (Pj), while Gj only forages on the resource. Pj also feeds on resource only whereas Pa feeds on both resource and juvenile heterospecifics (Gj). Due to the competitive advantage of P, the P-resource equilibrium is stable for all Rmax values (visible at FG ¼0 in Fig. 5 as the solid gray line). Like Hin et al. (2011) described for their system with one intraguild predator and prey, the introduction of predator G in our system is hampered by a juvenile bottleneck created by the competitive advantage of P. As an alternative outcome of dynamics a stable coexistence state exists alongside the P-resource equilibrium. Since sustenance of Ga is (largely) dependent on Pj when FG is small, P cannot be excluded from the coexistence equilibrium by G. Therefore, at low FG values the only productivity threshold present is Eg, marking the lower limit of Rmax for which the intraguild predator G can persist in coexistence (Fig. 5, right panel). Increasing productivity in this coexistence state increases biomass of G and the predatory control of G over P. Biomass of P therefore stays constant with changing productivity, releasing top-down control of resource biomass. In this coexistence state, predation by Ga acts as the main structuring force. Its predatory control over population P decreases competition between juvenile heterospecifics Gj and Pj, increases food availability for Gj and enables their coexistence T. Schellekens, T. van Kooten / Journal of Theoretical Biology 308 (2012) 36–44 41 Fig. 6. Diet proportion of adults of population P (FP) over resource productivity Rmax when FG ¼0.0. Changing positions of the coexistence productivity thresholds changing FP from 0.5 to 0.0 (G is worse competitor, but stronger predator than P; Ga relies mostly on predation of Pj). Coexistence thresholds (dashed: Eg, dotted: start of limit cycles). Note the logarithmic x-axis. (dashed line Fig. 6). Although the invasion boundary of population G moves to higher Rmax when FP is reduced, coexistence remains possible if the adult diets of the two omnivores remain different. 4. Discussion Fig. 5. Biomass equilibria of G, P and R over Rmax (from top to bottom panels reflecting trophic position) at two values of diet proportion; FG ¼0.2 at the left and FG ¼ 0.0 at the right panels (G is worse competitor, but stronger predator than P; Ga relies mostly on predation of Pj). Dotted equilibria: unstable. Solid equilibria: stable (green: resource only equilibria, gray: single population equilibria, black: coexistence equilibria). Green vertical lines: single population invasion thresholds (solid: lowest threshold (P), dashed: highest threshold). Black vertical lines: coexistence thresholds (solid: Ig, dashed: Eg). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) with population P. The equilibrium patterns in this stable coexistence state therefore largely resemble those of a three-species linear food chain (Oksanen et al., 1981). In an alternative stable state without predatory control of G over P unbalanced competition for resources between juvenile heterospecifics Gj and Pj creates a juvenile competitive bottleneck in population G. The bottleneck, in turn, restricts formation of adults and thereby decreases predatory control of G over P even further. In this alternative stable state, therefore, unbalanced interspecific competition structures the community leading to exclusion of population G. We show that the equilibrium pattern when FG is close to zero remains when the ‘fixed’ predator is also allowed to increase the proportion of heterospecific juveniles in the diet of adults in Fig. 6. For this purpose we vary FP from 0.5 (as it was fixed in previously) to 0. When adults of population P proportionally have a more predacious diet, they release the top-down control of resource but increase the mortality of juvenile heterospecifics. Given certain resource productivity the change in RnP with the decrease in FP is slower than the increase in mortality rate of juvenile heterospecifics mgj. Therefore, introduction of population G requires more resource productivity to balance these rates We have shown that even though both populations could prey on the other and both consume resource (in a linear trade-off), coexistence of two intraguild predators is enabled because the effect on community dynamics of either of these interactions is minimized through a change in population stage-structure. The change in stage-structure is an emergent effect of the community configuration (such as depicted in Fig. 1); the more efficient predator (and therefore the least efficient consumer) reduces juveniles of the other species and so decreases the competition among juveniles. The model predicts extended coexistence possibilities when the community consists of a niche widener and a life history omnivore. Stable coexistence only occurs, however, when community dynamics are shaped primarily by predation with competitive interactions playing only a marginal role. As a result, community dynamics in stable coexistence largely resemble those of a three-species linear food chain. Community dynamics may also be governed by strong competition, leading to an alternative stable state in which the better juvenile competitor outcompetes the other species by means of a juvenile bottleneck. When the varied population G is a pure resource consumer (FG ¼1) an increase in resource productivity can enable a small biomass of the intraguild predator to invade the system. The presented dynamics of the system at FG ¼1 is qualitatively equivalent to that of models with unstructured populations, but also resembles that of structured population models presented by Mylius et al. (2001) and van de Wolfshaar et al. (2006). In contrast to the situation at FG ¼1, establishment after an invasion of small biomass is impossible when adults of the varied population feed exclusively on juveniles of the fixed population P (at FG ¼0). In that case, the equilibrium with only the most efficient resource consumer present (P-resource equilibrium) is stable at all levels of resource productivity large enough for P to persist in the system. The varied population G is then excluded by resource competition 42 T. Schellekens, T. van Kooten / Journal of Theoretical Biology 308 (2012) 36–44 because juveniles Gj are not only preyed on by Pa but also experience a developmental bottleneck because resource is depleted. Invasion of the varied population (G) is only possible if maturation of juveniles is possible. Maturation only takes place if resource is sufficiently abundant. In other words, successful invasion is possible if Ga can inflict enough mortality on heterospecifics (Pj) such that resource is raised above the minimum required for Gj to mature. These invasion requirements are similar to what was found by Hin et al. (2011) for a life-history omnivore (like the varied population G at FG 0) invading a community of a consumer feeding on a basal resource. We, on the other hand, considered invasion in a community of basal resource fed upon by a population that also preys on heterospecifics. Compared to Hin et al. (2011) we hence introduce extra juvenile mortality in the intraguild predator. The main conclusion of the analysis of Hin et al. (2011) was that because the life-history omnivore has split its roles over its lifetime (a predator as adult and competitor as juvenile) the effect of these roles on community dynamics is split as well. Either the omnivore acts as a competitor or it acts as a predator. In the latter case, community dynamics follow simple trophic interactions with three trophic levels. Invasion of the life history omnivore (G) in this paper has similar dynamical results, which shows that the life history omnivore creates community dynamics that force it to primarily act as a predator and force heterospecifics (P) to primarily act as consumer of the basal resource, even though it preys on life history omnivores (G) as well. Both this study and that of Hin et al. (2011) offer an explanation as to why intraguild systems in nature often behave as three-species linear food chains (Oksanen et al., 1981) if life history omnivory is involved in the ontogeny of intraguild predators (Persson and De Roos, 2012). We furthermore show that this emergent community pattern is robust against extra juvenile mortality in both intraguild predators (when FG ¼0), through mutual predation and cannibalism, as long as dependency on predation exists and diets of omnivores are different. In addition, we show that like a niche shift (i.e. when the adult diet differs from the juvenile diet, F ¼0), niche widening (i.e. when adult diet is wider than that of juveniles so that F a0) also enables these community patterns. The coexistence of intraguild predators can be compared to that of competitors that feed on the same resources, but undergo extra (in this case juvenile) mortality in presence of the other competitor. In regard to interspecific competition and coexistence of populations with ontogenetic niche shifts, theory has focused on the interactions with populations exhibiting ontogenetic habitat shifts (Haefner and Edson, 1984; Loreau and Ebenhoh, 1994; Moll and Brown, 2008; Mougi and Nishimura, 2005). Some studies even represented competitive interactions as negative density dependence, affecting reproduction and maturation instead of explicitly representing competition for resources (Haefner and Edson, 1984; Moll and Brown, 2008; Mougi and Nishimura, 2005). This emphasizes the focus of these studies on the effect of habitat segregation on competition instead of the effect of differences in resource use. Loreau and Ebenhoh (1994) have studied the competitive interactions between two populations exhibiting ontogenetic habitat shifts during their lifetime. For coexistence to occur, each population should be most resource limited in the habitat where the other population was most efficient in resource use (Loreau and Ebenhoh, 1994). Also McCann (1998) analyzed a model describing competition between two consumers, both of which had ontogenetic niche shifts, without assuming an explicit change in habitat but a distinct resource for juvenile competitors from that of adults, excluding competition between the life stages. This resource segregation between life-history stages is conceptually identical to the habitat segregation between stages assumed in other studies (Haefner and Edson, 1984; Loreau and Ebenhoh, 1994; Mougi and Nishimura, 2005; Moll and Brown, 2008). Consequently, the type of coexistence occurs under the same conditions as coexistence in studies with explicit habitat segregation, namely, that a competitive advantage at one life stage has to be balanced by a disadvantage at another life stage. In contrast, competition in our model between stages was separated only when F ¼0. Furthermore, we did not a priori assume that individuals ever changed their competitive ability during their lifetimes. Instead, the changes in competitive abilities of the population and the resulting community dynamics were a property emerging from the life history omnivory itself. Coexistence of intraguild predators is clearly possible in nature (Polis, 1991, Polis and Strong 1996, Arim and Marquet, 2004), but this observation has been hard to reconcile with insights from theory. Intraguild predation theory shows that coexistence between predator and prey is limited to intermediate resource productivity because only there a balance is possible between competition and predation, such that prey do not undergo too much mortality and predators not too much competition. Coexistence possibilities of more than one intraguild predator have scarcely been investigated theoretically. From more complex food web models we learn that large sized species are likely to engage in omnivory, but few of these species are predicted to persist in food webs because of large overlap in resource use (e.g. Law et al., 2009). In size spectrum-based food web models, large species do not only engage in (intraguild) predation but can also engage in cannibalism. Cannibalism in both intraguild predator and prey has shown to facilitate and stabilize coexistence in IGPmodules (Rudolf, 2007). We have investigated the consequences of enabling cannibalism in both of the intraguild predator populations when either or both undergo a strong ontogenetic niche shift (FG ¼0) and find no qualitative changes (details of implementation and results shown in supplement) with respect to the results presented in this paper, other than stabilization of coexistence takes place at high rates of cannibalism in accordance with predictions from Rudolf (2007). Using a simple population dynamic model HilleRisLambers and Dieckmann (2003) show that in a system of two unstructured intraguild predators, coexistence occurs only when one is forced to play the role of consumer, profiting mostly from feeding on resource, while the other is forced to play the role of predator and relies on feeding on the consumer. Compared to the standard case with one intraguild predator and a consumer, HilleRisLambers and Dieckmann (2003) predict that coexistence between two intraguild predators occurs in a narrower range of productivities. HilleRisLambers and Dieckmann (2003) varied the diet of the unstructured populations by defining a trade-off between feeding on heterospecifics and resource. They then investigated the consequences of the strength of trade-offs on community structure and came to the conclusion that medium to strong trade-offs (when intraguild predators are punished compared to specialist consumers and predators) maximize coexistence possibilities. Coexistence, however, was negligible or non-existent if the trade-off was weak or linear. In contrast to HilleRisLambers and Dieckmann (2003), we considered stage-structured populations, where juveniles had different diets from adults. Similar to HilleRisLambers and Dieckmann (2003) we varied the proportion of predatory feeding and resource consumption, but only in adults and only in a linear fashion. Where HilleRisLambers and Dieckmann (2003) investigated the consequences of the strength of trade-offs on community structure, we investigated the dynamical causes of community structure and specifically the effect of life history omnivory. Our model setup results in coexistence possibilities as extensive as presented in classic intraguild predation theory or even extended beyond intermediate resource productivities, due to the inclusion of life history omnivory or ‘‘an ontogenetic specialist’’. This type of omnivore has not T. Schellekens, T. van Kooten / Journal of Theoretical Biology 308 (2012) 36–44 been considered in size-spectrum models or the model of HilleRisLambers and Dieckmann, (2003), since in those models omnivores widen their niches. ‘Ontogenetic specialists’ have been found to be common in nature and crucial in determining food web stability (Rudolf and Lafferty, 2011). Like Hin et al. (2011), we show that stable coexistence in our model occurs with life history omnivores (ontogenetic specialists) and ontogenetic niche wideners if these can actually shape their community through predation. Rudolf and Lafferty (2011) show that these species with sequential specialization in resource use are sensitive to resource loss and overexploitation, leading to the loss of the life history omnivore and changes in community structure that disable the reintroduction of this omnivore. The generic instability of the coexistence with life history omnivores can be a reason why food web models that generate food web structures stochastically (Brose et al., 2006; e.g. Hartvig et al., 2011; Law et al., 2009; Williams and Martinez, 2000; Woodward et al., 2005) underestimate the occurrence of coexistence of intraguild predators (with similar size ranges) and the response of ecosystems to (anthropogenic) change (Rudolf and Lafferty, 2011). Acknowledgments This research has been supported by EU FP7 grant FACTS (Forage Fish Interactions), grant agreement no. 244966. Appendix A. 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