The Effect of Differentiation of Prey Community on Stable Coexistence in a Three-Species Food–Web Model E. Shchekinova, M. G. J. L¨oder, M. Boersma, K. H. Wiltshirea aBiologische Anstalt Helgoland, Alfred-Wegener Institute for Polar and Marine Research, Kurpromenade 201, D-27498 Helgoland Germany Abstract Food webs with intraguild predation (IGP) are widespread in natural habitats. Their adaptation and resilience behaviour is principal for understanding restructuring of ecological communities. In spite of the importance of IGP food webs their behaviour even for the simplest 3-species systems has not been fully explored. One fundamental question is how an increase of diversity of the lowest trophic level impacts the persistence of higher trophic levels in IGP relationships. We analyze a 3-species food web model with a heterogeneous resources and IGP. The model consists of two predators directly coupled via IGP relation and indirectly via competition for resource. The resource is subdivided into distinct subpopulations. Individuals in the subpopulations are grazed at different rates by the predators. We consider two models: an IGP module with immobilization by the top predator and an IGP module with species turnover. We examine the effect of increasing enrichment and varying immobilization (resource transfer) rate on a stable coexistence of predators and resources. We explore how the predictions from the basic 3-species model are altered when the IGP module is extended to multiple resource subpopulations. We investigate which parameters support a robust coexistence in the IGP system. For the case of multiple subpopulations of the resource we present a numerical comparison of the percentage of food webs with stable coexistence for different dimensionalities of the resource community. At low immobilization (transfer) rates our model predicts a stable 3-species coexistence only for intermediate enrichment meanwhile at high rates a large set of stable equilibrium configurations is found for high enrichment as well. Keywords: Intraguild predation, Immobilization, Alternative resource, Multiple resource traits, Stable arXiv:1204.2822v1 [q-bio.PE] 12 Apr 2012 coexistence 1. Introduction Vadeboncoeur et al., 2005) in natural communities their population dynamics to date remain poorly In spite of the prevalence and importance understood, even for only three species in the of omnivory food webs (Pimm and Lawton, 1978; community. Even in simple systems a plethora Email address: [email protected] (E. Shchekinova, M. G. J. L¨oder, M. Boersma, K. H. Wiltshire) Preprint submitted to Elsevier September 9, 2018 of nonlinear effects such as flexible consumer be- for the communal resource (Diehl and Feißel, 2001). haviour (Leibold et al., 2005), intraspecific interac- Yet empirical data suggest a robust persistence tions between competing consumers and resources of IGP systems in both terrestrial (Brodeur et al., (Holt et al., 1994), inhomogeneity of the environ- 2000; Arim and Marquet, 2004) and aquatic com- ment (Amarasekare, 2007; Janssen et al., 2007) and munities (Polis et al., 1989; Mylius et al., 2001; adaptive foraging (Krivan, 1996; Krivan and Diehl, Borer et al., 2003; Denno and Fagan, 2003). 2005) precludes easy theoretical treatment and in- Theoretical models that are focused on the terpretation. aspects of stability and coexistence of species One example of a non-trivial omnivory food web in 3-level systems with the IGP (Polis and Holt, is a system with intraguild predation (Polis et al., 1992; Holt and Polis, 1997; Abrams et al., 1994a,b, 1989; Finke and Denno, 2002; Borer et al., 2003). 2010), as a rule, largely reduce the complex- Intraguild predation assumes that the same or- ity of interactions observed in realistic systems ganism is both competitor and predator to an- (Thomson et al., 2007). Such oversimplifications other member of the food web. The IGP mod- can influence the population dynamics as well as els encompass a rich dynamical behaviour in- critically impact species persistence. Even though cluding coexistence (Polis and Holt, 1992) and the simplest model of the IGP encompasses only alternative stable states (Holt and Huxel, 2007; three species (Polis and Holt, 1992; Holt and Polis, Daugherty et al., 2007). Simple mathematical 1997; Diehl and Feißel, 2000, 2001) a number of models (Polis and Holt, 1992; Diehl and Feißel, empirical studies deal with larger food webs that 2000; Namba et al., 2008) have been evoked in at- involve more than three species potentially en- tempt to explain the persistence of IGP interac- gaged in IGP interactions (Rosenheim et al., 1993; tions in natural habitats. However predictions from Woodward et al., 2005). the mathematical theory of 3-species IGP systems Spatiotemporal heterogeneity of the environ- state that a high resource carrying capacity pro- ment often is invoked as one of the explana- motes the exclusion of intermediate trophic levels tory mechanisms for the coexistence between mul- and thus destabilizes interactions (Diehl and Feißel, tiple species competing for the same resources 2001). What is puzzling that various empirical (Hutchinson, 1961). It has been observed that such studies of omnivory document however coexistence, a spatiotemporal heterogeneity can affect the di- but not exclusion, over the entire range of nat- versity in prey populations (Amarasekare, 2006). ural resource productivities (Mylius et al., 2001; Indeed an inhomogeneity in prey items that share Borer et al., 2003). On the basis of experimental common resource and predators is critical in deter- observations a theoretical 3-species omnivory model mining the responses of ecological community. For (Stoecker and Evans, 1985; Holt and Polis, 1997; systems with multiple prey composition various co- Diehl and Feißel, 2001) predicts the coexistence existence patterns can be found depending on the only at superior competitive abilities of the IG prey levels of resource productivity (Leibold, 1996). It is 2 not clear yet how the diversity in a prey community tems the IG prey has a mutualistic or at least will affect the behaviour in the IGP systems. facilitative relationship with the IG predator The effect of a habitat structure on the IGP is (Crowley and Cox, 2011). Including such facilita- discussed in various recent models (Amarasekare, tion in ecological theory will fundamentally change 2006, 2007; Janssen et al., 2007). For example a many basic predictions and will enable a better un- stable coexistence of the intraguild prey due to derstanding of functioning of many natural commu- inhomogeneity of a habitat can be supported by nities (Bruno et al., 2003). creating temporal refuges for prey and reducing Especially in the IGP systems an emphasis the encounter rates among preys and predators should be given to the elucidation of the effects of (Janssen et al., 2007). In addition the stability of facilitation on community composition and stabil- the IGP can be enhanced by an inclusion of addi- ity (Crowley and Cox, 2011). Contrary to the com- tional factors such as behaviourally mediated effects petitive exclusion principle in systems with com- (Janssen et al., 2007). petitors for a single resource stability stems from To include the effect of an increasing diversity of commensalism (Hosack et al., 2009). Hereby one resource and IG predators on population dynamics consumer can in some way alter the habitat to ben- recently the 3-species IGP model (Holt and Polis, efit the other. Recently such an interaction was 1997) was modified by Holt and Huxel (2007). observed in experiments with a microzooplankton The authors extended the basic 3-species omnivory food web community (L¨oder et al., xxxx). The ex- model to the so called ”partial IGP” model in which perimental system included two predators: a tintin- ”partial” overlap among competitors for a single re- nid species Favella ehrenbergii and a heterotrophic source exists and both predators have exclusive re- dinoflagellate species Gyrodinium dominans. They sources to exploit. It was shown (Holt and Huxel, are both grazing on a phototrophic dinoflagellate 2007) that an alternative resource enhances the Scrippsiella trochoidea. The authors showed that tolerance of the IG prey against attacks from IG the IG predator F. ehrenbergii can precondition a predators. Independently of a competitive status substantial part of the common resource S. tro- of the IG prey in exploitation for a shared re- choidea during its feeding procedure by immobiliz- source it can persists by utilizing an alternative re- ing the common prey without ingestion. Such pre- source. An extended formulation of the IGP model conditioned individuals can be captured more easily with trophic supplementation has been proposed by by the IG prey G. dominans than the mobile indi- Daugherty et al. (2007). The authors investigated viduals of the same resource species. This mutual- three forms of a supplementary feeding outside of istic interaction leads to higher growth rates of the the basic IGP module and postulated a higher po- IG prey in the presence of the IG predator. The au- tential for persistence of the IG prey due to its ef- thors characterized their experimental observations ficient exploitation of external resources. as a facilitative IGP relationship with a commen- There is growing evidence that in many sys- salistic pattern. Our motivation for this modeling 3 study was to investigate if such commensalistic pat- paper is a resource turnover mechanism. This terns can create loopholes for a stable coexistence mechanism describes mutual interactions between of all species in the investigated system. Of our species from distinct resource subpopulations. The major interest was if in the IGP system an immo- interaction term depends exclusively on the re- bilization (L¨oder et al., xxxx) or the partitioning source subpopulation densities. The rate of of prey populations into distinct groups of individ- turnover is constant. If no turnover or immobi- uals offers opportunities for competition avoidance lization of individuals from one group to another among both consumer species. occurs then the basic IGP model with a single pop- We reformulated the 3-species IGP model pro- ulation of resource is recovered.