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...to integrate theory from community ecology, evolutionary biology, and ecosystem science (Fussmann et al. 2007; Loeuille 2009; Loreau 2010a). These models generate realistic food web topologies, include important ecological traits (e.g. body size) in their design and, in some cases, allow for the evolution of ecologically relevant parameters (Loreau 2010a). The models arising from ecological theory are based on a few simple rules governing species interactions, and are often developed to compare with empirical data about food web structure or to test plausible mechanisms of food web stability (Rossberg et al. 2005; Gross et al. 2009). Dieckmann et al. (2007) proposed a class of community evolution models based on adaptive dynamics, whereby community structure evolves through recurrent evolutionary branching (i.e. speciation) and the invasibility of new phenotypes is determined based on equilibrium dynamics. These models allow for frequency and density-dependent selection by explicitly including population dynamics, but have a relatively simplified framework for modeling phenotypic evolution. In addition, they assume that evolutionary dynamics occur at a much slower rate than ecological dynamics (Fussma...

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...in the network build-up constrain species to be organized into ‘clades’ that share similar prey, thus having similar niches. Although based on different processes, both the niche and the nested hierarchy models predict a variety of food-web characteristics such as the proportion of basal species and of omnivores, and food-chain length (Williams & Martinez, 2000; Cattin et al., 2004). Mechanistic evolutionarily models were also built on the principles of speciation, extinction and migration (Caldarelli, Higgs & McKane, 1998; Drossel, Higgs & McKane, 2001; McKane, 2004; Loeuille & Loreau, 2005; Rossberg et al., 2005). By contrast with purely ecological models (May, 1973; Gross et al., 2009), these evolutionary models tend to produce diverse and persistent communities (Caldarelli et al., 1998; Loeuille & Loreau, 2005; Loeuille, 2010). These approaches are however still in their infancy (Loeuille & Loreau, 2009) and using phylogenetic information will help build more integrated macro-evolutionary models of network complexity. (2) Analyzing the links between phylogeny and interaction networks Using phylogenetic information can potentially bring novel insights on network organisation (Rezende, Jordano & Basco...

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... new species are not free to consume any kind of prey ifsthey are taxonomically related to already present species. Other modelssof food-web structure based on evolutionary dynamics have been deviseds=-=(192,193)-=-, and their ability to closely reproduce observed trophics400 L.-F. Bersiersstructures is impressive. This success of evolutionary models witnesses aschange in ecological thinking about communities. E...

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...oped that either assign feeding links by referring to phylogenetic constraints and thus implicitly include the evolutionary history of food webs [7] or that construct food webs in a dynamical process =-=[37, 38]-=-. These models focus ∗E-mail: guill@fkp.tu-darmstadt.de 139 Article published by EDP Sciences and available at http://www.mmnp-journal.org or http://dx.doi.org/10.1051/mmnp/20105607 C. Guill A model o...

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... understanding food-web structure provides important insights into, for example, the stability of ecosystems to perturbations (Allesina & Pascual 2008). Recent increases in the availability of computational tools have facilitated. Our ability to explore numerous properties of food webs. (Each of the contributions by Abrams 2009; Brose 2009; Loeuille 2009 in this issue is an excellent example on this theme.) In particular, several models have been proposed that aim to describe the structure of food webs (Cohen & Newman 1985; Williams & Martinez 2000; Cattin et al. 2004; Loeuille & Loreau 2005; Rossberg et al. 2005, 2006a; Beckerman, Petchey & Warren 2006; Petchey et al. 2008). Such models tend to fall into two broad categories: (i) phenomenological models and (ii) population-level models. Phenomenological models generally rely upon heuristic ‘rules’, for example how species might select their prey (Williams & Martinez 2000), to generate the food web. Typically, population-level models consider the behaviours and implications of an ecologically relevant process, such as the evolution of species’ body size (Loeuille & Loreau 2005), and the interactions between individual species produce the food-web stru...

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...ion dynamics (e.g., Montoya and Solé, 2003, Pimm, 1984) or evolutionary mechanisms (e.g., Amaral and Meyer, 1999, Camacho and Solé, 2000, Drossel, 1998) alone. The recently proposed speciation model (=-=Rossberg et al., 2005-=-) is of the purely evolutionary type. It combines mechanisms corresponding to speciations and extinctions with simple assumptions regarding the evolutionary inheritance of trophic links. In spirit, th...

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... are based on a few simple rules governing species interactions, and are often developed to compare with empirical data about food web structure or to test plausible mechanisms of food web stability (=-=Rossberg et al. 2005-=-; Gross et al. 2009). Dieckmann et al. (2007) proposed a class of community evolution models based on adaptive dynamics, whereby community structure evolves through recurrent evolutionary branching (i...

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...eity of empirical methodology in our food-web model and data analysis. The model proposed here (‘‘matching model’’) has some similarity with the ‘‘speciation model’’ that we had investigated earlier (=-=Rossberg et al., 2005-=-,2006). But the speciation model lacked crucial elements of the matching model, e.g., the trait matching between consumers and resources. As a result, it could reproduce some features of empirical foo...

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...among its species (Cohen et al., 1990). To this end, in the last years great effort has been devoted to the compilation of comprehensive empirical food webs (see for instance (Amaral and Meyer, 1999; =-=Rossberg et al., 2005-=-; Rossberg et al., 2006a,b), population biology (Yodzis, 1981), or mixtures of both (Caldarelli et al., 1998; Lassig et al., 2001). Other so-called static models do not contain the explicit dynamics o...