Second example of community evolution oligomorphic and stochastic

Some existing models of food web evolution incorporate realistic population dynamics, but at the same time rely on interactions mediated by high-dimensional traits that lack clear and direct ecological interpretations (e.g., Caldarelli et al. 1998; Drossel al. 2001). By contrast, a model by Brannstrom et al. (in preparation), described below, builds on previous foundational work by Loueille and Loreau (2005) and accordingly is based on body size as an evolving trait of high physiological and ecological relevance.

The considered community comprises one autotrophic and N hetero-trophic species evolving through mutation-limited phenotypic adaptation. Each species i possesses a trait value xi determining its body size on a logarithmic scale. From these body sizes, species-specific properties such as energy requirements, competitive interactions, and attack coefficients are determined. The community's demographic processes follow lotka-volterra dynamics, with the dynamics of the non-evolving autotrophic species i = 0 given by d - N

—no = no dt bo — no/ko — ^^ exp(xj — xo )F (Xj — xo )nj j=i and the per capita birth and death rates, respectively, of the heterotrophic species i = 1,...,N given by

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