Food-web formation with recursive evolutionary branching.

A reaction-diffusion model describing the evolutionary dynamics of a food-web was constructed. In this model, predator-prey relationships among organisms were determined by their position in a two-dimensional phenotype space defined by two traits: as prey and as predator. The mutation process is expressed with a diffusion process of biomass in the phenotype space. Numerical simulation of this model showed co-evolutionary dynamics of isolated phenotypic clusters, including various types of evolutionary branching, which were classified into branching as prey, branching as predators, and co-evolutionary branching of both prey and predators. A complex food-web develops with recursive evolutionary branching from a single phenotypic cluster. Biodiversity peaks at the medium strength of the predator-prey interaction, where the food-web is maintained at medium biomass by a balanced frequency between evolutionary branching and extinction.