Competition in di- and tri-trophic food web modules with many competing species is studied. The food web modules considered are apparent competition between n species sharing a single predator and a diamond-like food web with a single resource, a single top predator and many competing middle species. The predators have either fixed preferences for their prey, or they switch between available prey in a way that maximizes their fitness. Dependence of these food web dynamics on environmental carrying capacity and food web connectance is studied. The results predict that optimal flexible foraging strongly weakens apparent competition and promotes species coexistence. Food web robustness (defined here as the proportion of surviving species) does not decrease with increased connectance in these food-webs. Moreover, it is shown that flexible prey switching leads to the same population equilibria as in corresponding food webs with highly specialized predators. The results show that flexible foraging behavior by predators can have very strong impact on species richness, as well as the response of communities to changes in resource enrichment and food-web connectance when compared to the same food-web topology with inflexible top predators. Several results on global stability using Lyapunov functions are provided.

Department of Mathematics and Biomathematics Faculty of Science University of South Bohemia Branišovská 31 370 05 České Budějovice Czech Republic

Institute of Entomology Biology Center Academy of Sciences of the Czech Republic Czech Republic

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