The influence of predator-prey population dynamics on the long-term evolution of food web structure

We develop a set of equations to describe the population dynamics of many i nteracting species in food webs. Predator-prey interactions are nonlinear, and are based on ratio-dependent functional responses. The equations accoun t for competition for resources between members of the same species, and be tween members of different species. Predators divide their total hunting/fo raging effort between the available prey species according to an evolutiona rily stable strategy (ESS). The ESS foraging behaviour does not correspond to the predictions of optimal foraging theory. We use the population dynami cs equations in simulations of the Webworld model of evolving ecosystems. N ew species are added to an existing food web due to speciation events, whil st species become extinct due to coevolution and competition. We study the dynamics of species-diversity in Webworld on a macro-evolutionary time-scal e. Coevolutionary interactions are strong enough to cause continuous overtu rn of species, in contrast to our previous Webworld simulations with simple r population dynamics. Although there are significant fluctuations in speci es diversity because of speciation and extinction, very large-scale extinct ion avalanches appear to be absent from the dynamics, and we find no eviden ce for self-organized criticality. (C) 2001 Academic Press.