Theory suggests that pair-wise predator-prey interactions are inherently evolutionarily unstable. Over evolutionary time, the predator is predicted to evolve an increased attack rate that decreases the prey population, eventually to the point of extinction. More recent theory has shown that without tradeoffs or co-evolution, population spatial structure, where individual organisms do not interact randomly but rather according to their spatial location, can stabilize predator-prey interactions. A natural conjecture is that spatial structure may also play an important role in the evolutionary stability of larger food webs. However, to date no studies have examined the effect of spatial structure alone on the evolutionary stability of food webs. In fact, neither have studies examined the evolutionary stability of food webs in a non-spatial context without other stabilizing mechanisms. I use a simple population dynamic model of predator-prey interactions to explore the evolutionary stability of pair-wise predator-prey interactions and larger food webs in spatial and non-spatial contexts.
Results/Conclusions
The simple model used predicts evolutionary stability for pair-wise interactions. Further, in a non-spatial context, without other stabilizing mechanisms, the model predicts that three species food chains and five species webs are evolutionarily unstable. The time to extinction declines with the number of species in the web. Finally, in a spatial context the model also predicts that three species food chains and five species food webs are evolutionarily unstable. However, for three species webs, the entire food web does not collapse but instead reduces to an evolutionary stable pair-wise predator prey interactions. Though this outcome is less likely for five-species webs, it also occurs. The implications are that non-spatial models of food webs used to explore ecological phenomena ought to include evolutionary stabilizing mechanisms like prey co-evolution, ecological or allocation tradeoffs. Without these mechanisms, the web will be evolutionarily unstable and predictions arising from the model will have limited scope. In addition, if indeed spatial structure alone cannot stabilize entire webs, then the constant species turnover predicted by existing non-spatial evolutionary community assembly models might also characterize spatial evolutionary community assembly. A key difference may simply be that spatial structure reduces the likelihood of entire food web collapse.