1 Evolution of stabilising weak links in food webs

Conventional ecological models[1-4] show that complexity destabilises food webs, suggesting that food webs should have neither the large number of species nor the large number of interactions. However, in nature the opposite appears to be the case. More recent work[5] shows that the introduction of nonlinearity and weak interactions can enhance stability, and the observation of weak interactions in real systems is taken as justification for this. Here we show that if the interactions between species is allowed to evolve, such stabilising feedbacks and weak interactions emerge naturally. Moreover, we show that trophic levels[4] also emerge spontaneously from the evolutionary approach, and the efficiency of the unperturbed ecosystem increases with time. Ecosystems are a classic example of complexity[6], being formed from a myriad of interactions between various species. The mathematical study of ecosystems has a long history[1-11], dating back to the work of Lotka and Volterra[7,8]. Such models tread a delicate balance between including so much detail that they lose the capability to make qualitative predictions, and being so simple as to be wholly wrong. Striking features o