When do evolutionary food web models generate complex networks?

Evolutionary foodweb models are used to build food webs by the repeated addition of new species. Population dynamics leads to the extinction or establishment of a newly added species, and possibly to the extinction of other species. The food web structure that emerges after some time is a highly nontrivial result of the evolutionary and dynamical rules. We investigate the evolutionary food web model introduced by Loeuille and Loreau (2005), which characterizes species by their body mass as the only evolving trait. Our goal is to find the reasons behind the model's remarkable robustness and its capability to generate various and stable networks. In contrast to other evolutionary food web models, this model requires neither adaptive foraging nor allometric scaling of metabolic rates with body mass in order to produce complex networks that do not eventually collapse to trivial structures. Our study shows that this is essentially due to the fact that the difference in niche value between predator and prey as well as the feeding range are constrained so that they remain within narrow limits under evolution. Furthermore, competition between similar species is sufficiently strong, so that a trophic level can accommodate several species. We discuss the implications of these findings and argue that the conditions that stabilize other evolutionary food web models have similar effects because they also prevent the occurrence of extreme specialists or extreme generalists that have in general a higher fitness than species with a moderate niche width.