Interplay of spatial dynamics and local adaptation shapes species lifetime distributions and species-area relationships

The distributions of species lifetimes and species in space are related, since species with good local survival chances have more time to colonize new habitats and species inhabiting large areas have higher chances to survive local disturbances. Yet, both distributions have been discussed in mostly separate communities. Here, we study both patterns simultaneously using a spatially explicit, evolutionary meta-food web model, consisting of a grid of patches, where each patch contains a local food web. Species survival depends on predation and competition interactions, which in turn depend on species body masses as the key traits. The system evolves due to the migration of species to neighboring patches, the addition of new species as modifications of existing species, and local extinction events. The structure of each local food web thus emerges in a self-organized manner as the highly non-trivial outcome of the relative time scales of these processes. Our model generates a large variety of complex, multi-trophic networks and therefore serves as a powerful tool to investigate ecosystems on long temporal and large spatial scales. We find that the observed lifetime distributions and species-area relations resemble power laws over appropriately chosen parameter ranges and thus agree qualitatively with empirical findings. Moreover, we observe strong finite-size effects, and a dependence of the relationships on the trophic level of the species. By comparing our results to simple neutral models found in the literature, we identify the features that affect the values of the exponents.