Network structure and extinction statistics of evolving ecological networks

Background/Question/Methods

The mechanisms that structure natural food webs (the networks of feeding interactions in ecosystems) and their interplay with the processes that shape theses networks on evolutionary time scales are not yet completely understood. Existing models that successfully predict the structure of food webs often create the networks in an ad hoc manner and account for the evolutionary history of the networks only implicitly. Consequently, statistical data concerning the evolutionary history of the food webs are rarely evaluated. On the other hand, theoretical works that are concerned with the possibly self-organized critical signature of extinction events seen in paleobiological data mainly build on model communities with very simplified network structures. The objective of the presented work is to propose a model for the large-scale evolution of ecological networks which allows to analyze the extinction statistics of evolving food webs with biologically meaningful topologies. The model is based on the niche model and the structure of the networks evolves by speciation and extinction.

Results/Conclusions

Co-extinctions of species due to the loss of all resources are found to play a major role in determining the longterm shape of the food webs. It is demonstrated that an arbitrary choice of extinction and mutation rules can lead to unrealistic network structures and implausible size-frequency distributions of extinction avalanches. By refining the basic evolutionary algorithm of the model in two comprehensible steps, it is shown that the rules of the evolutionary process have to be adapted such that the constrains of the underlying network model are accounted for. If the risk of extinction depends on the competition pressure a species faces and if the stochastic variation of species traits in the mutation process is not undirected, large and complex networks emerge, the structure of which being compatible with modern data on food web structure. Additionally, in this case the size distribution of extinction avalanches follows a power law with exponent close to -2, as is seen in paleobiological data.