Simple MaxEnt Models for Food Web Degree Distributions

Degree distributions have been widely used to characterize biological networks including food webs, and play a vital role in recent models of food web structure. While food webs degree distributions have been suggested to follow various functional forms, to date there has been no mechanistic or statistical explanation for these forms. Here I introduce models for the degree distributions of food webs based on the principle of maximum entropy (MaxEnt) constrained by the number of species, number of links and the number of top or basal species. The MaxEnt predictions are compared to observed distributions in 51 food webs. The distributions of the number of consumers and resources in 23 (45%) and 35 (69%) of the food webs respectively are not significantly different at a 95% confidence level from the MaxEnt distribution. While the resource distributions of niche model webs are well-described by the MaxEnt model, the consumer distributions are more narrowly distributed than predicted by the MaxEnt model. These findings offer a new null model for the most probable degree distributions in food webs. Having an appropriate null hypothesis in place allows informative study of the deviations from it; for example these results suggest that there is relatively little pressure favoring generalist versus specialist consumption strategies