  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 but that there is more
pressure driving the consumer distribution away from the MaxEnt form. Given the
methodological idiosyncrasies of current food web data, further study of such
deviations will need to consider both biological drivers and methodological
bias.
