A stochastic theory of community food webs. VI. Heterogeneous alternatives to the cascade model

Abstract

This paper considers 14 models as possible explanations of three major structural trends observed in 113 community food webs: (1) The average proportion of species that are top species is roughly constant in webs with different total numbers of species. The same holds for the average proportions of intermediate and basal species. (2)The average proportion of links that are intermediate-top links is roughly constant in webs with different total numbers of species. The same constancy of proportions in webs with different numbers of species holds for the three other kinds of links. (3) The frequency distributions of chain lengths are unimodal with modes usually between two and five links. One model, the cascade model, explains these trends and other structural trends. The other 13 models relax in various ways the cascade model's assumption that the probability of predation is the same between every pair of potential predator and potential prey and its assumption that the average probability of predation is inversely proportional to the total number of species in the web. Numerical comparisons of the observed structural trends with the model predictions show that the only viable alternative to the cascade model is the predator-dominant, constant-column-sum, linear-link-scaling model. This model differs from the cascade model in assuming that the expected number of prey species of any potential predator is the same as that for any other potential predator. The biological lesson suggested by these findings is that potential predators appear to have a mean number of prey species that is closer to constant than to linearly increasing with rank in the cascade model. Models that assume that predation probabilities are determined primarily by the prey species or by the distance between species in a cascade make predictions that are inferior descriptions of the major structural trends. Models that assume the mean number of trophic links increases as the 1.35 power of the total number of species make predictions that are inferior to those of models that assume the mean number of trophic links increases linearly with the total number of species.