Quantitative Patterns in the Structure of Model and Empirical Food Webs

Abstract

We analyze the properties of model food webs and of fifteen community food webs from a variety of environments -including freshwater, marine-freshwater interfaces and terrestrial environments. We first perform a theoretical analysis of a recently proposed model for food webs-the niche model of Williams and Martinez (2000). We derive analytical expressions for the distributions of species' number of prey, number of predators, and total number of trophic links and find that they follow universal functional forms. We also derive expressions for a number of other biologically relevant parameters which depend on these distributions. These include the fraction of top, intermediate, basal, and cannibal species, the standard deviations of generality and vulnerability, the correlation coefficient between species' number of prey and number of predators, and assortativity. We show that our findings are robust under rather general conditions; a result which could not have been demonstrated without treating the problem analytically. We then use our analytical predictions as a guide to the analysis of fifteen of the most complete empirical food webs available. We uncover quantitative unifying patterns that describe the properties of the model food webs and most of the trophic webs considered. Our results support a strong new hypothesis that the empirical distributions of number of prey and number of predators follow universal functional forms that, without free parameters, match our analytical predictions. Further, we find that the empirically observed correlation coefficient, assortativity, and fraction of cannibal species are consistent with our analytical expressions and simulations of the niche model. Finally, we show that two quantities typically used to characterize complex networks, the average distance between nodes and the average clustering coefficient of the nodes, show a high degree of regularity for both the empirical data and simulations of the niche model. Our findings suggest that statistical physics concepts such as scaling and universality may be useful in the description of natural ecosystems.

Positive complexity–stability relations in food web models without foraging adaptation

“…We found that the niche model has an unrealistic distribution of predator numbers per prey species, with a hump at large predator numbers that becomes more pronounced with increasing C or S. This leads to a higher extinction probability with increasing food web complexity. In contrast, empirical data used in this paper and recent studies by other authors (Stouffer et al, 2005) suggest that realistic food web models should have exponential distributions of the numbers of prey and predator species. When we randomized the vulnerability distribution in the niche model, we found positive complexity-stability relations under the condition that Holling type II functional response and f ij = 1/B i is used in the simulations.…”

“…The bimodal shape has not been seen either in an analytical evaluation of the vulnerability distribution in the niche model (Stouffer et al, 2005), which was performed in the limit of large species numbers (S ∼ 1000) and a small connectivity z = 2 · L/S = 2 · S · C, (with z 5). For such extreme parameter values (which correspond to a connectance C = 0.005), exponentially decreasing distributions of the numbers of predator and prey species are obtained, which agree well with empirical distributions (which, however typically have connectance values around 0.15, as mentioned before (Dunne et al, 2002)).…”

Network structure and the biology of populations

“…One major problem lies in the extent to which constituent species are 'lumped' into functional groups, in ways that can bias analysis [55]. Interestingly, Stouffer et al [56] have shown that approximately exponential degree distributions similar to those observed can be derived from at least two apparently different models proposed earlier [57,58]; this finding is reminiscent of much earlier observations that significantly different mechanisms could result in identical distributions of the relative abundance of species.…”

Food webs: reconciling the structure and function of biodiversity

“…The niche model matches empirical data much better than the cascade or random models, and a probabilistic version of the niche model is providing ways to further explore the extent to which the constraints imposed by the niche model are consistent with empirical data [32]. These simple models allow exploration of how food-web structure systematically depends on the number of links and species in a system [20].…”

“…A central measure of all networks' structure is the variability of links among nodes or 'degree distributions' that, in food webs, describe the balance among trophic specialists and generalists. When normalized by L/S, degree distributions have a general exponential-type shape [20] indicating that most paths of energy flow through food webs go through relatively few species. This is consistent with species removal experiments in BEF studies, which have suggested a small sub-group of species disproportionately influences productivity [9].…”