Distances between species in food webs: Evaluating alternative metrics’ predictive power
In complex ecological systems, predicting how one species will respond to the perturbation of another is important but challenging. Some empirical and theoretical studies suggest that strong effects of food web perturbations rarely propagate more than two-three links, as measured by the shortest path between species. However, this measure of distance omits information concerning indirect paths between species, which other studies suggest are often dominant in determining the overall effect of one species on another. We compare how communicability, a topological metric containing information about both indirect and direct paths and walks between species, compares to shortest path distance in predicting one species' response to the perturbation of the other. We constructed simple food webs containing two trophic levels, and simulated dynamics using Lotka-Volterra models with Type I functional responses. We compared systems differing in size (species number), connectivity (average link number per node), and heterogeneity in node degree and attack rates, as well as other parameters. Starting from equilibrium, pulse perturbations were applied to a focal resource or consumer, and each species' response to that perturbation was measured as total magnitude of deviation in density from equilibrium, integrated over the time required for the system to return to equilibrium.
Both metrics proved to have predictive power, but the relative performance of each changed with food web parameters. Particularly, preliminary results indicate that as food web size (and hence maximum distance between species) increases, the correlation between communicability and response to perturbation increases, whereas the correlation between response and shortest path distance decreases. Our results suggest that the metric of communicability may be able to provide new insight concerning how one species' response to the perturbation of another might be predicted based on the relative topological positions of each in the web. A better understanding of this is pivotal for practical conservation and management purposes. The fact that communicability may be calculated based purely on network topology (without data concerning the strengths of species' interactions) enhances its potential usefulness in real-world situations, where such data may be limited.