MacArthur's 1955 Stability Function is Related to Formal Dynamic Measures of Food Web Stability

Community complexity-stability relationships have been at the centre of ecological thinking for many decades. MacArthur (1955) proposed a measure of stability that reflected the diversity in the number of pathways energy can flow up through a food web but how this index correlates with more formal ideas of dynamical stability remains unexplored. Here, we examine the relationship between MacArthurs proposed index and measures of local and global stability in Lotka-Volterra food web models. Our results provide support for MacArthurs intuitive hypothesis that increasing the diversity of energy pathways through food webs endows them with greater stability, as measured by both the probability of local and global point stabilities, and the return time to stable equilibria following perturbation.