The Effects of Connectivity on Community Stability

The stability properties of a highly symmetric two-predator two-prey system were explored using techniques of local stability analysis. The high degree of symmetry permitted analytic solution for all four eigenvalues and eigenvectors as functions of connectivity. I found that at the "trophic level" level of organization, stability is unaffected by changes in connectivity. Certain "community" properties, in contrast, are affected by changes in connectivity. In particular, the tendency of prey species to return rapidly to their equilibrium values is enhanced as connectivity is increased, a result in substantial agreement with MacArthur's (1955) conjecture. In contrast, the tendency of predator species to return rapidly to their equilibrium values is decreased as connectivity is increased. This last effect causes the stability of the entire system to decrease with increased connectivity. These results demonstrate that "the problem" of stability and complexity is not unitary, since different aspects of community stability react differently to the same change in connectivity. MacArthur's (1955, p. 534) conjecture that community stability can be related to the "patterns of interaction of the species forming a community" is confirmed, but is also shown to be a problem more complicated than MacArthur and others have supposed.