The Effects of Connectivity on Community Stability

Abstract

The stability properties of a highly symmetric 2 predator 2-prey system were explored using techniques of local stability analysis. The high degree of symmetry permitted analytic solution for all 4 eigenvalues and eigenvectors as functions of connectivity. 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. The tendency of prey species to return rapidly to their equilibrium values is enhanced as connectivity is increased, in agreement with MacArthur''s (1955) conjecture, and the tendency is decreased as connectivity is increased. This last effect causes the stability of the entire system to decrease with increased connectivity. 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) conjecture that community stability can be related to the patterns of interaction of the species forming a community is confirmed, but it is also a problem more complicated than MacArthur and others have supposed.