Self‐Assembling Food Webs: A Global Viewpoint of Coexistence of Species in Lotka‐Volterra Communities
1992
Law, Richard | Blackford, Jerry C.
It has been suggested that the structure of ecological communities is constrained by dynamical instability of certain configurations of interacting species. Analysis of this has most often been based on asymptotic (local) stability analysis of equilibria at which all species are present, on the grounds that a configuration with an unstable equilibrium is less likely to occur in the real world than one with an asymptotically stable equilibrium. Since species may also coexist on limit cycles or chaotic orbits, we argue that a global condition that species should increase when rare could be more appropriate. Conditions for such "permanence" exist and their use makes it possible to focus on fundamental qualitative questions of coexistence of species, even though the quantitative properties of their dynamics may be very complex. We describe a straightforward and general method for distinguishing between permanent and nonpermanent Lotka—Volterra food webs; this method is due to Jansen (1987). A numerical analysis of four—species food webs with different degrees of omnivory shows that many that would be rejected as unstable in a local analysis are at the same time permanent in the global analysis. Using permanence methods, food webs of high connectance are shown to rebuild themselves more readily than those of low connectance, and therefore to recover more readily from disturbance than those of low connectance. The significance of this result for the relationship between complexity and stability of communities is discussed, together with the merits and drawbacks of permanence for studying the coexistence of species in communities.
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