Complexity, Diversity, and Stability: A Reconciliation of Theoretical and Empirical Results

Abstract

Theoretical studies of the relationship between ecosystem complexity and stability usually conclude that systems with more species, more interspecific interactions per species (connectance), or stronger interactions are not as likely to be stable as systems with fewer of these attributes (Gardner and Ashby 1970; May 1972, 1974, 1979; DeAngelis 1975; Gilpin 1975; Pimm 1979a, 1979b, 1980). Yet, in one of the few empirical investigations of this problem, McNaughton (1977) concluded that increased complexity stabilized certain ecosystem properties; more precisely, that a large mammalian grazer changed total green plant biomass less in more diverse than in less diverse grassland plots. We try to resolve this apparent contradiction between theory and empiricism by investigating, in model grazing systems, the relationship between complexity and the lack of change in plant biomass (which we call biomass stability) following the removal of an herbivore. We established a set of structured food web models composed of one herbivore and n plant species. The models were based on the familiar Lotka-Volterra equations, and we selected their parameters over intervals designed to be biologically sensible and also to reflect the pattern of interactions in the food web. Only those models with a locally stable equilibrium involving species with positive biomasses were retained for further analysis. From each model of this subset, the herbivore was removed and the resultant change in total plant biomass followed until a new stable equilibrium was achieved. Relative biomass stability was calculated from the relative change in the total plant biomasses of the two equilibria. Clearly, a ratio near unity indicates biomass stability, while a large ratio indicates that biomass has increased considerably, following removal of the herbivore. We modeled webs of varying complexity as measured by: (1) the number of species; (2) the number of competitive interactions between plant species; and (3) species diversity (a measure combining the number of species and their relative abundances), and related these features to biomass stability. Our conclusion is that increased complexity can enhance biomass stability, even