Null models in ecology

Mathematical models and empirical studies have revealed two potentially disruptive influences on ecosystems; (1) instabilities caused by nonlinear feedbacks and time-lags in the interactions of biological species, and (2) stochastic forcings by a fluctuating environment Because both of these phenomena can severely affect system survival, ecol- ogists are confronted with the question of why complex ecosystems do, in fact, exist Our study analyzes the basic themes of this research and identifies five general hypotheses that, in recent years, theoretical ecologists have built into models to increase their stability against disruptive feedback and stochasticity To counter feedback instabilities, theoreti- cians have considered (1) functional interactions between species that act as stabilizers, (2) disturbance patterns that interrupt adverse feedback effects, and (3) the stabilizing effect of integrating small-spatial-scale systems into large landscapes To decrease the influence of stochasticity, modelers have hypothesized (4) compensatory mechanisms operating at low population densities, and (5) the moderating effect of spatial extent and heterogeneity We show that modeling based on these ideas can be organized in a systematic way We also show that the stable equilibrium state should not be viewed as a fundamental property of ecological systems, but as a property that can emerge asymptotically from extrapolation to sufficiently large spatial scales

Equilibrium and Nonequilibrium Concepts in Ecological Models

The essence of the contradiction between traditional ecological complexity-stability hypothesis and recent theoretical results is clarified. The distinction between resilience and resistance is stressed. The possibilities of field verification of May's model are discussed. No satisfactory method for estimation of connectance and mean interaction strength in plant communities has been found. Relation between these parameters and stability in real communities remains an open question. The relation between connectance and stability (resilience) in purely competitive model communities is more complicated than May's rule predicts. The certain value of connectance having been achieved, stability increases with increasing connectance. We assessed the positive relation between species diversity and resistance, and negative relation between species diversity and resilience in plant communities during old-field succession in xeric habitat. But there is no causal relationship between species diversity and both kinds of stability. Resistance and resilience of the plant communities studied were determined primarily by life history strategies of constituent species. The results are interpreted in terms of Grimes' life history strategies and imply the validity of Gleasonian, population-centered explanation of community phenomena.

Community stability, complexity and species life history strategies

Stuart L. Pimm Pimm, S. L. 1979. Complexity and stability: another look at MacArthur's original hypothesis. - Oikos 33: 351-357. Most species persist at fairly constant levels despite perturbations from a variety of abiotic and biotic factors that may affect their numbers. To model this persistence, most studies impose the constraint that species densities, when slightly perturbed from equilibrium, will return to that equilibrium. This is the condition of local sta- bility. This paper examines a different condition involving a more severe perturbation. I define a system to be species deletion stable if, when a species is removed from system, all the remaining species remain at a stable equilibrium involving only posi- tive densities. Species in the real world might be deleted through emigration, disease, or the effects of a predator - including man. The condition of species deletion stability seems closer to the concept of 'stability' used by MacArthur. He argued that increased model complexity should lead to greater resistance to perturbation but this idea has generally not been supported by studies on local stability. This paper shows that increasing model complexity does not result in increased species deletion stability. Indeed, species deletion stability varies widely with slight changes in model structure and the characteristics of the species deleted. Species deletion stable models do not differ in any recognizable structural properties from models that are sensitive to species deletion. I conclude that natural ecosystems have not been significantly modified in their structures to maximize their resistance to species deletion. This is in contrast to the condition of local stability. Locally stable models, differ in many structural properties from those that are unstable. Analyses of the structure of real food webs shows that these possess the structures that lead to local stability. S. L. Pimm, Dept of Biological Sciences, Texas Tech Univ., Lubbock, TX 79409, USA. Accepted 11 January 1979

Complexity and stability: another look at MacArthur's original hypothesis

A central question in theoretical ecology is how diverse species can coexist in communities, and how that coexistence depends on network properties. Here, Grilli et al. quantify the extent of feasible coexistence of empirical networks, showing that it is smaller for trophic than mutualism networks.

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L.S. Jennings

Papers

Feasibility and stability in randomly assembled Lotka-Volterra models