Spatial Heterogeneity and Population Stability

Abstract

THE ability of populations to absorb perturbations is often investigated theoretically by some variant on the prey-predator, Lotka–Volterra, equations. Usually the treatment is in terms of linearised equations and thus deals with very small perturbations from a steady state. Recently, May¹ has enlarged the scope of investigation by considering perturbations from limit cycles rather than divergence from the simple steady state. This theoretical approach assumes populations uniform in space if not in time, but much of the variability found in nature is not only in large temporal cycles but in smaller-scale spatial patchiness. This variability may be handled statistically to give, for some specified area, a mean and variance for the populations. These can be used for ‘sensitivity analysis’ of the output from a theory or computer model, or as a basis for stochastic treatment. In either case this variability, as a function of changes in space, is not an intrinsic part of the model. Yet much experimental work shows that populations of prey or predator with limited abilities to disperse can produce spatially heterogeneous patterns, and the scale and complexity of these patterns may have some effect on persistence of these populations^2,3.