Environmental Variability Promotes Coexistence in Lottery Competitive Systems

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Abstract
In deterministic approaches to modeling, 2 spp. are generally regarded as capable of coexistence if the model has a stable equilibrium with both species in positive numbers. Temporal environmental variability is assumed to reduce the likelihood of coexistence by keeping species abundances away from equilibrium. A contrasting view is presented based on a model of competition for space among coral reef fishes, or any similarly territorial animals. The model has no stable equilibrium point with both species in positive abundance, yet both species persist in the system, provided environmental variability in birth rates is sufficiently high. The higher the environmental variability the more likely it is that coexistence will occur. This conclusion is not affected by 1 sp. having a mean advantage over the other. Not all kinds of environmental variability necessarily lead to coexistence for when the deaths rates of the 2 spp. are highly variable and negatively correlated, the extinction of 1 sp., determined by change, is likely to occur. The results depend on the nonlinearity of the dynamics of the system. This nonlinearity arises from the fact that the animals have overlapping generations. When applied to the coral reef fish setting, the analysis confirms the view that coexistence can occur in a system where space is allocated largely at random, provided environmental variability is sufficiently great (Sale 1977); but these explanations and predictions differ in detail with those of Sale.