Models of Facultative Mutualism: Density Effects

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Abstract
Six population models of facultative mutualism are formulated in terms of per capita births and deaths. Each explicitly considers the per capita impact of mutualism with respect to recipient density. The models include 1 with per capita benefits of mutualism independent of recipient density, 3 models of density-dependent mutualism with effects most pronounced at high recipient density, and 2 models with mutualistic benefits most pronounced at low recipient density. The dynamic behavior of systems of species pairs with like density responses is analyzed. The model incorporating density-independent mutualism results in a system that, depending on parameter values, is either unstable or has stability equal to that of systems of noninteracting species. The 3 models with high density mutualism each result in systems that are either unstable or that are stable, but less so than comparable systems with noninteracting species. The 2 models with low density mutualism each result in systems that are always stable, and always more stable than comparable systems with noninteracting species. All of these mutualistic systems, whether stable or unstable, exhibit species persistence.