Coexistence of mutualists and exploiters on spatial landscapes
Mutualisms are almost ubiquitously exploited by species that gain the benefits that mutualists offer to each other, but that offer nothing in return. This paper investigates the possible dynamical outcomes of a mechanistically formulated model system, involving two obligate mutualists and one exploiter. The model is based conceptually on a mutualism between a plant species and its pollinating seed parasite, in the presence of an obligate, nonpollinating seed parasite. Of particular interest are the conditions under which the exploiter species can invade and coexist with a mutualism that, by itself, possesses an equilibrium stabilized by other density-dependent regulating factors. Two types of models are used in the analyses: a deterministic, nonspatial model described by a set of discrete time equations, and an individual-based simulation incorporating stochastic interactions and spatial structure. Comparing the results of these two models uncovers the temporal dynamics of both well-mixed local systems and spatially distributed populations. Using these two situations, we examine how the predictions of the nonspatial model are affected by habitat structure. In the nonspatial case, and without the exploiters, there are typically two stable equilibria: one having zero densities for both mutualist species, and the other having nonzero densities. This bi-stability is a characteristic feature of obligate mutualisms. When the exploiter species is included, the system always retains the stability of the zero-density equilibrium, but the dynamics of the upper equilibrium can be more complicated, including limit cycle and extinction dynamics. Simulation results demonstrate that spatial structure is a highly stabilizing influence on the three-species system as long as the exploiter's dispersal distance is large relative to the seed dispersal distance of the plant species. Given this condition, the model predicts spatial distributions that are marked by a patchy distribution of plants, with mutualists and exploiters situated about these patches.
Wilson, WG; Morris, WF; Bronstein, JL
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