Evolutionary stable dispersal with pattern formation in a mutualist-antagonist system
Question: How does the evolution of dispersal distance affect the persistence, distribution, and population dynamics of a mutualist-antagonist system capable of endogenous pattern formation? Modelling approach: We let dispersal distance evolve within an individual-based model involving an obligate plant-pollinating seed parasite pair and a parasitoid that preys upon pollinator larvae. The model incorporates demographic parameters for ovule production, pollinator oviposition, pollinator and parasitoid visitation rates, in addition to background mortality probabilities for each of the three species. A corresponding non-spatial mathematical model verifies our representation of the interspecific dynamics. Key assumptions: Individuals move over a homogeneous underlying environment with dispersal distances drawn from probability distribution kernels. Each species is subject to density-dependent reproduction. Pollinators and parasitoids make multiple visits per time step that are Poisson distributed. Conclusions: Dependent on demographic parameter values, there is a spectrum of outcomes, including: (1) runaway selection for increased dispersal distance resulting in homogeneous distributions of all three species; (2) an evolutionarily stable state with pattern formation and metapopulation-like dynamics; and (3) rapid extinction of one or more species. Interestingly, a weak relaxation of the obligacy between the plants and the pollinators erodes the evolutionarily stable state with pattern formation. We argue that this dependence upon and sensitivity to obligacy may explain the lack of empirical observations of endogenous pattern formation in nature. © 2007 Curtis A. Smith.
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