Evol Ecol Res 11: 611-635 (2009)     Full PDF if your library subscribes.

Evolutionary distributions

Yosef Cohen

Department of Fisheries, Wildlife and Conservation Biology, University of Minnesota, St. Paul, Minnesota, USA

Correspondence: Y. Cohen, Department of Fisheries, Wildlife and Conservation Biology, University of Minnesota, St. Paul, MN 55108, USA.
e-mail: yc@umn.edu


Aims: (i) Based on first principles, develop partial differential equation models of evolution by natural selection operating on phenotypic traits. (ii) Use the models to draw conclusions about possible outcomes of evolution, their stability, resistance to invasion, and co-existence of phenotypes.

Assumptions: (i) Populations are large. (ii) Mutations are random – they are introduced at birth and by immigration. (iii) Selection operates through mortality and emigration. (iv) The selection unit is a phenotype.

Conclusions: (i) Stable evolutionary distributions represent evolutionarily stable strategies in that the co-existing set of phenotypes cannot be invaded by mutants. (ii) Because adaptive traits are bounded, phenotypes evolving on the boundaries are subject to less mortality due to competition than those in the interior of the adaptive space. (iii) Phenotypic plasticity allows the increase in density of a prey phenotype that would otherwise be depressed – the density increases because prey evolve lower susceptibility to predation. (iv) Host–pathogen co-evolution can lead to stable (possibly Turing) pattern formation of a phenotype’s density in the adaptive space. (v) Phenotypic co-evolution in model ecosystems can stabilize a potentially local chaotic dynamics.

Keywords: adaptive traits, competition, evolutionary distributions, host–parasite, predator–prey.

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