Self–organization in evolution: a mathematical perspective

Abstract
The neo–Darwinian view of evolution centres upon the role of the gene. Here there seems to be little scope for self–organization. This conclusion is reinforced by traditional models of polymorphism in terms of allele frequencies in a mean–field gene–pool. However, models based on phenotypes, and including nonlinear and collective effects, suggest that evolution can indeed be viewed as a process whereby the ecosystem self–organizes. Here we focus on the phenomenon of speciation, and discuss a series of phenotypic models which together illuminate some of the issues surrounding the role of self–organization, including new approaches to fitness landscapes and species selection. All of these models represent speciation as a symmetry–breaking bifurcation, but in different mathematical contexts including deterministic dynamical systems, stochastic dynamical systems, and iterated function schemes. The main conclusions are surprisingly robust, despite the diversity of the models.

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