Self-organization in evolution: a mathematical perspective

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.