Name: Alastair Rucklidge
Title: Speciation as a symmetry-breaking bifurcation
A central problem in evolutionary biology is the occurrence in the fossil record of new species of organisms. One possible mechanism for the generation of new species is symmetry breaking -- when the single-species state loses stability to a multiple species state.
This project involves looking at a model of speciation: the model takes the form of a set of nonlinear differential equations that have special symmetry properties. As a result, some background in both nonlinear differential equations and the representation theory of groups will be helpful. Neither of these is absolutely essential, but the nonlinear differential equations aspect is more important.
During the project, you'll learn about how the model was developed, how to investigate features of the model, and interpret the model and draw biological conclusions from the results. In particular, you'll look at third-order and higher sets of differential equations, find equilibrium points, look at stability, and find some numerical solutions of the equations, perhaps using Maple. You'll use the representation theory of the symmetry groups involved in the problem to learn a little about equivariant bifurcation theory, aiming to understand how to look for equilibrium points with particular symmetries. There is thus the scope for both analytical and numerical work in this project, depending on the interests of the student.
You could go on to look at:
the influence of environmental noise on the results.
Symmetry breaking in all-to-all coupled systems.
Biological interpretation in terms of genotype and phenotype.
The open-ended nature of the project means it is suitable for third and fourth-year students.
Interested candidates should consult Dr A.M. Rucklidge.
Symmetry-breaking as an Origin of Species, by Ian Stewart, Toby
Elmhirst and Jack Cohen. In `Bifurcations, Symmetry and Patterns', (2003)