Name: **Alastair Rucklidge**

email: A.M.Rucklidge@leeds.ac.uk

tel: 35161

office: 8.17f

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.

Reference:

Symmetry-breaking as an Origin of Species, by Ian Stewart, Toby

Elmhirst and Jack Cohen. In `Bifurcations, Symmetry and Patterns', (2003)

Birkhauser.