Professor ** Alison Etheridge**, University of Oxford:

** Modelling evolution in a spatial continuum**

**Abstract**. Since the pioneering work of Fisher, Haldane and Wright at the beginning of the 20th Century,
mathematics has played a central role in theoretical population genetics. In turn, population
genetics has provided the motivation both for important classes of probabilistic models, such as
coalescent processes, and for deterministic models, such as the celebrated Fisher-KPP equation.
Whereas coalescent models capture ’relatedness’ between genes, the Fisher-KPP equation captures
something of the interaction between natural selection and spatial structure. What has proved to
be remarkably difficult is to combine the two, at least in the biologically relevant setting of a
two-dimensional spatial continuum.
In this talk we describe some of the challenges of modelling evolution in a spatial continuum,
present a model that addresses those challenges, and, as time permits, describe some applications.