Details of Grant 

EPSRC Reference:	GR/R98563/01
Title:	Evolution of regulated populations: stochastic models and their analysis
Principal Investigator:	Etheridge, Professor A
Other Investigators:
Researcher Co-Investigators:
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Department:	Statistics
Organisation:	University of Oxford
Scheme:	Standard Research (Pre-FEC)
Starts:	01 January 2003	Ends:	31 May 2006	Value (£):	124,643
EPSRC Research Topic Classifications:	Mathematical Analysis Population Ecology
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
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Summary on Grant Application Form
Many biological organisms are distributed across a continuous two-dimensional environemnt in which individuals disperse, reproduce and interact with their neighbours. Key issues in evolution and ecology can only be resolved via an understanding of the influence of this spatial structure, but until recently progress has been obstructed by the lack of a satisfactory model for the population dynamics in a truly continuous space. The Principal Investigator recently proved that a class of models based on branching diffusion processes, but in which the fecundity of an individual depends on the local population density, can lead to stable population dynamics. These models, of essentially the same form as those introduced into the ecology literature by Bolker & Pacala (1997), provide a natural starting point for a study of spatially structured populations.The first step will be to study the behaviour of a pair of populations in which fecundity for each type is controlled by the combined population density. Do we see qualitatively different behaviour from that predicted by models in which local population density is maintained constant? Thinking of the populations as different genetic types, can one find approximate expressions for correlations in gene frequency over large spatial scales and thus understand the influence of the local fluctuations in population density on evolutionary parameters? There are many natural ways to extend the basic model. Can we find a simple model for long-range correlations in gene frequency, parametrised in terms of a small number of measurable parameters, that can be used to approximate correlations in populations with a wide range of local structures?
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