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NCTS Seminar on Mathematical Biology
 
14:30 - 15:30, July 12, 2018 (Thursday)
Room 734, 4th Floor, The 3rd General Building, NTHU
(清華大學綜合三館 4樓734室)
Invasion Speeds in a Competition-diffusion Model with Mutation
Elaine Crooks (Swansea University)

Abstract:

We consider a reaction-diffusion system modelling the growth, dispersal and mutation of two phenotypes. This model was proposed in by Elliott and Cornell (2012), who presented evidence that for a class of dispersal and growth coefficients and a small mutation rate, the two phenotypes spread into the unstable extinction state at a single speed that is faster than either phenotype would spread in the absence of mutation. After first showing that, under reasonable conditions on the mutation and competition parameters, the spreading speed of the two phenotypes is indeed determined by the linearisation about the extinction state, we prove that the spreading speed is a non-increasing function of the mutation rate (implying that greater mixing between phenotypes leads to slower propagation), determine the ratio at which the phenotypes occur in the leading edge in the limit of vanishing mutation, and discuss the effect of trade-offs between dispersal and growth on the spreading speed of the phenotypes. This talk is based on joint work with Luca Brger and Aled Morris (Swansea).


 

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