| Abstract: |
| We consider a reaction-diffusion system modelling the growth, dispersal and mutation of two phenotypes. This model was proposed by Elliott and Cornell (PLOS One, 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 verifying that, under reasonable conditions on the mutation and competition parameters, the spreading speed of the two phenotypes is 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 small-mutation limit, and discuss the effect of trade-offs between dispersal and growth on the spreading speed of the phenotypes. This is joint work with Luca B\orger and Aled Morris (Swansea). |
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