We present a diffusion-competition model to describe the mteraction between the externally introduced grey squirrel and the indigenous red squirrel in Britain. We estimate the model parameters from field data. Solution of the model predicts waves of grey squirrel invasion with speed of invasion typical of that observed in the field. Numerical solution of the model on a two-dimensional domain gives population distributions qualitatively similar to those observed. We suggest that competition alone could account for the observed displacement of the red squirrel by the grey in large regions of Britain. The solutions are qualitatively similar to those for a single species spreading in the absence of competition. The quantitative difference is because competition slows down the speed of advance of the invading species
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