The Spread of a Reinvading Species: Range Expansion in the California Sea Otter

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Abstract
The spread of the California sea otter population provides excellent material for studying the spread of an invading species because the data are not confounded by spread in multiple spatial dimensions. We analyze data on the range expansion of the California sea otter within the context of a classical mathematical model incorporating growth, diffusion, and advection. Classical theory predicts that population fronts will form, that asymptotic rates of advance will be constant within homogeneous habitat, and that these asymptotic rates are given by twice the square root of the product of two factors, the intrinsic rate of increase and the diffusion coefficient. These patterns were observed in the historical data for range expansion of the otter, and the central remaining problem is explaining the observed differences in the rate of spread between the northern and southern fronts. Our analysis suggests that advection plays, at most, a minor role in those differences and, moreover, that estimated differences in the diffusion coefficients are sufficient to account for the observed patterns. Habitat-dependent differences in mortality seem to present the major competing hypothesis, and we regard as quite reasonable the possibility that both factors contribute to the observed differences. Further studies should be undertaken to provide the independent parameters necessary to resolve the issue and permit testing and further application of the model.