Relating dispersal and range expansion of California sea otters

Linking dispersal and range expansion of invasive species has long challenged theoretical and quantitative ecologists. Subtle differences in dispersal can yield large differences in geographic spread, with speeds ranging from constant to rapidly increasing. We developed a stage-structured integrodifference equation (IDE) model of the California sea otter range expansion that occurred between 1914 and 1986. The non-spatial model, a linear matrix population model, was coupled to a suite of candidate dispersal kernels to form stage-structured IDEs. Demographic and dispersal parameters were estimated independent of range expansion data. Using a single dispersal parameter, alpha, we examined how well these stage-structured IDEs related small scale demographic and dispersal processes with geographic population expansion. The parameter alpha was estimated by fitting the kernels to dispersal data and by fitting the IDE model to range expansion data. For all kernels, the alpha estimate from range expansion data fell within the 95% confidence intervals of the alpha estimate from dispersal data. The IDE models with exponentially bounded kernels predicted invasion velocities that were captured within the 95% confidence bounds on the observed northbound invasion velocity. However, the exponentially bounded kernels yielded range expansions that were in poor qualitative agreement with range expansion data. An IDE model with fat (exponentially unbounded) tails and accelerating spatial spread yielded the best qualitative match. This model explained 94% and 97% of the variation in northbound and southbound range expansions when fit to range expansion data. These otters may have been fat-tailed accelerating invaders or they may have followed a piece-wise linear spread first over kelp forests and then over sandy habitats. Further, habitat-specific dispersal data could resolve these explanations.