Using model identification to analyze spatially explicit data with habitat, and temporal, variability

Abstract

Range expansion rates vary by species, habitat, and time since initiation. These speeds are a key issue in the analysis of biological invasions and a wide variety of mathematical models address them. Many such models may provide an adequate estimate of invasion speeds, and hence, an adequate qualitative fit to spread data. In general, however, because of flexibility in choice of dispersal kernels, integrodifference equation (IDE) models are superior to reaction–diffusion (RD) models when spread rates increase through time. Nevertheless, additional differences in model complexity may arise through different approaches for dealing with habitat, and temporal, variability. This diversity of potential methodologies suggests the need for quantitative model selection criteria, although to our knowledge, IDE models have not been compared to RD models with diffusion that varies in space and time. To demonstrate our approach for choosing between a suite of spatially explicit models that vary in complexity, we use the classic California sea otter range expansion data and the Akaike Information Criterion, which balances fit and parsimony. Our results show that the increasing speeds in the otter range expansion overwhelmingly support an IDE model for characterizing the entire data set. When focusing on certain stages of the range expansion, however, the more parsimonious reaction–diffusion model can provide the best description. Thus, the ideal spatial modeling framework can depend upon the temporal scale of the question.