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.

Biological invasions are multi-stage processes comprising chance demographic events, species interactions, and dispersal. Despite this complexity, simple models can increase understanding of the invasion process. We model the spread of aquatic invasive species through a network of lakes to evaluate the effectiveness of two intervention strategies. The first, which we call offense, contains the invader at sources; the second, which we call defense, protects uninvaded destinations. Deterministic models reveal the effects of these intervention strategies on spread rates. Practical applications involve finite collections of uninvaded lakes, however, and we therefore also present a stochastic model to describe how these strategies affect expected times to important invasion milestones. When the goal is to reduce overall spread rates, both approaches agree that offense is better early in invasions, but that defense is better after 1/2 the lakes are invaded. When the goal is to protect areas of high conservation value, however, defensive site protection always provides lower per site introduction rates. Although we focus on lakes, our results are quite general, and could be applied to any discrete habitat patches including, for example, fragmented terrestrial habitats.