Geometric theory on large-scale and local determination of density dependence of a recovering large carnivore population

Abstract

Density-dependent population growth is a feature of large carnivores like wolves ($\textit{Canis lupus}$), with mechanisms typically attributed to resource (e.g. prey) limitation. Such mechanisms are local phenomena and rely on individuals having access to information, such as prey availability at their location. Using over four decades of wolf population and range expansion data from Wisconsin (USA) wolves, we found that the population not only exhibited density dependence locally but also at landscape scale. Superficially, one may consider space as yet another limiting resource to explain landscape-scale density dependence. However, this view poses an information puzzle: most individuals do not have access to global information such as range-wide habitat availability as they would for local prey availability. How would the population "know" when to slow their range expansion? To understand observed large-scale spatial density dependence, we propose a reaction-diffusion model, first introduced by Fisher and Kolmogorov, with a "travelling wave" solution, wherein the population expands from a core range that quickly achieves local carrying capacity. Early-stage acceleration and later-stage deceleration of population growth can be explained by early elongation of an expanding frontier and a later collision of the expanding frontier with a habitat boundary. Such a process does not require individuals to have global density information. We illustrate our proposal with simulations and spatial visualizations of wolf recolonization in the western Great Lakes region over time relative to habitat suitability. We further synthesize previous studies on wolf habitat selection in the western Great Lakes region and argue that the habitat boundary appeared to be driven by spatial variation in mortality, likely associated with human use of the landscape.