Geometric theory on large-scale and local determination of density dependence of a recovering large carnivore population
arxiv(2023)
摘要
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.
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