Abstract
In this study, we use a discrete, two-patch population model of an Allee species to examine different methods in managing invasions. We first analytically examine the model to show the presence of the strong Allee effect, and then we numerically explore the model to test the effectiveness of different management strategies. As expected invasion is facilitated by lower Allee thresholds, greater carrying capacities and greater proportions of dispersers. These effects are interacting, however, and moderated by population growth rate. Using the gypsy moth as an example species, we demonstrate that the effectiveness of different invasion management strategies is context-dependent, combining complementary methods may be preferable, and the preferred strategy may differ geographically. Specifically, we find methods for restricting movement to be more effective in areas of contiguous habitat and high Allee thresholds, where methods involving mating disruptions and raising Allee thresholds are more effective in areas of high habitat fragmentation.
Highlights
The increased international movement of humans and commercial products over the last couple of centuries has facilitated the introduction of unprecedented numbers of nonnative species worldwide (Vitousek, D’Antonio, Loope, & Westbrooks, 1996)
We provide biological context by linking the parameters to common management strategies that are applied to species invasions
We justify the use of this model by proving the expanded two-patch model has the properties of a species with a strong Allee effect
Summary
The increased international movement of humans and commercial products over the last couple of centuries has facilitated the introduction of unprecedented numbers of nonnative species worldwide (Vitousek, D’Antonio, Loope, & Westbrooks, 1996) While most of these introductions fail to establish due to environmental unsuitability or stochasticallydriven extinctions, or persist at innocuous population densities, a subset of these introductions becomes economic and ecological pests (Williamson & Fitter, 1996). We focus on populations with strong Allee effects, which are defined as having a positive Allee threshold, a density below which the population will decline towards extinction If this threshold is high a species may have difficulty persisting and expanding into new territory (Keitt et al, 2001; Lanchier, 2013), if its movement is restricted (Ackleh, Allen, & Carter, 2007). We show that geographical differences in demographic and landscape features may alter the effectiveness of different management strategies at inhibiting expansion; the most effective strategy may differ across a species’ range
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