Authors: Bingtuan Li William F Fagan Kimberly I Meyer
Publish Date: 2014/02/23
Volume: 70, Issue: 1-2, Pages: 265-287
Abstract
We study a model that describes the spatial spread of a species along a habitat gradient on which the species’ growth increases Mathematical analysis is provided to determine the spreading dynamics of the model We demonstrate that the species may succeed or fail in local invasion depending on the species’ growth function and dispersal kernel We delineate the conditions under which a spreading species may be stopped by poor quality habitat and demonstrate how a species can escape a region of poor quality habitat by climbing a resource gradient to good quality habitat where it spreads at a constant spreading speed We show that dispersal may take the species from a good quality region to a poor quality region where the species becomes extinct We also provide formulas for spreading speeds for the model that are determined by the dispersal kernel and linearized growth rates in both directionsIf cinfty 0 choose small epsilon 0 such that cinfty +epsilon 0 Lemma 33 a shows that there exists an integer N 20 such that for nge N 2 and xge barx u nx varepsilon This together with 625 shows that for nge max N 1 N 2 u nx varepsilon for all x This proves the second part of the Theorem square
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