Effects of environmental heterogeneity on species spreading via numerical analysis of some free boundary models

Abstract

<p style='text-indent:20px;'>This paper investigates the effect of environmental heterogeneity on species spreading via numerical simulation of suitable reaction-diffusion models with free boundaries. We focus on the changes of long-time dynamics (establishment or extinction) and spreading speeds of the species as the parameters describing the heterogeneity of the environment are varied. For the single species model in time-periodic environment and in space-periodic environment theoretically treated in [<xref ref-type="bibr" rid="b15">15</xref>,<xref ref-type="bibr" rid="b16">16</xref>], we obtain more detailed properties here. Among other results, our numerical simulation suggests that, in a time-periodic or space-periodic environment, moderate increase of the oscillation scale enhances the chances of establishment as well as the spreading speed of the species. We also numerically examine a related model with two competing species, which was treated in [<xref ref-type="bibr" rid="b34">34</xref>,<xref ref-type="bibr" rid="b28">28</xref>,<xref ref-type="bibr" rid="b24">24</xref>] recently and reduces to the single species free boundary model when one of the species is absent. Our numerical results, obtained by varying the parameters in the time-periodic and space-periodic terms of the model, suggest that heterogeneity of the environment enhances the invasion of the two species (as in the single species model), although there are subtle differences of the influences felt by the two. Some intriguing phenomena revealed in our simulations suggest that heterogeneity of the environment decreases the level of predictability of the competition outcome.</p>