Document Type
Article
Publication Date
2012
Publication Title
Journal of Biological Dynamics
Abstract
We address several conjectures raised in Cantrell et al. [Evolution of dispersal and ideal free distribution, Math. Biosci. Eng. 7 (2010), pp. 17–36 [9 Cantrell, R. S., Cosner, C. and Lou, Y. 2010. Evolution of dispersal and ideal free distribution. Math. Biosci. Eng., 7: 17–36. [CrossRef], [PubMed], [Web of Science ®], [Google Scholar]]] concerning the dynamics of a diffusion–advection–competition model for two competing species. A conditional dispersal strategy, which results in the ideal free distribution of a single population at equilibrium, was found in Cantrell et al. [9 Cantrell, R. S., Cosner, C. and Lou, Y. 2010. Evolution of dispersal and ideal free distribution. Math. Biosci. Eng., 7: 17–36. [CrossRef], [PubMed], [Web of Science ®], [Google Scholar]]. It was shown in [9 Cantrell, R. S., Cosner, C. and Lou, Y. 2010. Evolution of dispersal and ideal free distribution. Math. Biosci. Eng., 7: 17–36. [CrossRef], [PubMed], [Web of Science ®], [Google Scholar]] that this special dispersal strategy is a local evolutionarily stable strategy (ESS) when the random diffusion rates of the two species are equal, and here we show that it is a global ESS for arbitrary random diffusion rates. The conditions in [9 Cantrell, R. S., Cosner, C. and Lou, Y. 2010. Evolution of dispersal and ideal free distribution. Math. Biosci. Eng., 7: 17–36. [CrossRef], [PubMed], [Web of Science ®], [Google Scholar]] for the coexistence of two species are substantially improved. Finally, we show that this special dispersal strategy is not globally convergent stable for certain resource functions, in contrast with the result from [9 Cantrell, R. S., Cosner, C. and Lou, Y. 2010. Evolution of dispersal and ideal free distribution. Math. Biosci. Eng., 7: 17–36. [CrossRef], [PubMed], [Web of Science ®], [Google Scholar]], which roughly says that this dispersal strategy is globally convergent stable for any monotone resource function.
Repository Citation
Averill, Isabel; Lou, Yuan; and Munther, Daniel, "On Several Conjectures From Evolution of Dispersal" (2012). Mathematics and Statistics Faculty Publications. 130.
https://engagedscholarship.csuohio.edu/scimath_facpub/130
DOI
10.1080/17513758.2010.529169
Version
Publisher's PDF
Volume
6
Issue
2
Comments
This research was partially supported by the NSF grant DMS-1021179.