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Ideal Free Dispersal: Dynamics of Two and Three Competing Species
Munther, Daniel S.

2011, Doctor of Philosophy, Ohio State University, Mathematics.

We utilize reaction-diffusion-advection equations in an adaptive dynamic framework
to study the evolution of dispersal of two competing species. The species are
assumed to be identical except for their dispersal strategies which consist of random
movement (diffusion) and biased movement (advection) upward along resource gradients.
We focus on how spatial heterogeneity in the habitat influences selection. A key facet of this relationship is that diffusion creates a mismatch between a species population density at steady state and the resource function [9]. This led Cantrell et al. [9] to introduce a conditional strategy which can perfectly match the resource, resulting in the ideal free distribution of the species at equilibrium.


This ideal free strategy (IFS) serves as a basis for our study. Not only do we show
that it is a global evolutionarily stable strategy, but we find conditions under which it
is convergent stable, varying random dispersal rates, advection rates, or both of these
parameters at the same time. For two similar strategies on the "same side" of the
IFS we show that when resource function is monotone, the strategy which is closer
to the IFS is generally selected. For nonmonotone resource functions, we find that
there may exist nonideal free strategies which are locally evolutionarily stable and/or
convergent stable [21]. In addition, we find that for certain nonmonotone resource
functions, two similarly competing species can coexist, which enables us to also show
how three species coexistence is possible.

Yuan Lou, PhD (Advisor)
Chiu-Yen Kao, PhD (Committee Member)
Barbara Keyfitz, PhD (Committee Member)
135 p.

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Munther, D. (2011). Ideal Free Dispersal: Dynamics of Two and Three Competing Species. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Munther, Daniel. "Ideal Free Dispersal: Dynamics of Two and Three Competing Species." Electronic Thesis or Dissertation. Ohio State University, 2011. OhioLINK Electronic Theses and Dissertations Center. 26 Sep 2017.

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Munther, Daniel "Ideal Free Dispersal: Dynamics of Two and Three Competing Species." Electronic Thesis or Dissertation. Ohio State University, 2011. https://etd.ohiolink.edu/

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