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The Evolution of Dispersal for the Case of Two-Patches and Two-Species with Travel Loss

Hamida, Youcef
http://rave.ohiolink.edu/etdc/view?acc_num=osu149259130964176

Abstract Details

2017, Master of Mathematical Sciences, Ohio State University, Mathematical Sciences.
Two cases of species competition were considered. The first was the case of two-species-in-two-patches with both species being drifted from patch 1 to patch 2 at the same rate with the assumption that the organisms have an unconditional dispersal strategy (i.e. migrating from patch 1 to patch 2 at the same rate as from patch 2 to patch 1). In this case, ideal free distribution (IFD) only exists if the carrying capacity of patch 2, K2, is greater than K1, the carrying capacity of patch 1. If K2 is less or equal to K1, then, the resident species may have an evolutionarily stable strategy (ESS) only if it migrates from patch 1 to patch 2 at the rate d = infinity or d = 0, depending on the drift rate. The second case, was also two-species-in-two-patches; both species are assumed to migrate (drifted) from patch 1 to patch 2 at the same rate, but have a different rate of dispersal from patch 2 to patch 1. Furthermore, we assume that there is travel loss (i.e. species die during migration). In this case, although we showed that IFD does not exist, we analytically proved the existence of an ESS strategy. If the resident has such an ESS strategy, we proved that the equilibium point, at which the resident survives and the mutants vanish, is globally asymptotically stable.
Yuan Lou (Advisor)
Adrian Lam (Committee Member)
36 p.
Mathematics
evolution; patch; dispersal; travel; loss; IFD; ESS; CSS

Recommended Citations

Citations

  • Hamida, Y. (2017). The Evolution of Dispersal for the Case of Two-Patches and Two-Species with Travel Loss [Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu149259130964176

    APA Style (7th edition)

  • Hamida, Youcef. The Evolution of Dispersal for the Case of Two-Patches and Two-Species with Travel Loss. 2017. Ohio State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu149259130964176.

    MLA Style (8th edition)

  • Hamida, Youcef. "The Evolution of Dispersal for the Case of Two-Patches and Two-Species with Travel Loss." Master's thesis, Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu149259130964176

    Chicago Manual of Style (17th edition)

osu149259130964176
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This open access ETD is published by The Ohio State University and OhioLINK.