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Asymmetric dispersal and evolutional selection in two-patch system

  • * Corresponding author: Changwook Yoon

    * Corresponding author: Changwook Yoon
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  • Biological organisms leave their habitat when the environment becomes harsh. The essence of a biological dispersal is not in the rate, but in the capability to adjust to the environmental changes. In nature, conditional asymmetric dispersal strategies appear due to the spatial and temporal heterogeneity in the environment. Authors show that such a dispersal strategy is evolutionary selected in the context two-patch problem of Lotka-Volterra competition model. They conclude that, if a conditional asymmetric dispersal strategy is taken, the dispersal is not necessarily disadvantageous even for the case that there is no temporal fluctuation of environment at all.

    Mathematics Subject Classification: Primary: 35F50, 92D25, 97M60, 74G30, 34D20; Secondary: 34D05.


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  • Figure 5.  Asymptotic behavior of numerical computation of (31)-(32) with $ \epsilon = 0.02 $. The legends are ordered by the size of asymptotic limits

    Figure 1.  A mega patch is a collection of many smaller patches. Dispersal across mega patches are counted in a two-patch system

    Figure 2.  Steady state solutions of (14). In the left figure, $ (K_1,K_2) = (2,5) $ and $ \theta_i $'s are monotone. In the right one, $ (K_1,K_2) = (0.2,5) $ and $ \theta_1 $ has maximum at $ d = 0.6613 $

    Figure 3.  Diagrams for $ y = -x(1-\frac{x}{K_1}) $ and $ y = x(1-\frac{x}{K_2}) $. Steady states are intersection points with $ y = R $. See (19)

    Figure 4.  The graph of motility function $ \gamma(s) $ without uniqueness. We have chosen a piecewise linear motility $ \gamma $ which takes the values in (20). Since $ s_i $ and $ \tilde s_i $ are close to each other, $ \gamma $ increases steeply for $ s\in(s_i,\tilde s_i) $

    Figure 6.  Asymptotic behavior ($ h = 0.1, \ell = 0.01, d = 0.02 $). The legends are ordered by the size of asymptotic limits

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