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We consider a system of two competing populations in two-dimensional heterogeneous environments. The populations are assumed to move horizontally and vertically with different probabilities, but are otherwise identical. We regard these probabilities as dispersal strategies. We show that the evolutionarily stable strategies are to move in one direction only. Our results predict that it is more beneficial for the species to choose the direction with smaller variation in the resource distribution. This finding seems to be in agreement with the classical results of Hasting [15] and Dockery et al. [11] for the evolution of slow dispersal, i.e. random diffusion is selected against in spatially heterogeneous environments. These conclusions also suggest that broader dispersal strategies should be considered regarding the movement in heterogeneous habitats.
Classical ecological theory predicts that environmental stochasticity increases extinction risk by reducing the average per-capita growth rate of populations. To understand the interactive effects of environmental stochasticity, spatial heterogeneity
Many studies on animal and human movement patterns report the existence of scaling laws and power-law distributions. Whereas a number of random walk models have been proposed to explain observations, in many situations individuals actually rely on me
We present new empirical evidence, based on millions of interactions on Twitter, confirming that human contacts scale with population sizes. We integrate such observations into a reaction-diffusion metapopulation framework providing an analytical exp
This work is concerned with the large time behavior of the solutions of a parabolic-ODE hybrid system, modeling the competition of two populations which are identical except their movement behaviors: one species moves by random dispersal while the ot
We study the asymptotic spreading of Kolmogorov-Petrovsky-Piskunov (KPP) fronts in heterogeneous shifting habitats, with any number of shifting speeds, by further developing the method based on the theory of viscosity solutions of Hamilton-Jacobi equ