Population Dynamics in an Advective Environment
King-Yeung Lam, Ray Lee, Yuan Lou
Communications on Applied Mathematics and Computation ›› 2023, Vol. 6 ›› Issue (1) : 399-430.
Population Dynamics in an Advective Environment
We consider a one-dimensional reaction-diffusion equation describing single- and two-species population dynamics in an advective environment, based on the modeling frameworks proposed by Lutscher et al. in 2006. We analyze the effect of rate of loss of individuals at both the upstream and downstream boundaries. In the single-species case, we prove the existence of the critical domain size and provide explicit formulas in terms of model parameters. We further derive qualitative properties of the critical domain size and show that, in some cases, the critical domain size is either strictly decreasing over all diffusion rates, or monotonically increasing after first decreasing to a minimum. We also consider competition between species differing only in their diffusion rates. For two species having large diffusion rates, we give a sufficient condition to determine whether the faster or slower diffuser wins the competition. We also briefly discuss applications of these results to competition in species whose spatial niche is affected by shifting isotherms caused by climate change.
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