Abstract
We study the effect of changes in flow speed on competition of an arbitrary number of species living in advective environments, such as streams and rivers. We begin with a spatial Lotka-Volterra model which is described by n reaction-diffusion-advection equations with Danckwerts boundary conditions. Using the dominant eigenvalue [Formula: see text] of the diffusion-advection operator subject to boundary conditions, we reduce the model to a system of ordinary differential equations. We impose a "transitive arrangement" of the competitors in terms of their interspecific coefficients and growth rates, which means that in the absence of advection, we have the following situation: for all [Formula: see text], species i out-competes species j, while species j has higher intrinsic growth rate than species i. Changing advection speed in the original spatial model corresponds to changing the value of [Formula: see text] in the spatially implicit model. Considering the cases of the odd and even n separately, we obtain explicit intervals of the values of [Formula: see text] that allow all n species to be present in the habitat (coexistence interval). Stability of this equilibrium is shown for [Formula: see text].
Published Version
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