Advection-diffusion equations for generalized tactic searching behaviors
The paper describes some aspects and consequences of subject movements in population dynamics, especially tactic gradient climbing strategies in terms of partial differential equations for fluxes of populations. The equations analyzed describe the probability density flux for individuals performing a biased random walk with non-random taxis. The objective is to determine the expected or population level effectiveness of various individual-level behavioural responses to environmental heterogeneity. This leads to a Patlack-Keller-Segel-type advection-diffusion equation. The analysis uses methods described by \textit{W. Alt} [J. Math. Biol. 9, 147-177 (1980; Zbl 0434.92001)] by a biased random walk. The derivation generalizes the turning behaviour specified either in terms of the turning time distribution or of turning rates. An example shows how to examine the effectiveness of two classes of stochastic responses of searching animals to randomly distributed discrete resource patches.
scientific article; zbMATH DE number 1271807