On the shape of invading population in oriented environments

TL;DR

This paper analytically studies how populations spread in anisotropic environments using a lattice model of biased random walkers, revealing that shape characteristics depend solely on directional transition probabilities.

Contribution

It provides analytical expressions for shape metrics of population spread in anisotropic settings, linking them directly to transition probabilities, and models invasion in environments with oriented fibers.

Findings

Shape characteristics depend only on asymmetric transition probabilities.

Analytical formulas for asphericity and prolateness are derived.

Model captures invasion dynamics in environments with oriented fibers.

Abstract

We analyze the properties of population spreading in environments with spatial anisotropy within the frames of a lattice model of asymmetric (biased) random walkers. The expressions for the universal shape characteristics of the instantaneous configuration of population, such as asphericity $A$ and prolateness $S$ are found analytically and proved to be dependent only on the asymmetric transition probabilities in different directions. The model under consideration is shown to capture, in particular, the peculiarities of invasion in presence of an array of oriented tubes (fibers) in the environment.