The collective effect of finite-sized inhomogeneities on the spatial spread of populations in two dimensions

TL;DR

This study investigates how finite-sized inhomogeneities like obstacles and hotspots affect the spatial spread of populations in two-dimensional habitats, combining analytical, algorithmic, and numerical approaches.

Contribution

It introduces a principle of least time to predict front dynamics in heterogeneous environments and applies it to large-scale habitats using the Eikonal equation.

Findings

Obstacles slow down population spread depending on their density and size.

Hotspots accelerate spread depending on their strength and density.

Dimensionality significantly influences the impact of inhomogeneities.

Abstract

The dynamics of a population expanding into unoccupied habitat has been primarily studied for situations in which growth and dispersal parameters are uniform in space or vary in one dimension. Here we study the influence of finite-sized individual inhomogeneities and their collective effect on front speed if randomly placed in a two-dimensional habitat. We use an individual-based model to investigate the front dynamics for a region in which dispersal or growth of individuals is reduced to zero (obstacles) or increased above the background (hotspots), respectively. In a regime where front dynamics is determined by a local front speed only, a principle of least time can be employed to predict front speed and shape. The resulting analytical solutions motivate an event-based algorithm illustrating the effects of several obstacles or hotspots. We finally apply the principle of least time to large heterogeneous environments by solving the Eikonal equation numerically. Obstacles lead to a slow-down that is dominated by the number density and width of obstacles, but not by their precise shape. Hotspots result in a speedup, which we characterise as function of hotspot strength and density. Our findings emphasise the importance of taking the dimensionality of the environment into account.