Selective advantage of diffusing faster

TL;DR

This paper demonstrates that even small differences in diffusion rates can significantly bias the outcome of species competition, favoring the faster-diffusing species, with theoretical quantification of this advantage.

Contribution

It introduces a stochastic spatial model showing how slight diffusivity differences influence competitive dynamics, providing analytical formulas for growth and fixation probabilities.

Findings

Small diffusivity differences lead to a strong bias in coarsening.

The faster species has a quantifiable selective advantage.

Analytical formulas predict growth and fixation probabilities.

Abstract

We study a stochastic spatial model of biological competition in which two species have the same birth and death rates, but different diffusion constants. In the absence of this difference, the model can be considered as an off-lattice version of the Voter model and presents similar coarsening properties. We show that even a relative difference in diffusivity on the order of a few percent may lead to a strong bias in the coarsening process favoring the more agile species. We theoretically quantify this selective advantage and present analytical formulas for the average growth of the fastest species and its fixation probability.