Invasive Allele Spread under Preemptive Competition

TL;DR

This paper models the spread of an invasive allele in a spatial setting with preemptive competition, showing that its dynamics follow nucleation theory and Avrami's law, providing insights into invasion timing.

Contribution

It introduces a discrete spatial model for allele invasion under preemptive competition and demonstrates that the invasion dynamics follow nucleation and growth principles, specifically Avrami's law.

Findings

Spread of advantageous allele follows homogeneous nucleation.

Global resident allele density approximates Avrami's law.

Model applies to large systems with predictable invasion timing.

Abstract

We study a discrete spatial model for invasive allele spread in which two alleles compete preemptively, initially only the "residents" (weaker competitors) being present. We find that the spread of the advantageous mutation is well described by homogeneous nucleation; in particular, in large systems the time-dependent global density of the resident allele is well approximated by Avrami's law.