Nucleation and Spread of an Invasive Allele

We analyze a prototypical discrete spatial model for the spread of an invasive allele when individuals compete preemptively for common limiting resources. Initially, the population is genetically monomorphic with the resident allele at high density. The invasive allele is introduced through rare, but recurrent, mutation. The mutant allele is the better competitor (has an individual-level advantage) but its spread is limited by the local availability of resources. We find that each successful introduction of the mutant leads to strong spatial clustering. Spatial patterns in simulation resemble nucleation and subsequent growth, articulately described by Avrami's law in sufficiently large systems\footnote{G. Korniss and T. Caraco, J. Theor. Biol. (in press, 2004); http://www.rpi.edu/~korniss/Research/JTB04.pdf}.