Front Propagation, Roughening, and Extreme Fluctuations in an Individual-Based, Two-Allele Model of Evolutionary Invasion Individual-Based, Two-Allele Model of Evolutionary Invasion

Lauren O'Malley, Rensselaer Polytechnic Institute,

For sedentary organisms with localized reproduction, spatially clustered growth drives the invasive advance of a favorable mutation [1,2]. We model competition between two alleles where recurrent mutation introduces a genotype with a rate of local propagation exceeding the resident's rate [1]. We capture ecologically important properties of the rare invader's stochastic dynamics by assuming discrete individuals and local neighborhood interactions. To understand how individual-level processes may govern population patterns, we invoke the physical theory for nucleation of spatial systems. As the cluster sizes of the mutant allele become sufficiently large, we treat the invading front as that of a linear front. We study the roughening of the front, using the framework of non-equilibrium interface growth [2]. Our analysis indicates that initially flat, linear invading fronts exhibit Kardar-Parisi-Zhang (KPZ) roughening in one transverse dimension. Further, we investigate the fluctuations of the invading linear front, namely, the distribution of the average and the extreme fluctuations of the front in the steady state. By studying the distribution of strongly correlated random variables' extreme values, we can increase general understanding of interactions among frontal velocity, interface roughening and system size.

[1] L. O'Malley, J. Basham, J.A. Yasi, G. Korniss, A. Allstadt, and Tom Caraco, Theoretical Population Biology 70, 464-478 (2006).
[2] L. O'Malley, B. Kozma, G. Korniss, Z. Racz, T. Caraco, Phys. Rev. E 74, 041116 (2006).