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