Fisher Waves and Front Roughening in a Two-Species Invasion Model with
Rensselaer Polytechnic Institute
Last modified: March 14, 2006
The dynamics of propagating fronts are fundamental in the study of
the spread of advantageous alleles, species, or opinions. Most notably,
Fisher and Kolmogorov et al. first addressed the velocity
characteristics of a simple front by way of a reaction-diffusion
equation, which served as a one-dimensional model for the spread of a
favorable gene. Here, we consider an individual-based two-dimensional
spatial model with nearest-neighbor preemptive competition to study
front propagation between an invader and resident species. In
particular, we investigate the asymptotic front velocity and compare it
with mean-field predictions. Further, we examine the "roughening" of the
invading front and analyze its statistical and scaling properties
employing the framework of non-equilibrium interface growth.
 L. O'Malley, B. Kozma, G. Korniss, Z. Racz, T. Caraco,
"Fisher Waves and the Velocity of Front Propagation in a Two-Species
Invasion Model with Preemptive Competition",
Computer Simulation Studies in Condensed Matter Physics XIX, edited by
D.P. Landau, S.P. Lewis, and H.-B. Schuttler, (Springer, Heidelberg,
Berlin, in press); http://www.arxiv.org/abs/q-bio.PE/0603013
 L. O'Malley, J. Basham, J. Yasi, A. Allstadt, G. Korniss, T. Caraco,
``Invasive Advance of an Advantageous Mutation: Nucleation Theory",
(preprint, 2005); http://www.arxiv.org/abs/q-bio.PE/0602023
 L. O'Malley, A. Allstadt, G. Korniss, T. Caraco,
"Nucleation and Global Time Scales in Ecological Invasion under
Preemptive Competition", in Fluctuations and Noise in Biological,
Biophysical, and Biomedical Systems III, edited by N.G. Stocks, D.
Abbott, and R.P. Morse, Proceedings of SPIE Vol. 5841 (SPIE, Bellingham,
WA, 2005), pp. 117-124.
 G. Korniss and T. Caraco,
``Spatial Dynamics of Invasion: The Geometry of Introduced Species",
Journal of Theoretical Biology 233, 137-150 (2005).