Spatial Gene Frequency Waves Under Genotype-Dependent Dispersal.
Dispersal is a crucial factor in natural evolution, since it determines the habitat experienced by any population and defines the spatial scale of interactions between individuals. There is compelling evidence for systematic differences in dispersal characteristics within the same population, i.e., genotype-dependent dispersal. The consequences of genotype-dependent dispersal on other evolutionary phenomena, however, are poorly understood. In this article we investigate the effect of genotype-dependent dispersal on spatial gene frequency patterns, using a generalization of the classical diffusion model of selection and dispersal. Dispersal is characterized by the variance of dispersal (diffusion coefficient) and the mean displacement (directional advection term). We demonstrate that genotype-dependent dispersal may change the qualitative behavior of Fisher waves, which change from being "pulled" to being "pushed" wave fronts as the discrepancy in dispersal between genotypes increases. The speed of any wave is partitioned into components due to selection, genotype-dependent variance of dispersal, and genotype-dependent mean displacement. We apply our findings to wave fronts maintained by selection against heterozygotes. Furthermore, we identify a benefit of increased variance of dispersal, quantify its effect on the speed of the wave, and discuss the implications for the evolution of dispersal strategies.
Institute of Science and Technology Austria, 3400 Klosterneuburg, Austria sebastian.novak@ist.ac.at.
Sebastian
0000-0002-2519-824X
S
Novak
Department of Applied Mathematics and Statistics, Comenius University, 842 48 Bratislava, Slovakia.
Richard
R
Kollár
D025041:Animal Migration; D000818:Animals; D005075:Biological Evolution; D017753:Ecosystem; D005787:Gene Frequency; D005828:Genetics, Population / Q000379:methods; D005838:Genotype; D008957:Models, Genetic; D015233:Models, Statistical; D011157:Population Dynamics
Fisher wave; dispersal evolution; population genetics; selection-migration dynamics; wave speed