title: Neutral Genetic Patterns for Expanding Populations with Nonoverlapping Generations.
abstract: We investigate the inside dynamics of solutions to integrodifference equations to understand the genetic consequences of a population with nonoverlapping generations undergoing range expansion. To obtain the inside dynamics, we decompose the solution into neutral genetic components. The inside dynamics are given by the spatiotemporal evolution of the neutral genetic components. We consider thin-tailed dispersal kernels and a variety of per capita growth rate functions to classify the traveling wave solutions as either pushed or pulled fronts. We find that pulled fronts are synonymous with the founder effect in population genetics. Adding overcompensation to the dynamics of these fronts has no impact on genetic diversity in the expanding population. However, growth functions with a strong Allee effect cause the traveling wave solution to be a pushed front preserving the genetic variation in the population. In this case, the contribution of each neutral fraction can be computed by a simple formula dependent on the initial distribution of the neutral fractions, the traveling wave solution, and the asymptotic spreading speed.
authors.affiliation: Department of Mathematical and Statistical Sciences, Centre for Mathematical Biology, University of Alberta, Edmonton, AB, T6G 2G1, Canada. marculis@ualberta.ca.
authors.forename: Nathan G
authors.initials: NG
authors.lastname: Marculis
authors.affiliation: Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA, 01609, USA.
authors.forename: Roger
authors.initials: R
authors.lastname: Lui
authors.affiliation: Department of Mathematical and Statistical Sciences, Centre for Mathematical Biology, University of Alberta, Edmonton, AB, T6G 2G1, Canada.|Department of Biological Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada.
authors.forename: Mark A
authors.initials: MA
authors.lastname: Lewis
mesh_terms: D014644:Genetic Variation; D005828:Genetics, Population; D006801:Humans; D008962:Models, Theoretical; D011156:Population Density; D011157:Population Dynamics
keywords: Allee effect; Founder effect; Integrodifference equations; Neutral genetic diversity; Range expansion; Traveling wave