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Neutral genetic patterns for expanding populations

Banff International Research Station for Mathematical Innovation and Discovery

We investigate the inside dynamics of integrodifference equations to understand the genetic consequences of a population with non overlapping generations undergoing a range expansion. To obtain the inside dynamics, we decompose the solution into several neutral genetic components. The inside dynamics are then given by the spatio-temporal evolution of the neutral genetic components. We consider thin-tailed dispersal kernels and a variety of per capita growth functions in order 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. Growth functions with overcompensation are shown not to promote genetic diversity in the expanding population. Growth functions with a strong Allee effect cause the traveling wave solution to be a pushed front preserving the genetic variation in the population. We show that 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.

Mathematics; Dynamical systems and ergodic theory; Difference and functional equations

video/mp4

Author affiliation: University of Alberta

2017-03-21

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60955

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/