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.

Fluctuations uncover a distinct class of traveling waves

“…Despite the critical role that evolution plays in biological invasions ( 10 , 18 , 27 , 68 – 74 ), only a handful of studies have examined the link between genetic diversity and species ecology in this context ( 35 , 36 , 56 , 59 ). The main result of the previous work is that Allee effects reduce genetic drift and preserve diversity.…”

“…The transition from pulled to pushed dynamics is also evident in the number of organisms that trace their ancestry to the leading edge vs. the bulk of the front. The expected number of descendants has been determined for any spatial position along the front for both pulled and pushed waves ( 35 , 36 , 55 , 56 ). For pulled waves, only the very tip of the expansion contributes to future generations.…”

Expansion history and environmental suitability shape effective population size in a plant invasion

“…Our results support the prediction that both range expansion and habitat quality can increase the genetic drift experienced by leading edge populations. There is particular interest in whether these effects can hinder adaptation, slow further colonization, and establish static range boundaries (Birzu, Hallatschek, & Korolev, 2018;Bosshard et al, 2017;Lehe et al, 2012;Marculis, Lui, & Lewis, 2017;Peischl et al, 2013Peischl et al, , 2015. Recent studies have demonstrated a link between differences in historical values of N e and differences in the efficacy of selection across species (Jensen & Bachtrog, 2011;Slotte, Foxe, Hazzouri, & Wright, 2010;Strasburg et al, 2011), and both theoretical and experimental studies of bacteria have shown that the process of range expansion can reduce contemporary N e and impose limits to adaptation and further colonization at the expansion front (Gralka et al, 2016;Hallatschek & Nelson, 2010;Lehe et al, 2012;Peischl et al, 2013Peischl et al, , 2015.…”

Eco‐evolutionary dynamics of range expansion

“…Through these sequential colonization bottlenecks, alleles initially present at or near the leading edge, or those that arise there by mutation, can "surf" to high frequency on the expanding front simply by chance. This is true for neutral alleles, the best studied case (Klopfstein et al 2006, Hallatschek and Nelson 2008, Marculis et al 2017. It is also true for non-neutral alleles, including beneficial alleles that enhance demographic or dispersal traits and whose rise in frequency is reinforced by natural selection or spatial sorting.…”