Theoretical Population Biology 98 (2014) 1–10 Contents lists available at ScienceDirect Theoretical Population Biology journal homepage: www.elsevier.com/locate/tpb The genetic signature of rapid range expansions: How dispersal, growth and invasion speed impact heterozygosity and allele surfing Devin W. Goodsman a,∗ , Barry Cooke c , David W. Coltman a , Mark A. Lewis a,b a Department of Biological Sciences, CW 405, Biological Sciences Bldg., University of Alberta, Edmonton, Alberta, Canada T6G 2E9 b Mathematical and Statistical Sciences, 632 CAB, University of Alberta, Edmonton, Alberta, Canada T6G 2G1 c Canadian Forest Service, Northern Forestry Centre, 5320 122 Street Northwest, Edmonton, Alberta, Canada T6H 3S5 article info Article history: Received 6 December 2013 Available online 6 September 2014 Keywords: Dispersal Genetic diversity Heterozygosity Invasion Range expansion abstract As researchers collect spatiotemporal population and genetic data in tandem, models that connect demography and dispersal to genetics are increasingly relevant. The dominant spatiotemporal model of invasion genetics is the stepping-stone model which represents a gradual range expansion in which individuals jump to uncolonized locations one step at a time. However, many range expansions occur quickly as individuals disperse far from currently colonized regions. For these types of expansion, stepping-stone models are inappropriate. To more accurately reflect wider dispersal in many organisms, we created kernel-based models of invasion genetics based on integrodifference equations. Classic theory relating to integrodifference equations suggests that the speed of range expansions is a function of population growth and dispersal. In our simulations, populations that expanded at the same speed but with spread rates driven by dispersal retained more heterozygosity along axes of expansion than range expansions with rates of spread that were driven primarily by population growth. To investigate surfing we introduced mutant alleles in wave fronts of simulated range expansions. In our models based on random mating, surfing alleles remained at relatively low frequencies and surfed less often compared to previous results based on stepping-stone simulations with asexual reproduction. © 2014 Elsevier Inc. All rights reserved. 1. Introduction Range expansions explain the wide spatial distribution of many dominant species. Unfortunately however, researchers often have only a snapshot of the extent of a recently expanded range rather than a complete spatiotemporal dataset. Genetic data have been used to elucidate processes underlying range expansions based on these snapshots, from our own planetary conquest (Ramachandran et al., 2005) to the post-glacial expansion of grasshoppers (Hewitt, 1999). Such insights, based on snapshots of genetic patterns on the landscape, are predicated on models that connect the dynamics, movement and genetics of populations. Thus, spatiotemporal genetic models are increasingly relevant as we accumulate large genetic databases. In this research we introduce integrodifference models as an alternative modeling framework in invasion genetics ∗ Corresponding author. E-mail addresses: goodsman@ualberta.ca (D.W. Goodsman), Barry.Cooke@NRCan-RNCan.gc.ca (B. Cooke), dcoltman@ualberta.ca (D.W. Coltman), mark.lewis@ualberta.ca (M.A. Lewis). with a sound mathematical and ecological basis. Integrodifference equations are discrete-time, continuous-space models that apply to range expansions in which populations have synchronized growth and dispersal stages (Neubert et al., 1995). Thus, they are useful for many herbaceous, invertebrate, and vertebrate species prone to invasion (Kot et al., 1996). Currently, invasion models with analytical solutions for the patterns of genetic diversity that they produce are limited to the island model (Wright, 1951; Buerger and Akerman, 2011) and the stepping-stone model (Kimura and Weiss, 1964; Thibault et al., 2009; DeGiorgio et al., 2011; Slatkin and Excoffier, 2012). In the island model, subpopulations receive migrants at a constant rate from a single unchanging source population, whereas in the stepping-stone model, unoccupied demes are colonized sequen- tially one after another, and only receive migrants from adjacent subpopulations (Kimura and Weiss, 1964; DeGiorgio et al., 2009, 2011). Many dispersing organisms however, can move to locations beyond adjacent unoccupied areas (Levin et al., 2003) and dispersal is an important determinant of the speed of population expansion in space (Kot et al., 1996). For these reasons, neither the island nor the stepping-model in their original form is realistic in terms of population processes or dispersal (Le Corre and Kremer, 1998). http://dx.doi.org/10.1016/j.tpb.2014.08.005 0040-5809/© 2014 Elsevier Inc. All rights reserved.