Genealogical structure changes as range expansions transition from pushed to pulled

Abstract

Range expansions accelerate evolution through multiple mechanisms including gene surfing and genetic drift. The inference and control of these evolutionary processes ultimately relies on the information contained in genealogical trees. Currently, there are two opposing views on how range expansions shape genealogies. In invasion biology, expansions are typically approximated by a series of population bottlenecks producing genealogies with only pairwise mergers between lineages--a process known as the Kingman coalescent. Conversely, traveling-wave models predict a coalescent with multiple mergers, known as the Bolthausen-Sznitman coalescent. Here, we unify these two approaches and show that expansions can generate an entire spectrum of coalescent topologies. Specifically, we show that tree topology is controlled by growth dynamics at the front and exhibits large differences between pulled and pushed expansions. These differences are explained by the fluctuations in the total number of descendants left by the early founders. High growth cooperativity leads to a narrow distribution of reproductive values and the Kingman coalescent. Conversely, low growth cooperativity results in a broad distribution, whose exponent controls the merger sizes in the genealogies. These broad distribution and non-Kingman tree topologies emerge due to the fluctuations in the front shape and position and do not occur in quasi-deterministic simulations. Overall, our results show that range expansions provide a robust mechanism for generating different types of multiple mergers, which could be similar those observed in populations with strong selection or high fecundity. Thus, caution should be exercised in making inferences about the origin of non-Kingman genealogies. Significance statementSpatial dynamics are important for understanding genetic diversity in many contexts, such as cancer and infectious diseases. Coalescent theory offers a powerful framework for interpreting and predicting patters of genetic diversity in populations, but incorporating spatial structure into the theory has proven difficult. Here, we address this long-standing problem by studying the coalescent in a spatially expanding population. We find the topology of the coalescent changes depending on the growth dynamics at the front. Using analytical arguments, we show that the transition between coalescent topologies is universal and is controlled by a parameter related to the expansion velocity. Our theory makes precise predictions about the effects of population dynamics on genetic diversity at the expansion front, which we confirm in simulations.