Spatial Expansions and Serial Bottlenecks Produce Different Topologies of Genealogical Trees

What do the genealogies of expanding populations look like? While recent studies recognize the importance of genealogies for inferring and predicting evolutionary dynamics, very little is known about genealogies in expanding populations. Here, we show that range expansions can produce extremely different topologies of genealogical trees, which are very sensitive to the growth dynamics at the front. When growth is cooperative, genealogies are described by the Kingman coalescent—a backward-in-time analog to neutral evolution in which only pairwise mergers between lineages occur. Weakly cooperative and non-cooperative growth result in fundamentally different trees, with multiple lineages merging at the same time. We explain these results by deriving the distribution of the effective offspring number at the front, and show that the transition between the two topologies occurs when the variance of this distribution diverges. This divergence arises due to rare fluctuations of the front shape and position. Thus, evolutionary dynamics of range expansions cannot be approximated by a deterministic model of serial bottlenecks. Our results also show that range expansions provide a robust mechanism for non-Kingman genealogies, which previously have only been attributed to natural selection.