Fluctuations in population density change topology of genealogical trees in range expansions

Spatial expansions shape patterns of genetic diversity in a wide range of biological contexts, from the growth of bacterial colonies to the spread of epidemics. Such diversity patterns are encoded in the shape of genealogical trees, which trace the ancestry of individuals in the population. However, it is not known which factors determine the shape of these genealogies in expanding populations. Here, we show that different growth dynamics lead to qualitative changes in the topology of genealogies at the front. In particular, we find that highly cooperative growth leads to genealogies in which only pairwise mergers between branches occur. In contrast, moderate and low growth cooperativity lead to genealogies in which multiple branches merge simultaneously. Importantly, we find that the transition between these regimes is universal and results from the coupling between growth dynamics and population fluctuations at the front. While previous studies have relied on approximating expansions by a series of bottlenecks of fixed size, we show that such deterministic approximations lead to qualitatively different topologies, even when front fluctuations are small. Our results thus demonstrate that density fluctuations play a key role in shaping genetic diversity in expansions.