Connecting the Dots: Range Expansions across Landscapes with Quenched Noise

When biological populations expand into new territory, the evolutionary outcomes can be strongly influenced by genetic drift, the random fluctuations in allele frequencies. Meanwhile, spatial variability in the environment can also significantly influence the competition between sub-populations vying for space. Little is known about the interplay of these intrinsic and extrinsic sources of noise in population dynamics: When does environmental heterogeneity dominate over genetic drift or vice versa, and what distinguishes their population genetics signatures? Here, in the context of neutral evolution, we examine the interplay between a population's intrinsic, demographic noise and an extrinsic, quenched-random noise provided by a heterogeneous environment. Using a multi-species Eden model, we simulate a population expanding over a landscape with random variations in local growth rates and measure how this variability affects genealogical tree structure, and thus genetic diversity. We find that, when the heterogeneity is sufficiently strong, the population front is dominated by genealogical lineages that are pinned to a small number of optimal paths. The landscape-dependent statistics of these optimal paths then supersede those of the population's intrinsic noise as the main determinant of evolutionary dynamics. Remarkably, the statistics for coalescence of genealogical lineages, derived from those deterministic paths, strongly resemble the statistics emerging from demographic noise alone in uniform landscapes. This cautions interpretations of coalescence statistics and raises new challenges for inferring past population dynamics.