  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, for strong heterogeneity, the genetic makeup of the expansion front
is to a great extent predetermined by the set of fastest paths through the
environment. 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.
