The collective effect of finite-sized inhomogeneities on the spatial spread of populations in two dimensions

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 subpopulations 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 multispecies 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.

Assisted percolation of slow-spreading mutants in heterogeneous environments

Environmental heterogeneity can drive genetic heterogeneity in expanding populations; mutant strains may emerge that trade overall growth rate for an improved ability to survive in patches that are hostile to the wild type. This evolutionary dynamic is of practical importance when seeking to prevent the emergence of damaging traits. We show that a subcritical slow-spreading mutant can attain dominance even when the density of patches is below their percolation threshold and predict this transition using geometrical arguments. This work demonstrates a phenomenon of "assisted percolation", where one subcritical process assists another to achieve supercriticality.

Increased rates of dispersal of free-ranging cane toads (Rhinella marina) during their global invasion

Invasions often accelerate through time, as dispersal-enhancing traits accumulate at the expanding range edge. How does the dispersal behaviour of individual organisms shift to increase rates of population spread? We collate data from 44 radio-tracking studies (in total, of 650 animals) of cane toads (Rhinella marina) to quantify distances moved per day, and the frequency of displacement in their native range (French Guiana) and two invaded areas (Hawai’i and Australia). We show that toads in their native-range, Hawai’i and eastern Australia are relatively sedentary, while toads dispersing across tropical Australia increased their daily distances travelled from 20 to 200 m per day. That increase reflects an increasing propensity to change diurnal retreat sites every day, as well as to move further during each nocturnal displacement. Daily changes in retreat site evolved earlier than did changes in distances moved per night, indicating a breakdown in philopatry before other movement behaviours were optimised to maximise dispersal.