Allee effect promotes diversity in traveling waves of colonization

Abstract

Most mathematical studies on expanding populations have focused on the rate of range expansion of a population. However, the genetic consequences of population expansion remain an understudied body of theory. Describing an expanding population as a traveling wave solution derived from a classical reaction-diffusion model, we analyze the spatio-temporal evolution of its genetic structure. We show that the presence of an Allee effect (i.e., a lower per capita growth rate at low densities) drastically modifies genetic diversity, both in the colonization front and behind it. With an Allee effect (i.e., pushed colonization waves), all of the genetic diversity of a population is conserved in the colonization front. In the absence of an Allee effect (i.e., pulled waves), only the furthest forward members of the initial population persist in the colonization front, indicating a strong erosion of the diversity in this population. These results counteract commonly held notions that the Allee effect generally has adverse consequences. Our study contributes new knowledge to the surfing phenomenon in continuous models without random genetic drift. It also provides insight into the dynamics of traveling wave solutions and leads to a new interpretation of the mathematical notions of pulled and pushed waves. R apid increases in the number of biological invasions by alien organisms (1) and the movement of species in response to their climatic niches shifting as a result of climate change have caused a growing number of empirical and observational studies to address the phenomenon of range expansion. Numerous mathematical approaches and simulations have been developed to analyze the processes of these expansions (2, 3). Most results focus on the rate of range expansion (4), and the genetic consequences of range expansion have received little attention from mathematicians and modelers (5). However, range expansions are known to have an important effect on genetic diversity (6, 7) and generally lead to a loss of genetic diversity along the expansion axis due to successive founder effects (8). Simulation studies have already investigated the role of the geometry of the invaded territory (9-11), the importance of long-distance dispersal and the shape of the dispersal kernel (12-14), the effects of local demography (15), or existence of a juvenile stage (13). Further research is needed to obtain mathematical results supporting these empirical and simulation studies, as such results could determine the causes of diversity loss and the factors capable of increasing or reducing it.In a simulation study using a stepping-stone model with a lattice structure, Edmonds et. al (16) analyzed the fate of a neutral mutation present in the leading edge of an expanding population. Although in most cases the mutation remains at a low frequency in its original position, in some cases the mutation increases in frequency and propagates among the leading edge. This phenomenon is described as "surfing" (15). Surfing is caused by the strong genetic drift ...

Range expansions transition from pulled to pushed waves as growth becomes more cooperative in an experimental microbial population

“…Predicting the rate of colonization may be particularly challenging for pushed waves because they can advance slowly in the beginning due to an Allee effect but accelerate later as the bulk density increases (47,56). Pushed waves are also expected to have slower rates of neutral evolution and diversity loss compared with pulled expansions (26,57). The conservation strategies to limit pulled and pushed invasions could also be very different.…”

Efficient mitigation of founder effects during the establishment of a leading-edge oak population

“…More importantly, our results support the idea that negative demographic consequences of Allee effects can be counter-balanced by their beneficial impacts on gene flow. A good example of this seemingly paradoxical conclusion is the work of Roques et al [7], which modelled a scenario of expansion with Allee effects (but without long-distance gene flow). Our expectation is that most leading-edge populations of tree species that managed to establish and eventually expand should have benefitted from this rescue effect, in view of their typically high inbreeding depression (that make them prone to Allee effects).…”

“…Those populations that form the leading edge of an expanding species range are predicted to experience profound evolutionary changes [5][6][7]. In many organisms, including trees, range expansions are typically promoted by rare events of long-distance dispersal that enable small pioneer populations to establish far ahead of the continuous range and to fill the empty area with their progeny [5,8].…”

Range expansion promotes cooperation in an experimental microbial metapopulation

“…The cooperator strain also displays an Allee effect (where the per capita growth rate of the population is maximal at intermediate population densities). This type of growth is predicted to have a strong effect on the dynamics of expanding populations (36)(37)(38)(39).…”