The coalescent in boundary-limited range expansions

Specialization at an expanding front

As a population grows, spreading to new environments may favor specialization. In this paper, we introduce and explore a model for specialization at the front of a colony expanding synchronously into new territory. We show through numerical simulations that, by gaining fitness through accumulating mutations, progeny of the initial seed population can differentiate into distinct specialists. With competition and selection limited to the growth front, the emerging specialists first segregate into sectors, which then expand to dominate the entire population. We quantify the scaling of the fixation time with the size of the population and observe different behaviors corresponding to distinct universality classes: unbounded and bounded gains in fitness lead to superdiffusive (z=3/2) and diffusive (z=2) stochastic wanderings of the sector boundaries, respectively.

Emergence of evolutionary driving forces in pattern-forming microbial populations

Evolutionary dynamics are controlled by a number of driving forces, such as natural selection, random genetic drift and dispersal. In this perspective article, we aim to emphasize that these forces act at the population level, and that it is a challenge to understand how they emerge from the stochastic and deterministic behaviour of individual cells. Even the most basic steric interactions between neighbouring cells can couple evolutionary outcomes of otherwise unrelated individuals, thereby weakening natural selection and enhancing random genetic drift. Using microbial examples of varying degrees of complexity, we demonstrate how strongly cell-cell interactions influence evolutionary dynamics, especially in pattern-forming systems. As pattern formation itself is subject to evolution, we propose to study the feedback between pattern formation and evolutionary dynamics, which could be key to predicting and potentially steering evolutionary processes. Such an effort requires extending the systems biology approach from the cellular to the population scale.This article is part of the theme issue 'Self-organization in cell biology'.

Mutation load dynamics during environmentally-driven range shifts

The fitness of spatially expanding species has been shown to decrease over time and space, but specialist species tracking their changing environment and shifting their range accordingly have been little studied. We use individual-based simulations and analytical modeling to compare the impact of range expansions and range shifts on genetic diversity and fitness loss, as well as the ability to recover fitness after either a shift or expansion. We find that the speed of a shift has a strong impact on fitness evolution. Fastest shifts show the strongest fitness loss per generation, but intermediate shift speeds lead to the strongest fitness loss per geographic distance. Range shifting species lose fitness more slowly through time than expanding species, however, their fitness measured at equal geographic distances from the source of expansion can be considerably lower. These counter-intuitive results arise from the combination of time over which selection acts and mutations enter the system. Range shifts also exhibit reduced fitness recovery after a geographic shift and may result in extinction, whereas range expansions can persist from the core of the species range. The complexity of range expansions and range shifts highlights the potential for severe consequences of environmental change on species survival.

Fluctuations uncover a distinct class of traveling waves

Epidemics, flame propagation, and cardiac rhythms are classic examples of reaction-diffusion waves that describe a switch from one alternative state to another. Only two types of waves are known: pulled, driven by the leading edge, and pushed, driven by the bulk of the wave. Here, we report a distinct class of semipushed waves for which both the bulk and the leading edge contribute to the dynamics. These hybrid waves have the kinetics of pushed waves, but exhibit giant fluctuations similar to pulled waves. The transitions between pulled, semipushed, and fully pushed waves occur at universal ratios of the wave velocity to the Fisher velocity. We derive these results in the context of a species invading a new habitat by examining front diffusion, rate of diversity loss, and fluctuation-induced corrections to the expansion velocity. All three quantities decrease as a power law of the population density with the same exponent. We analytically calculate this exponent, taking into account the fluctuations in the shape of the wave front. For fully pushed waves, the exponent is -1, consistent with the central limit theorem. In semipushed waves, however, the fluctuations average out much more slowly, and the exponent approaches 0 toward the transition to pulled waves. As a result, a rapid loss of genetic diversity and large fluctuations in the position of the front occur, even for populations with cooperative growth and other forms of an Allee effect. The evolutionary outcome of spatial spreading in such populations could therefore be less predictable than previously thought.

Admixture on the northern front: population genomics of range expansion in the white-footed mouse (Peromyscus leucopus) and secondary contact with the deer mouse (Peromyscus maniculatus)

Range expansion has genetic consequences expected to result in differentiated wave-front populations with low genetic variation and potentially introgression from a local species. The northern expansion of Peromyscus leucopus in southern Quebec provides an opportunity to test these predictions using population genomic tools. Our results show evidence of recent and post-glacial expansion. Genome-wide variation in P. leucopus indicates two post-glacial lineages are separated by the St. Lawrence River, with a more recent divergence of populations isolated by the Richelieu River. In two of three transects we documented northern populations with low diversity in at least one genetic measure, although most relationships were not significant. Consistent with bottlenecks and allele surfing during northward expansion, we document a northern-most population with low nucleotide diversity, divergent allele frequencies and the most private alleles, and observed heterozygosity indicates outcrossing. Ancestry proportions revealed putative hybrids of P. leucopus and P. maniculatus. A formal test for gene flow confirmed secondary contact, showing that a reticulate population phylogeny between P. maniculatus and P. leucopus was a better fit to the data than a bifurcating model without gene flow. Thus, we provide the first genomic evidence of gene flow between this pair of species in natural populations. Understanding the evolutionary consequences of secondary contact is an important conservation concern as climate-induced range expansions are expected to result in new hybrid zones between closely related species.

On the role played by the carrying capacity and the ancestral population size during a range expansion

Most species are structured and various population genetics models have been proposed to investigate their history. For mathematical tractability, most of these models make the simplifying assumption of equilibrium. Here we focus on the properties of a nonequilibrium spatial explicit model, range expansions (REs). Despite their abundance, many details of their genetic consequences need yet to be fully investigated. The model we studied is characterized by four main parameters: the effective population size of each deme (N), the migration rate per generation per deme (m), the time of the expansion (T_exp) and the effective size of the deme from which the expansion started (N_anc). By means of extensive coalescent simulations, we focused on two aspects of range expansions for fixed Nm: (1) the separate influence of N and m and (2) the role of N_anc. We compared our results with an equilibrium stepping stone model and found two main features typical of REs: an excess of rare variants for larger N and a complex interaction between N, T_exp and N_anc in shaping the degree of population differentiation (which depends only on Nm in the stepping stone model). Finally, we developed an approximate Bayesian computation approach to jointly estimate N and m and to infer N_anc. When applied to pseudo-observed data sets, we could correctly recover both N and m (but not N_anc), provided a large number of demes were sampled. These findings highlight how it will be possible to estimate the dispersal rate in nonequilibrium metapopulations by using population genetics approaches.

Genetic signatures of a range expansion in natura: when clones play leapfrog

The genetic consequences of range expansions have generally been investigated at wide geographical and temporal scales, long after the colonization event. A unique ecological system enabled us to both monitor the colonization dynamics and decipher the genetic footprints of expansion over a very short time period. Each year an epidemic of the poplar rust (Melampsora larici‐populina) expands clonally and linearly along the Durance River, in the Alps. The colonization dynamics observed in 2004 showed two phases with different genetic outcomes. Upstream, fast colonization maintained high genetic diversity. Downstream, the colonization wave progressively faltered, diversity eroded, and differentiation increased, as expected under recurrent founder events. In line with the high dispersal abilities of rust pathogens, we provide evidence for leapfrog dispersal of clones. Our results thus emphasize the importance of colonization dynamics in shaping spatial genetic structure in the face of high gene flow.

Spatial genetic structure patterns of phenotype-limited and boundary-limited expanding populations: a simulation study

Range expansions may create a unique spatial genetic pattern characterized by alternate genetically homogeneous domains and allele frequency clines. Previous attempts to model range expansions have mainly focused on the loss of genetic diversity during expansions. Using individual-based models, we examined spatial genetic patterns under two expansion scenarios, boundary-limited range expansions (BLRE) and phenotype-limited range expansions (PhLRE). Our simulation revealed that the genetic diversity within populations lost quickly during the range expansion, while the genetic difference accumulated between populations. Consequently, accompanying the expansions, the overall diversity featured a slow decrease. Specifically, during BLREs, high speed of boundary motion facilitated the maintenance of total genetic diversity and sharpened genetic clines. Very slight constraints on boundary motion of BLREs drastically narrowed the homogeneous domains and increased the allele frequency fluctuations from those levels exhibited by PhLREs. Even stronger constraints, however, surprisingly brought the width of homogeneous domains and the allele frequency fluctuations back to the normal levels of PhLREs. Furthermore, high migration rates maintained a higher total genetic diversity than low ones did during PhLREs. Whereas, the total genetic diversities during BLREs showed a contrary pattern: higher when migration was low than those when migration was high. Besides, the increase of migration rates helped maintain a greater number of homogeneous domains during PhLREs, but their effects on the number of homogeneous domains during BLREs were not monotonous. Previous studies have showed that the homogenous domains can merge to form a few broad domains as the expansion went on, leading to fewer homogeneous domains. Our simulations, meanwhile, revealed that the range expansions could also rebuild homogeneous domains from the clines during the range expansion. It is possible that that the number of homogeneous domains was determined by the interaction of merging and newly emerging homogeneous domains.