Genealogies of rapidly adapting populations

The genetic diversity of a species is shaped by its recent evolutionary history and can be used to infer demographic events or selective sweeps. Most inference methods are based on the null hypothesis that natural selection is a weak or infrequent evolutionary force. However, many species, particularly pathogens, are under continuous pressure to adapt in response to changing environments. A statistical framework for inference from diversity data of such populations is currently lacking. Toward this goal, we explore the properties of genealogies in a model of continual adaptation in asexual populations. We show that lineages trace back to a small pool of highly fit ancestors, in which almost simultaneous coalescence of more than two lineages frequently occurs. While such multiple mergers are unlikely under the neutral coalescent, they create a unique genetic footprint in adapting populations. The site frequency spectrum of derived neutral alleles, for example, is non-monotonic and has a peak at high frequencies, whereas Tajima's D becomes more and more negative with increasing sample size. Since multiple merger coalescents emerge in many models of rapid adaptation, we argue that they should be considered as a null-model for adapting populations.Comment: to appear in PNA

The rate of beneficial mutations surfing on the wave of a range expansion

Many theoretical and experimental studies suggest that range expansions can have severe consequences for the gene pool of the expanding population. Due to strongly enhanced genetic drift at the advancing frontier, neutral and weakly deleterious mutations can reach large frequencies in the newly colonized regions, as if they were surfing the front of the range expansion. These findings raise the question of how frequently beneficial mutations successfully surf at shifting range margins, thereby promoting adaptation towards a range-expansion phenotype. Here, we use individual-based simulations to study the surfing statistics of recurrent beneficial mutations on wave-like range expansions in linear habitats. We show that the rate of surfing depends on two strongly antagonistic factors, the probability of surfing given the spatial location of a novel mutation and the rate of occurrence of mutations at that location. The surfing probability strongly increases towards the tip of the wave. Novel mutations are unlikely to surf unless they enjoy a spatial head start compared to the bulk of the population. The needed head start is shown to be proportional to the inverse fitness of the mutant type, and only weakly dependent on the carrying capacity. The second factor is the mutation occurrence which strongly decreases towards the tip of the wave. Thus, most successful mutations arise at an intermediate position in the front of the wave. We present an analytic theory for the tradeoff between these factors that allows to predict how frequently substitutions by beneficial mutations occur at invasion fronts. We find that small amounts of genetic drift increase the fixation rate of beneficial mutations at the advancing front, and thus could be important for adaptation during species invasions.Comment: 21 pages, 7 figures; to appear in PLoS Computational Biolog

Genetic drift at expanding frontiers promotes gene segregation

Competition between random genetic drift and natural selection plays a central role in evolution: Whereas non-beneficial mutations often prevail in small populations by chance, mutations that sweep through large populations typically confer a selective advantage. Here, however, we observe chance effects during range expansions that dramatically alter the gene pool even in large microbial populations. Initially well-mixed populations of two fluorescently labeled strains of Escherichia coli develop well-defined, sector-like regions with fractal boundaries in expanding colonies. The formation of these regions is driven by random fluctuations that originate in a thin band of pioneers at the expanding frontier. A comparison of bacterial and yeast colonies (Saccharomyces cerevisiae) suggests that this large-scale genetic sectoring is a generic phenomenon that may provide a detectable footprint of past range expansions.Comment: Please visit http://www.pnas.org/content/104/50/19926.abstract for published articl

Population dynamics in compressible flows

Organisms often grow, migrate and compete in liquid environments, as well as on solid surfaces. However, relatively little is known about what happens when competing species are mixed and compressed by fluid turbulence. In these lectures we review our recent work on population dynamics and population genetics in compressible velocity fields of one and two dimensions. We discuss why compressible turbulence is relevant for population dynamics in the ocean and we consider cases both where the velocity field is turbulent and when it is static. Furthermore, we investigate populations in terms of a continuos density field and when the populations are treated via discrete particles. In the last case we focus on the competition and fixation of one species compared to anotherComment: 16 pages, talk delivered at the Geilo Winter School 201

Mechanically driven growth of quasi-two dimensional microbial colonies

We study colonies of non-motile, rod-shaped bacteria growing on solid substrates. In our model, bacteria interact purely mechanically, by pushing each other away as they grow, and consume a diffusing nutrient. We show that mechanical interactions control the velocity and shape of the advancing front, which leads to features that cannot be captured by established Fisher-Kolmogorov models. In particular, we find that the velocity depends on the elastic modulus of bacteria or their stickiness to the surface. Interestingly, we predict that the radius of an incompressible, strictly two-dimensional colony cannot grow linearly in time. Importantly, mechanical interactions can also account for the nonequilibrium transition between circular and branching colonies, often observed in the lab.Comment: 5 pages, 4 colour figure

Dynamic structure factor of a stiff polymer in a glassy solution

We provide a comprehensive overview of the current theoretical understanding of the dynamic structure factor of stiff polymers in semidilute solution based on the wormlike chain (WLC) model. We extend previous work by computing exact numerical coefficients and an expression for the dynamic mean square displacement (MSD) of a free polymer and compare various common approximations for the hydrodynamic interactions, which need to be treated accurately if one wants to extract quantitative estimates for model parameters from experimental data. A recent controversy about the initial slope of the dynamic structure factor is thereby resolved. To account for the interactions of the polymer with a surrounding (sticky) polymer solution, we analyze an extension of the WLC model, the glassy wormlike chain (GWLC), which predicts near power-law and logarithmic long-time tails in the dynamic structure factor.Comment: 14 pages, 5 figures, final versio

A simple mathematical model of gradual Darwinian evolution: Emergence of a Gaussian trait distribution in adaptation along a fitness gradient

We consider a simple mathematical model of gradual Darwinian evolution in continuous time and continuous trait space, due to intraspecific competition for common resource in an asexually reproducing population in constant environment, while far from evolutionary stable equilibrium. The model admits exact analytical solution. In particular, Gaussian distribution of the trait emerges from generic initial conditions.Comment: 21 pages, 2 figures, as accepted to J Math Biol 2013/03/1