Competition between random genetic drift and natural selection play a central role in evolution: Whereas nonbeneficial 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.genetic distance ͉ founder effect ͉ microorganisms ͉ range expansion A principal tenet of modern evolutionary biology is that Darwinian selection and random genetic drift compete in driving evolutionary change (1). It is widely accepted that genetic drift can have significant effects on small populations (2) that may even lead to speciation (3). In large populations, however, random sampling effects are generally considered weak compared with selection (4-6) (law of large numbers). A major departure from this paradigmatic behavior occurs when large populations undergo range expansions. The descendents of individuals first settling in a new territory are most likely to dominate the gene pool as the expansion progresses (7-9). Random sampling effects among these pioneers results in genetic drift that can have profound consequences on the diversity of the expanding population. Indeed, spatially varying levels of genetic diversity and colonization patterns appear to be correlated in many species (10-13). For example, the often observed south-north gradient in neutral genetic diversity [''southern richness to northern purity'' (14)] on the northern hemisphere is thought to reflect past range expansions induced by glacial cycles (12). Although these trends indicate that genetic drift during range expansions has shaped the gene pool of many species, the underlying spatial mechanism remains obscure: Diversity gradients are often difficult to interpret and potentially interfere with the signal of spreading beneficial mutations (15,16). In fact, a major challenge of present-day population genetics is to decide whether natural selection or a past demographic process is responsible for the prevalence of common mutations (17).Here, we use simple microbial systems to study the nature of random genetic drift in range expansions of large populations. We observe chance effects that segregate the gene pool into well defined, sector-like regions of reduced genetic diversity. The genetic segregation on the population level is the consequence of number fluctuations on a much smaller scale, within a thin region of reproducing p...

Loss of sexual reproduction is considered an evolutionary dead end for metazoans, but bdelloid rotifers challenge this view as they appear to have persisted asexually for millions of years 1 . Neither male sex organs nor meiosis have ever been observed in these microscopic animals: oocytes are formed through mitotic divisions, with no reduction of chromosome number and no indication of chromosome pairing 2 . However, current evidence does not exclude that they may engage in sex on rare, cryptic occasions. Here we report the genome of a bdelloid rotifer, Adineta vaga (Davis, 1873) 3 , and show that its structure is incompatible with conventional meiosis. At gene scale, the genome of A. vaga is tetraploid and comprises both anciently duplicated segments and less divergent allelic regions. However, in contrast to sexual species, the allelic regions are rearranged and sometimes even found on the same chromosome. Such structure does not allow meiotic pairing; instead, we find abundant evidence of gene conversion, which may limit the accumulation of deleterious mutations in the absence of meiosis. Gene families involved in resistance to oxidation, carbohydrate metabolism and defence against transposons are significantly expanded, which may explain why transposable elements cover only 3% of the assembled sequence. Furthermore, 8% of the genes are likely to be of non-metazoan origin and were probably acquired horizontally. This apparent convergence between bdelloids and prokaryotes sheds new light on the evolutionary significance of sex.With more than 460 described species 4 , bdelloid rotifers ( Fig. 1) represent the highest metazoan taxonomic rank in which males, hermaphrodites and meiosis are unknown. Such persistence and diversification of an ameiotic clade of animals are in contradiction with the supposed long-term disadvantages of asexuality, making bdelloids an 'evolutionary scandal' 5 . Another unusual feature of bdelloid rotifers is their extreme resistance to desiccation at any stage of their life cycle 6 , enabling these microscopic animals to dwell in ephemeral freshwater habitats such as mosses, lichens and forest litter; this ability is presumably the source of their extreme resistance to ionizing radiation 7 .We assembled the genome of a clonal A. vaga lineage into separate haplotypes with a N 50 of 260 kilobases (kb) (that is, half of the assembly was composed of fragments longer than 260 kb). Assembly size was 218 megabases (Mb) but 26 Mb of the sequence had twice the average sequencing coverage, suggesting that some nearly identical regions were not resolved during assembly ( Supplementary Fig. 3); hence, the total genome size is likely to be 244 Mb, which corresponds to the estimate obtained independently using fluorometry (Supplementary Note C2). Annotation of the complete assembly (including all haplotypes) yielded 49,300 genes. Intragenomic sequence comparisons revealed numerous homologous blocks with conserved gene order (colinear regions). For each such block we computed the per-site synonymous d...

Spatially resolved genetic data is increasingly used to reconstruct the migrational history of species. To assist such inference, we study, by means of simulations and analytical methods, the dynamics of neutral gene frequencies in a population undergoing a continual range expansion in one dimension. During such a colonization period, lineages can fix at the wave front by means of a "surfing" mechanism [Edmonds C.A., Lillie A.S. & Cavalli-Sforza L.L. (2004) Proc Natl Acad Sci USA 101: 975-979]. We quantify this phenomenon in terms of (i) the spatial distribution of lineages that reach fixation and, closely related, (ii) the continual loss of genetic diversity (heterozygosity) at the wave front, characterizing the approach to fixation. Our simulations show that an effective population size can be assigned to the wave that controls the (observable) gradient in heterozygosity left behind the colonization process. This effective population size is markedly higher in pushed waves than in pulled waves, and increases only sub-linearly with deme size. To explain these and other findings, we develop a versatile analytical approach, based on the physics of reaction-diffusion systems, that yields simple predictions for any deterministic population dynamics.Population expansions in space are common events in the evolutionary history of many species [1,2,3,4,5,6,7] and have a profound effect on their genealogy. It is widely appreciated that any range expansion leads to a reduction of genetic diversity ("Founder Effect") because the gene pool for the new habitat is provided only by a small number of individuals, which happen to arrive in the unexplored territory first. In many species, the genetic footprints of these pioneers are still recognizable today and provide information about the migrational history of the species. For instance, a frequently observed south-north gradient in genetic diversity ("southern richness to northern purity" [8]) on the northern hemisphere is thought to reflect the range expansions induced by the glacial cycles. In the case of humans, the genetic diversity decreases essentially linearly with increasing geographic distance from Africa [2,3], which is indicative of the human migration out of Africa. It is hoped [9], that the observed patterns of neutral genetic diversity can be used to infer details of the corresponding colonization pathways.Such an inference requires an understanding of how a colonization process generates a gradient in genetic diversity, and which parameters chiefly control the magnitude of this gradient. Traditional models of population genetics [10], which mainly focus on populations of constant size and distribution, apply to periods before and after a range expansion has occurred, when the population is at demographic equilibrium. However, the spatio-temporal dynamics in the transition period, on which we focus in this article, is less amenable to the standard analytical tools of population genetics, and has been so far studied mostly by means of simulations [11,12,13,14,15...

Results for mutation, selection, genetic drift, and migration in a one-dimensional continuous population are reviewed and extended. The population is described by a continuous limit of the stepping stone model, which leads to the stochastic Fisher-Kolmogorov-Petrovsky-Piscounov equation with additional terms describing mutations. Although the stepping stone model was first proposed for population genetics, it is closely related to "voter models" of interest in nonequilibrium statistical mechanics. The stepping stone model can also be regarded as an approximation to the dynamics of a thin layer of actively growing pioneers at the frontier of a colony of micro-organisms undergoing a range expansion on a Petri dish. The population tends to segregate into monoallelic domains. This segregation slows down genetic drift and selection because these two evolutionary forces can only act at the boundaries between the domains; the effects of mutation, however, are not significantly affected by the segregation. Although fixation in the neutral well-mixed (or "zerodimensional") model occurs exponentially in time, it occurs only algebraically fast in the onedimensional model. An unusual sublinear increase is also found in the variance of the spatially averaged allele frequency with time. If selection is weak, selective sweeps occur exponentially fast in both well-mixed and one-dimensional populations, but the time constants are different. The relatively unexplored problem of evolutionary dynamics at the edge of an expanding circular colony is studied as well. Also reviewed are how the observed patterns of genetic diversity can be used for statistical inference and the differences are highlighted between the well-mixed and one-dimensional models. Although the focus is on two alleles or variants, q-allele Potts-like models of gene segregation are considered as well. Most of the analytical results are checked with simulations and could be tested against recent spatial experiments on range expansions of inoculations of Escherichia coli and Saccharomyces cerevisiae.

When large asexual populations adapt, competition between simultaneously segregating mutations slows the rate of adaptation and restricts the set of mutations that eventually fix. This phenomenon of interference arises from competition between mutations of different strengths as well as competition between mutations that arise on different fitness backgrounds. Previous work has explored each of these effects in isolation, but the way they combine to influence the dynamics of adaptation remains largely unknown. Here, we describe a theoretical model to treat both aspects of interference in large populations. We calculate the rate of adaptation and the distribution of fixed mutational effects accumulated by the population. We focus particular attention on the case when the effects of beneficial mutations are exponentially distributed, as well as on a more general class of exponential-like distributions. In both cases, we show that the rate of adaptation and the influence of genetic background on the fixation of new mutants is equivalent to an effective model with a single selection coefficient and rescaled mutation rate, and we explicitly calculate these effective parameters. We find that the effective selection coefficient exactly coincides with the most common fixed mutational effect. This equivalence leads to an intuitive picture of the relative importance of different types of interference effects, which can shift dramatically as a function of the population size, mutation rate, and the underlying distribution of fitness effects.E volutionary adaptation is driven by the accumulation of beneficial mutations, and yet many aspects of this process are still poorly understood. In asexual populations, this subject can be distilled into two main lines of inquiry: (i) what are the possible mutations available to the population? and (ii) which of these mutations are actually incorporated into the population, and what are the dynamics by which they fix?The first question is essentially an empirical matter. At any given instant in time, the set of accessible beneficial mutations is likely to depend on the history of the population as well as its environment and any epistatic interactions between mutations. Nonetheless, if history and epistatic effects do not significantly affect the statistics of the available mutations, we can define a constant distribution of fitness effects ρðsÞ that gives the relative probability of obtaining a mutation that increases the fitness of an individual by s.Gillespie (1) and Orr (2) have argued that there are general theoretical reasons to expect that ρðsÞ should follow an exponential distribution, although more recent theoretical work has challenged the ubiquity of this claim (3). Many experimental studies are roughly consistent with this exponential prediction (4-6), although here, too, we find significant exceptions (6-10). In the present work, we maintain a relatively agnostic view toward the precise form of ρðsÞ, although we devote special attention to the exponential case because of i...

Gut microbiota are shaped by a combination of ecological and evolutionary forces. While the ecological dynamics have been extensively studied, much less is known about how species of gut bacteria evolve over time. Here, we introduce a model-based framework for quantifying evolutionary dynamics within and across hosts using a panel of metagenomic samples. We use this approach to study evolution in approximately 40 prevalent species in the human gut. Although the patterns of between-host diversity are consistent with quasi-sexual evolution and purifying selection on long timescales, we identify new genealogical signatures that challenge standard population genetic models of these processes. Within hosts, we find that genetic differences that accumulate over 6-month timescales are only rarely attributable to replacement by distantly related strains. Instead, the resident strains more commonly acquire a smaller number of putative evolutionary changes, in which nucleotide variants or gene gains or losses rapidly sweep to high frequency. By comparing these mutations with the typical between-host differences, we find evidence that some sweeps may be seeded by recombination, in addition to new mutations. However, comparisons of adult twins suggest that replacement eventually overwhelms evolution over multi-decade timescales, hinting at fundamental limits to the extent of local adaptation. Together, our results suggest that gut bacteria can evolve on human-relevant timescales, and they highlight the connections between these short-term evolutionary dynamics and longer-term evolution across hosts.

The evolutionary history of many species exhibits episodes of habitat expansions and contractions, often caused by environmental changes, such as glacial cycles. These range changes affect the dynamics of biological evolution in multiple ways. Recent microbial experiments suggest that enhanced genetic drift at the frontier of a two-dimensional range expansion can cause genetic sectoring patterns with fractal domain boundaries.Here, we propose and analyze a simple model of asexual biological evolution at expanding frontiers to explain these neutral patterns and predict the effect of natural selection. Our model attributes the observed gradual decrease in the number of sectors at the leading edge to an unbiased random walk of sector boundaries. The long time sectoring pattern depends on the geometry of the frontier. Whereas planar fronts are ultimately dominated by only one sector, circular colonies permit the coexistence of multiple sectors, whose number is proportional, in the simplest case, to the square root of the radius of the initial habitat. Natural selection introduces a deterministic bias in 1 present address: MPI for Dynamics and Self-Organization, Bunsenstr. 10, 37073 Göttingen, Germany, phone:+49-551-5176-670, fax: +49-551-5176-669 -2 -the wandering of domain boundaries that renders beneficial mutations more likely to escape genetic drift and become established in a sector. We find that the opening angle of those sectors and the rate at which they become established depend sensitively on the selective advantage of the mutants. Deleterious mutations, on the other hand, are not able to establish a sector permanently. They can, however, temporarily "surf" on the population front, and thereby reach unusually high frequencies. As a consequence, expanding frontiers are susceptible to deleterious mutations as revealed by the high fraction of mutants at mutation-selection balance. Numerically, we also determine the condition at which the wild type is lost in favor of deleterious mutants (genetic meltdown) at a growing front. Our prediction for this error threshold differs qualitatively from existing well-mixed theories, and sets tight constraints on sustainable mutation rates for populations that undergo frequent range expansions. IntroductionPopulation expansions in space are common events in the evolutionary history of many species (Cavalli-Sforza et al. 1993;Hewitt 2000;Templeton 2002;Rosenberg et al. 2003;Ramachandran et al. 2005;Phillips et al. 2006;, ranging from biofilms to humans. Species expand from where they first evolved, invade into favorable habitats, or move in response to environmental changes, such as the recent climate warming, glacial cycles, or gradients in nutrients, salinity, ambient temperature, etc., in the case of biofilms. Some species undergo range expansions rarely, because environments change slowly, others like epidemic pathogens do so frequently as part of their ecology.These range expansions cause strong differences between the genetic diversity of the ancestral and the...

The synchronization of coupled oscillators is a fascinating manifestation of self-organization that nature uses to orchestrate essential processes of life, such as the beating of the heart. Although it was long thought that synchrony and disorder were mutually exclusive steady states for a network of identical oscillators, numerous theoretical studies in recent years have revealed the intriguing possibility of "chimera states," in which the symmetry of the oscillator population is broken into a synchronous part and an asynchronous part. However, a striking lack of empirical evidence raises the question of whether chimeras are indeed characteristic of natural systems. This calls for a palpable realization of chimera states without any fine-tuning, from which physical mechanisms underlying their emergence can be uncovered. Here, we devise a simple experiment with mechanical oscillators coupled in a hierarchical network to show that chimeras emerge naturally from a competition between two antagonistic synchronization patterns. We identify a wide spectrum of complex states, encompassing and extending the set of previously described chimeras. Our mathematical model shows that the self-organization observed in our experiments is controlled by elementary dynamical equations from mechanics that are ubiquitous in many natural and technological systems. The symmetry-breaking mechanism revealed by our experiments may thus be prevalent in systems exhibiting collective behavior, such as power grids, optomechanical crystals, or cells communicating via quorum sensing in microbial populations.ensemble dynamics | statistical physics | nonlinear dynamics