LIFE AT THE FRONT OF AN EXPANDING POPULATION

Environmental changes have caused episodes of habitat expansions in the evolutionary history of many species. These range changes affect the dynamics of biological evolution in multiple ways. Recent microbial experiments as well as simulations 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 that explains these neutral patterns and predicts the effect of natural selection. We find that beneficial mutations give rise to sectors with an opening angle that depends 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 loaded with a 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.     

Deleterious mutations can surf to high densities on the wave front of an expanding population

There is an increasing recognition that evolutionary processes play a key role in determining the dynamics of range expansion. Recent work demonstrates that neutral mutations arising near the edge of a range expansion sometimes surf on the expanding front leading them rather than that leads to reach much greater spatial distribution and frequency than expected in stationary populations. Here, we extend this work and examine the surfing behavior of nonneutral mutations. Using an individual-based coupled-map lattice model, we confirm that, regardless of its fitness effects, the probability of survival of a new mutation depends strongly upon where it arises in relation to the expanding wave front. We demonstrate that the surfing effect can lead to deleterious mutations reaching high densities at an expanding front, even when they have substantial negative effects on fitness. Additionally, we highlight that this surfing phenomenon can occur for mutations that impact reproductive rate (i.e., number of offspring produced) as well as mutations that modify juvenile competitive ability. We suggest that these effects are likely to have important consequences for rates of spread and the evolution of spatially expanding populations.     

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 precise location dependence of surfing probabilities is derived from the non-extinction probability of a branching process within a moving field of growth rates. 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.     

The Fate of Cooperation during Range Expansions

Species expand their geographical ranges following an environmental change, long range dispersal, or a new adaptation. Range expansions not only bring an ecological change, but also affect the evolution of the expanding species. Although the dynamics of deleterious, neutral, and beneficial mutations have been extensively studied in expanding populations, the fate of alleles under frequency-dependent selection remains largely unexplored. The dynamics of cooperative alleles are particularly interesting because selection can be both frequency and density dependent, resulting in a coupling between population and evolutionary dynamics. This coupling leads to an increase in the frequency of cooperators at the expansion front, and, under certain conditions, the entire front can be taken over by cooperators. Thus, a mixed population wave can split into an expansion wave of only cooperators followed by an invasion wave of defectors. After the splitting, cooperators increase in abundance by expanding into new territories faster than they are invaded by defectors. Our results not only provide an explanation for the maintenance of cooperation but also elucidate the effect of eco-evolutionary feedback on the maintenance of genetic diversity during range expansions. When cooperators do not split away, we find that defectors can spread much faster with cooperators than they would be able to on their own or by invading cooperators. This enhanced rate of expansion in mixed waves could counterbalance the loss of genetic diversity due to the founder effect for mutations under frequency-dependent selection. Although we focus on cooperator-defector interactions, our analysis could also be relevant for other systems described by reaction-diffusion equations.     

Deleterious Passengers in Adapting Populations

Most new mutations are deleterious and are eventually eliminated by natural selection. But in an adapting population, the rapid amplification of beneficial mutations can hinder the removal of deleterious variants in nearby regions of the genome, altering the patterns of sequence evolution. Here, we analyze the interactions between beneficial “driver” mutations and linked deleterious “passengers” during the course of adaptation. We derive analytical expressions for the substitution rate of a deleterious mutation as a function of its fitness cost, as well as the reduction in the beneficial substitution rate due to the genetic load of the passengers. We find that the fate of each deleterious mutation varies dramatically with the rate and spectrum of beneficial mutations and the deleterious substitution rate depends nonmonotonically on the population size and the rate of adaptation. By quantifying this dependence, our results allow us to estimate which deleterious mutations will be likely to fix and how many of these mutations must arise before the progress of adaptation is significantly reduced.     

The fate of mutations surfing on the wave of a range expansion

Many species, including humans, have dramatically expanded their range in the past, and such range expansions had certainly an impact on their genetic diversity. For example, mutations arising in populations at the edge of a range expansion can sometimes surf on the wave of advance and thus reach a larger spatial distribution and a much higher frequency than would be expected in stationary populations. We study here this surfing phenomenon in more detail, by performing extensive computer simulations under a two-dimensional stepping-stone model. We find that the probability of survival of a new mutation depends to a large degree on its proximity to the edge of the wave. Demographic factors such as deme size, migration rate, and local growth rate also influence the fate of these new mutations. We also find that the final spatial and frequency distributions depend on the local deme size of a subdivided population. This latter result is discussed in the light of human expansions in Europe as it should allow one to distinguish between mutations having spread with Paleolithic or Neolithic expansions. By favoring the spread of new mutations, a consequence of the surfing phenomenon is to increase the rate of evolution of spatially expanding populations.     

Surfing downhill: when should population range expansion be characterized by reductions in fitness?

Deleterious mutations are found in all populations. Their existence at low frequencies is easily understood, but explaining how they reach high frequencies has long been a challenging problem for population geneticists and evolutionary biologists. Some cases of apparently deleterious alleles are explained by pleiotropy or environmental context dependence, but for universally deleterious alleles, two mechanisms are generally invoked to explain how they can reach high frequencies: (i) genetic drift in small populations and (ii) ‘hitchhiking’ (sensu Maynard Smith J, Haigh J, Genetical Research, 1974, 23, 23–35) involving tight linkage to beneficial mutations. However, these oft‐cited explanations do not immediately resolve the problem because many real populations of interest have population sizes and recombination rates that are large enough to render it nearly impossible for all but the most weakly deleterious (i.e. nearly neutral) mutations to establish and persist. Furthermore, both mechanisms are usually silent about patterns of intraspecific variation in mutation load. In this issue, Peischl S, Dupanloup I, Kirkpatrick M, Excoffier L (Molecular Ecology, 2013) develop and explore a mechanism that puts drift and hitchhiking of deleterious mutations into a specific spatial and demographic context: range expansions. Importantly, their findings provide a plausible explanation for puzzling empirical patterns, such as the paradoxical observation that genotypes at the leading edge of a range expansion are sometimes less fit than those in the ancestral range (when fitness is assessed in a common environment).     

The frequency of fitness peak shifts is increased at expanding range margins due to mutation surfing

Dynamic species' ranges, those that are either invasive or shifting in response to environmental change, are the focus of much recent interest in ecology, evolution, and genetics. Understanding how range expansions can shape evolutionary trajectories requires the consideration of nonneutral variability and genetic architecture, yet the majority of empirical and theoretical work to date has explored patterns of neutral variability. Here we use forward computer simulations of population growth, dispersal, and mutation to explore how range-shifting dynamics can influence evolution on rugged fitness landscapes. We employ a two-locus model, incorporating sign epistasis, and find that there is an increased likelihood of fitness peak shifts during a period of range expansion. Maladapted valley genotypes can accumulate at an expanding range front through a phenomenon called mutation surfing, which increases the likelihood that a mutation leading to a higher peak will occur. Our results indicate that most peak shifts occur close to the expanding front. We also demonstrate that periods of range shifting are especially important for peak shifting in species with narrow geographic distributions. Our results imply that trajectories on rugged fitness landscapes can be modified substantially when ranges are dynamic.     

A resolution of the mutation load paradox in humans

Current information on the rate of mutation and the fraction of sites in the genome that are subject to selection suggests that each human has received, on average, at least two new harmful mutations from its parents. These mutations were subsequently removed by natural selection through reduced survival or fertility. It has been argued that the mutation load, the proportional reduction in population mean fitness relative to the fitness of an idealized mutation-free individual, allows a theoretical prediction of the proportion of individuals in the population that fail to reproduce as a consequence of these harmful mutations. Application of this theory to humans implies that at least 88% of individuals should fail to reproduce and that each female would need to have more than 16 offspring to maintain population size. This prediction is clearly at odds with the low reproductive excess of human populations. Here, we derive expressions for the fraction of individuals that fail to reproduce as a consequence of recurrent deleterious mutation () for a model in which selection occurs via differences in relative fitness, such as would occur through competition between individuals. We show that is much smaller than the value predicted by comparing fitness to that of a mutation-free genotype. Under the relative fitness model, we show that depends jointly on U and the selective effects of new deleterious mutations and that a species could tolerate 10's or even 100's of new deleterious mutations per genome each generation.     

Compensating for our load of mutations: freezing the meltdown of small populations

We have investigated the reduction of fitness caused by the fixation of new deleterious mutations in small populations within the framework of Fisher's geometrical model of adaptation. In Fisher's model, a population evolves in an n-dimensional character space with an adaptive optimum at the origin. The model allows us to investigate compensatory mutations, which restore fitness losses incurred by other mutations, in a context-dependent manner. We have conducted a moment analysis of the model, supplemented by the numerical results of computer simulations. The mean reduction of fitness (i.e., expected load) scaled to one is approximately n/(n+2Ne), where Ne is the effective population size. The reciprocal relationship between the load and Ne implies that the fixation of deleterious mutations is unlikely to cause extinction when there is a broad scope for compensatory mutations, except in very small populations. Furthermore, the dependence of load on n implies that pleiotropy plays a large role in determining the extinction risk of small populations. Differences and similarities between our results and those of a previous study on the effects of Ne and n are explored. That the predictions of this model are qualitatively different from studies ignoring compensatory mutations implies that we must be cautious in predicting the evolutionary fate of small populations and that additional data on the nature of mutations is of critical importance.     

PURGING THE GENOME WITH SEXUAL SELECTION: REDUCING MUTATION LOAD THROUGH SELECTION ON MALES

Healthy males are likely to have higher mating success than unhealthy males because of differential expression of condition‐dependent traits such as mate searching intensity, fighting ability, display vigor, and some types of exaggerated morphological characters. We therefore expect that most new mutations that are deleterious for overall fitness may also be deleterious for male mating success. From this perspective, sexual selection is not limited to influencing those genes directly involved in exaggerated morphological traits but rather affects most, if not all, genes in the genome. If true, sexual selection can be an important force acting to reduce the frequency of deleterious mutations and, as a result, mutation load. We review the literature and find various forms of indirect evidence that sexual selection helps to eliminate deleterious mutations. However, direct evidence is scant, and there are almost no data available to address a key issue: is selection in males stronger than selection in females? In addition, the total effect of sexual selection on mutation load is complicated by possible increases in mutation rate that may be attributable to sexual selection. Finally, sexual selection affects population fitness not only through mutation load but also through sexual conflict, making it difficult to empirically measure how sexual selection affects load. Several lines of enquiry are suggested to better fill large gaps in our understanding of sexual selection and its effect on genetic load.     

Lethal mutagenesis and evolutionary epidemiology

The lethal mutagenesis hypothesis states that within-host populations of pathogens can be driven to extinction when the load of deleterious mutations is artificially increased with a mutagen, and becomes too high for the population to be maintained. Although chemical mutagens have been shown to lead to important reductions in viral titres for a wide variety of RNA viruses, the theoretical underpinnings of this process are still not clearly established. A few recent models sought to describe lethal mutagenesis but they often relied on restrictive assumptions. We extend this earlier work in two novel directions. First, we derive the dynamics of the genetic load in a multivariate Gaussian fitness landscape akin to classical quantitative genetics models. This fitness landscape yields a continuous distribution of mutation effects on fitness, ranging from deleterious to beneficial (i.e. compensatory) mutations. We also include an additional class of lethal mutations. Second, we couple this evolutionary model with an epidemiological model accounting for the within-host dynamics of the pathogen. We derive the epidemiological and evolutionary equilibrium of the system. At this equilibrium, the density of the pathogen is expected to decrease linearly with the genomic mutation rate U. We also provide a simple expression for the critical mutation rate leading to extinction. Stochastic simulations show that these predictions are accurate for a broad range of parameter values. As they depend on a small set of measurable epidemiological and evolutionary parameters, we used available information on several viruses to make quantitative and testable predictions on critical mutation rates. In the light of this model, we discuss the feasibility of lethal mutagenesis as an efficient therapeutic strategy.     

Mutation accumulation and the formation of range limits

The dynamics of range formation are important for understanding and predicting species distributions. Here, we focus on a process that has thus far been overlooked in the context of range formation; the accumulation of mutation load. We find that mutation accumulation severely reduces the extent of a range across an environmental gradient, especially when dispersal is limited, growth rate is low and mutations are of intermediate deleterious effect. Our results illustrate the important role deleterious mutations can play in range formation. We highlight this as a necessary focus for further work, noting particularly the potentially conflicting effects dispersal may have in reducing mutation load and simultaneously increasing migration load in marginal populations.     

Bottlenecks in large populations: the effect of immigration on population viability

We model a large population that is subject to successive short bottlenecks, in order to investigate the impact of different extents of immigration on the change in genetic load and on viability. A first simple genetic model uncovers the opposite effects of immigration on fitness according to the type of deleterious mutations considered: immigration increases fitness if the genetic load is comprised of mildly deleterious mutations, whereas it decreases fitness if it is comprised of lethals. When considering both types of mutations and adding explicit stochastic demographic considerations, in which bottlenecks are engendered by random catastrophes, the global impact of immigration on viability is dependent upon a balance between its opposite effects on the two components of the genetic load and on demographic stochasticity. In this context, immigration tends to increase the probability of extinction if occurring preferentially when population density is high, while it decreases extinction if occurring preferentially towards low-density populations.     

Mistranslation Reduces Mutation Load in Evolving Proteins through Negative Epistasis with DNA Mutations

Translational errors during protein synthesis cause phenotypic mutations that are several orders of magnitude more frequent than DNA mutations. Such phenotypic mutations may affect adaptive evolution through their interactions with DNA mutations. To study how mistranslation may affect the adaptive evolution of evolving proteins, we evolved populations of green fluorescent protein (GFP) in either high-mistranslation or low-mistranslation Escherichia coli hosts. In both hosts, we first evolved GFP under purifying selection for the ancestral phenotype green fluorescence, and then under directional selection toward the new phenotype yellow fluorescence. High-mistranslation populations evolved modestly higher yellow fluorescence during each generation of evolution than low-mistranslation populations. We demonstrate by high-throughput sequencing that elevated mistranslation reduced the accumulation of deleterious DNA mutations under both purifying and directional selection. It did so by amplifying the fitness effects of deleterious DNA mutations through negative epistasis with phenotypic mutations. In contrast, mistranslation did not affect the incidence of beneficial mutations. Our findings show that phenotypic mutations interact epistatically with DNA mutations. By reducing a population’s mutation load, mistranslation can affect an important determinant of evolvability.     

Accelerating invasion rates result from the evolution of density-dependent dispersal

Evolutionary processes play an important role in shaping the dynamics of range expansions, and selection on dispersal propensity has been demonstrated to accelerate rates of advance. Previous theory has considered only the evolution of unconditional dispersal rates, but dispersal is often more complex. For example, many species emigrate in response to crowding. Here, we use an individual-based model to investigate the evolution of density dependent dispersal into empty habitat, such as during an invasion. The landscape is represented as a lattice and dispersal between populations follows a stepping-stone pattern. Individuals carry three ‘genes’ that determine their dispersal strategy when experiencing different population densities. For a stationary range we obtain results consistent with previous theoretical studies: few individuals emigrate from patches that are below equilibrium density. However, during the range expansion of a previously stationary population, we observe evolution towards dispersal strategies where considerable emigration occurs well below equilibrium density. This is true even for moderate costs to dispersal, and always results in accelerating rates of range expansion. Importantly, the evolution we observe at an expanding front depends upon fitness integrated over several generations and cannot be predicted by a consideration of lifetime reproductive success alone. We argue that a better understanding of the role of density dependent dispersal, and its evolution, in driving population dynamics is required especially within the context of range expansions.     

The impact of habitat fragmentation on fitness‐related traits in a native prairie plant,Chamaecrista fasciculata (Fabaceae)

Loss and fragmentation of the native prairies in the Midwestern United States have resulted in isolated and smaller habitats and populations. The populations remaining in these prairies are expected to show a decline in the extent of genetic variation and an increase in genetic drift load (accumulation of deleterious recessive alleles due to genetic drift) in fitness‐related traits. Using complementary greenhouse experiments, we tested whether these expected changes have occurred in the native annual prairie plant Chamaecrista fasciculata. In the first experiment, open pollinated C. fasciculata seeds from 12 prairie fragments representing a range in area of habitat were grown in competition with Schizachyrium scoparium to determine if there are changes in plant vigour with changes in fragment size and corresponding changes in population size. Plants from smaller prairie fragments exhibited a slight but significant decline in biomass, suggesting an increase in genetic drift load. In the second experiment, a formal genetic crossing design of four prairie fragment populations was used to estimate quantitative genetic diversity and genetic drift load. We did not find extensive quantitative genetic variation, but we did find a strong effect of genetic drift load on five traits in this experiment. Our overall conclusion is that a decline in relative‐fitness traits in smaller prairie fragments is probably associated with fixation of deleterious alleles due to more isolated and smaller populations, i.e. genetic drift load. © 2012 The Linnean Society of London, Biological Journal of the Linnean Society, 2012, ?? , ??–??.     

The evolution of sex chromosomes in organisms with separate haploid sexes

The evolution of dimorphic sex chromosomes is driven largely by the evolution of reduced recombination and the subsequent accumulation of deleterious mutations. Although these processes are increasingly well understood in diploid organisms, the evolution of dimorphic sex chromosomes in haploid organisms (U/V) has been virtually unstudied theoretically. We analyze a model to investigate the evolution of linkage between fitness loci and the sex‐determining region in U/V species. In a second step, we test how prone nonrecombining regions are to degeneration due to accumulation of deleterious mutations. Our modeling predicts that the decay of recombination on the sex chromosomes and the addition of strata via fusions will be just as much a part of the evolution of haploid sex chromosomes as in diploid sex chromosome systems. Reduced recombination is broadly favored, as long as there is some fitness difference between haploid males and females. The degeneration of the sex‐determining region due to the accumulation of deleterious mutations is expected to be slower in haploid organisms because of the absence of masking. Nevertheless, balancing selection often drives greater differentiation between the U/V sex chromosomes than in X/Y and Z/W systems. We summarize empirical evidence for haploid sex chromosome evolution and discuss our predictions in light of these findings.