VARIANCE-INDUCED PEAK SHIFTS

The increase in phenotypic variance that occurs in some populations as a result of bottlenecks and founder events can cause a dramatic increase in the probability of a peak shift from one adaptive state to another. Periods of small population size allow drift in the amount of phenotypic variance. Increases in phenotypic variance, coupled with a constant individual fitness function with multiple peaks, can cause the mean fitness landscape to change from bimodal to unimodal, thereby allowing the population's mean phenotype to change deterministically by selection. As the amount of phenotypic variance is returned to an equilibrium state, the multiple peaks reemerge, but the population has moved from one stable state to another. These variance-induced peak shifts allow punctuational evolution from one peak to another at a rate that can be much higher than that predicted by Wright's shifting-balance process alone.     

THE PROBABILITY OF PEAK SHIFTS IN A FOUNDER POPULATION. II. AN ADDITIVE POLYGENIC TRAIT

Stochastic shifts between two alternative stable equilibria in an additive polygenic system are modelled. The effect of selection on the character is represented by a double-peaked function relating individual fitness to phenotypic value. The mean of a large population will equilibrate near one of the two peaks, although with weak selection there may be a substantial displacement from the closest peak, due to the attraction exerted by the other peak. It is assumed that a small population is founded as a random sample from a large population at equilibrium under selection, and that genetic drift and selection interact to determine the evolution of the mean and variance of the polygenic character during the phase of exponential population growth that follows the foundation of the population. The effects on the frequencies of peak shifts of selectively induced linkage disequilibrium, randomly induced linkage disequilibrium, and random deviations from Hardy-Weinberg equilibrium are investigated by computer simulation. The results are compared with the probabilities of shifts calculated by an approximate analytic method. It is found that the approximations are reasonably accurate when the heights of the peaks in fitness are similar, but the approximations fail when one of the peaks is much higher than the other. The probability of a peak shift is shown to be a decreasing function of the strength of selection on the character. Although substantial changes in phenotypic mean can be induced by a founder event, the probability of a peak shift that induces a significant degree of reproductive isolation is low. The significance of these findings in relation to theories of speciation is discussed.     

Expected relative fitness and the adaptive topography of fluctuating selection

Wright's adaptive topography describes gene frequency evolution as a maximization of mean fitness in a constant environment. I extended this to a fluctuating environment by unifying theories of stochastic demography and fluctuating selection, assuming small or moderate fluctuations in demographic rates with a stationary distribution, and weak selection among the types. The demography of a large population, composed of haploid genotypes at a single locus or normally distributed phenotypes, can then be approximated as a diffusion process and transformed to produce the dynamics of population size, N, and gene frequency, p, or mean phenotype, . The expected evolution of p or is a product of genetic variability and the gradient of the long-run growth rate of the population, , with respect to p or . This shows that the expected evolution maximizes , the mean Malthusian fitness in the average environment minus half the environmental variance in population growth rate. Thus, as a function of p or represents an adaptive topography that, despite environmental fluctuations, does not change with time. The haploid model is dominated by environmental stochasticity, so the expected maximization is not realized. Different constraints on quantitative genetic variability, and stabilizing selection in the average environment, allow evolution of the mean phenotype to undergo a stochastic maximization of . Although the expected evolution maximizes the long-run growth rate of the population, for a genotype or phenotype the long-run growth rate is not a valid measure of fitness in a fluctuating environment. The haploid and quantitative character models both reveal that the expected relative fitness of a type is its Malthusian fitness in the average environment minus the environmental covariance between its growth rate and that of the population.     

Rapid increase in southern elephant seal genetic diversity after a founder event

Genetic diversity provides the raw material for populations to respond to changing environmental conditions. The evolution of diversity within populations is based on the accumulation of mutations and their retention or loss through selection and genetic drift, while migration can also introduce new variation. However, the extent to which population growth and sustained large population size can lead to rapid and significant increases in diversity has not been widely investigated. Here, we assess this empirically by applying approximate Bayesian computation to a novel ancient DNA dataset that spans the life of a southern elephant seal (Mirounga leonina) population, from initial founding approximately 7000 years ago to eventual extinction within the past millennium. We find that rapid population growth and sustained large population size can explain substantial increases in population genetic diversity over a period of several hundred generations, subsequently lost when the population went to extinction. Results suggest that the impact of diversity introduced through migration was relatively minor. We thus demonstrate, by examining genetic diversity across the life of a population, that environmental change could generate the raw material for adaptive evolution over a very short evolutionary time scale through rapid establishment of a large, stable population.     

PEAK SHIFTS PRODUCED BY CORRELATED RESPONSE TO SELECTION

Traits may evolve both as a consequence of direct selection and also as a correlated response to selection on other traits. While correlated response may be important for both the production of evolutionary novelty and in the build-up of complex characters, its potential role in peak shifts has been neglected empirically and theoretically. We use a quantitative genetic model to investigate the conditions under which a character, Y, which has two alternative optima, can be dragged from one optimum to the other as a correlated response to selection on a second character, X. High genetic correlations between the two characters make the transition, or peak shift, easier, as does weak selection tending to restore Y to the optimum from which it is being dragged. When selection on Y is very weak, the conditions for a peak shift depend only on the location of the new optimum for X and are independent of the strength of selection moving it there. Thus, if the “adaptive valley” for Y is very shallow, little reduction in mean fitness is needed to produce a shift. If the selection acts strongly to keep Y at its current optimum, very intense directional selection on X, associated with a dramatic drop in mean fitness, is required for a peak shift. When strong selection is required, the conditions for peak shifts driven by correlated response might occur rarely, but still with sufficient frequency on a geological timescale to be evolutionarily important.     

The implications of rapid eco‐evolutionary processes for biological control ‐ a review

Novel environmental conditions experienced by introduced species can drive rapid evolution of diverse traits. In turn, rapid evolution, both adaptive and non‐adaptive, can influence population size, growth rate, and other important ecological characteristics of populations. In addition, spatial evolutionary processes that arise from a combination of assortative mating between highly dispersive individuals at the expanding edge of populations and altered reproductive rates of those individuals can accelerate expansion speed. Growing experimental evidence shows that the effects of rapid evolution on ecological dynamics can be quite large, and thus it can affect establishment, persistence, and the distribution of populations. We review the experimental and theoretical literature on such eco‐evolutionary feedbacks and evaluate the implications of these processes for biological control. Experiments show that evolving populations can establish at higher rates and grow larger than non‐evolving populations. However, non‐adaptive processes, such as genetic drift and inbreeding depression can also lead to reduced fitness and declines in population size. Spatial evolutionary processes can increase spread rates and change the fitness of individuals at the expansion front. These examples demonstrate the power of eco‐evolutionary dynamics and indicate that evolution is likely more important in biocontrol programs than previously realized. We discuss how this knowledge can be used to enhance efficacy of biological control.     

The role of founder effects on the evolution of reproductive isolation

Several theories argue that large changes in allele frequencies through genetic drift after a small founding population becomes allopatrically isolated can lead to significant changes in reproductive isolation and thus trigger the origin of new species. For this reason, founder speciation has been proposed as a potent force in the generation of new species. Nonetheless, the relative importance of such ‘founder effects’ remains largely untested. In this report, I used experimental evolution to create one thousand replicates that underwent an extreme bottleneck and to study whether founder effects can lead to an increase in reproductive isolation in Drosophila yakuba. Even though the most common outcome of inbreeding is extinction, founder effects can lead to increased premating reproductive isolation in a very small proportion of cases. Changes in reproductive isolation after a founding population bottleneck are similar to changes in other phenotypic traits, in which inbreeding might displace the mean phenotypic value and substantially increase the phenotypic variance. This increase in phenotypic variance does not confer an increase in the response to selection for reproductive isolation in artificial selection experiments, indicating that the increased phenotypic variance is not caused by increases in additive genetic variance. These results also demonstrate that, similar to morphological and life‐history traits, behavioural traits can be affected by inbreeding and genetic drift.     

Evolution by small steps and rugged landscapes in the RNA virus phi6

Fisher's geometric model of adaptive evolution argues that adaptive evolution should generally result from the substitution of many mutations of small effect because advantageous mutations of small effect should be more common than those of large effect. However, evidence for both evolution by small steps and for Fisher's model has been mixed. Here we report supporting results from a new experimental test of the model. We subjected the bacteriophage phi6 to intensified genetic drift in small populations and caused viral fitness to decline through the accumulation of a deleterious mutation. We then propagated the mutated virus at a range of larger population sizes and allowed fitness to recover by natural selection. Although fitness declined in one large step, it was usually recovered in smaller steps. More importantly, step size during recovery was smaller with decreasing size of the recovery population. These results confirm Fisher's main prediction that advantageous mutations of small effect should be more common. We also show that the advantageous mutations of small effect are compensatory mutations whose advantage is conditional (epistatic) on the presence of the deleterious mutation, in which case the adaptive landscape of phi6 is likely to be very rugged.     

The impact of random frequency-dependent mutations on the average population fitness

ABSTRACT: BACKGROUND: In addition to selection, the process of evolution is accompanied by stochastic effects, such as changing environmental conditions, genetic drift and mutations. Commonly it is believed that without genetic drift, advantageous mutations quickly fixate in a halpoid population due to strong selection and lead to a continuous increase of the average fitness. This conclusion is based on the assumption of constant fitness. However, for frequency dependent fitness, where the fitness of an individual depends on the interactions with other individuals in the population, this does not hold. RESULTS: We propose a mathematical model that allows to understand the consequences of random frequency dependent mutations on the dynamics of an infinite large population. The frequencies of different types change according to the replicator equations and the fitness of a mutant is random and frequency dependent. To capture the interactions of different types, we employ a payoff matrix of variable size and thus are able to accommodate an arbitrary number of mutations. We assume that at most one mutant type arises at a time. The payoff entries to describe the mutant type are random variables obeying a probability distribution which is related to the fitness of the parent type. CONCLUSIONS: We show that a random mutant can decrease the average fitness under frequency dependent selection, based on analytical results for two types, and on simulations for n types. Interestingly, in the case of at most two types the probabilities to increase or decrease the average fitness are independent of the concrete probability density function. Instead, they only depend on the probability that the payoff entries of the mutant are larger than the payoff entries of the parent type.     

From nature to the laboratory: the impact of founder effects on adaptation

Most founding events entail a reduction in population size, which in turn leads to genetic drift effects that can deplete alleles. Besides reducing neutral genetic variability, founder effects can in principle shift additive genetic variance for phenotypes that underlie fitness. This could then lead to different rates of adaptation among populations that have undergone a population size bottleneck as well as an environmental change, even when these populations have a common evolutionary history. Thus, theory suggests that there should be an association between observable genetic variability for both neutral markers and phenotypes related to fitness. Here, we test this scenario by monitoring the early evolutionary dynamics of six laboratory foundations derived from founders taken from the same source natural population of Drosophila subobscura. Each foundation was in turn three‐fold replicated. During their first few generations, these six foundations showed an abrupt increase in their genetic differentiation, within and between foundations. The eighteen populations that were monitored also differed in their patterns of phenotypic adaptation according to their immediately ancestral founding sample. Differences in early genetic variability and in effective population size were found to predict differences in the rate of adaptation during the first 21 generations of laboratory evolution. We show that evolution in a novel environment is strongly contingent not only on the initial composition of a newly founded population but also on the stochastic changes that occur during the first generations of colonization. Such effects make laboratory populations poor guides to the evolutionary genetic properties of their ancestral wild populations.     

Limits of Neutral Drift: Lessons From the In Vitro Evolution of Two Ribozymes

The relative contributions of adaptive selection and neutral drift to genetic change are unknown but likely depend on the inherent abundance of functional genotypes in sequence space and how accessible those genotypes are to one another. To better understand the relative roles of selection and drift in evolution, local fitness landscapes for two different RNA ligase ribozymes were examined using a continuous in vitro evolution system under conditions that foster the capacity for neutral drift to mediate genetic change. The exploration of sequence space was accelerated by increasing the mutation rate using mutagenic nucleotide analogs. Drift was encouraged by carrying out evolution within millions of separate compartments to exploit the founder effect. Deep sequencing of individuals from the evolved populations revealed that the distribution of genotypes did not escape the starting local fitness peak, remaining clustered around the sequence used to initiate evolution. This is consistent with a fitness landscape where high-fitness genotypes are sparse and well isolated, and suggests, at least in this context, that neutral drift alone is not a primary driver of genetic change. Neutral drift does, however, provide a repository of genetic variation upon which adaptive selection can act.     

Investigating the Interactions of Yeast Prions: [SWI+], [PSI+], and [PIN+]

The relationship between quantitative genetics and population genetics has been studied for nearly a century, almost since the existence of these two disciplines. Here we ask to what extent quantitative genetic models in which selection is assumed to operate on a polygenic trait predict adaptive fixations that may lead to footprints in the genome (selective sweeps). We study two-locus models of stabilizing selection (with and without genetic drift) by simulations and analytically. For symmetric viability selection we find that ∼16% of the trajectories may lead to fixation if the initial allele frequencies are sampled from the neutral site-frequency spectrum and the effect sizes are uniformly distributed. However, if the population is preadapted when it undergoes an environmental change (i.e., sits in one of the equilibria of the model), the fixation probability decreases dramatically. In other two-locus models with general viabilities or an optimum shift, the proportion of adaptive fixations may increase to >24%. Similarly, genetic drift leads to a higher probability of fixation. The predictions of alternative quantitative genetics models, initial conditions, and effect-size distributions are also discussed.     

Niche construction and the environmental term of the price equation: How natural selection changes when organisms alter their environments

Organisms construct their own environments and phenotypes through the adaptive processes of habitat choice, habitat construction, and phenotypic plasticity. We examine how these processes affect the dynamics of mean fitness change through the environmental change term of the Price Equation. This tends to be ignored in evolutionary theory, owing to the emphasis on the first term describing the effect of natural selection on mean fitness (the additive genetic variance for fitness of Fisher's Fundamental Theorem). Using population genetic models and the Price Equation, we show how adaptive niche constructing traits favorably alter the distribution of environments that organisms encounter and thereby increase population mean fitness. Because niche-constructing traits increase the frequency of higher-fitness environments, selection favors their evolution. Furthermore, their alteration of the actual or experienced environmental distribution creates selective feedback between niche constructing traits and other traits, especially those with genotype-by-environment interaction for fitness. By altering the distribution of experienced environments, niche constructing traits can increase the additive genetic variance for such traits. This effect accelerates the process of overall adaption to the niche-constructed environmental distribution and can contribute to the rapid refinement of alternative phenotypic adaptations to different environments. Our findings suggest that evolutionary biologists revisit and reevaluate the environmental term of the Price Equation: owing to adaptive niche construction, it contributes directly to positive change in mean fitness; its magnitude can be comparable to that of natural selection; and, when there is fitness G × E, it increases the additive genetic variance for fitness, the much-celebrated first term.     

The adaptive value of epigenetic mutation: Limited in large but high in small peripheral populations

The fate of populations during range expansions, invasions and environmental changes is largely influenced by their ability to adapt to peripheral habitats. Recent models demonstrate that stable epigenetic modifications of gene expression that occur more frequently than genetic mutations can both help and hinder adaptation in panmictic populations. However, these models do not consider interactions between epimutations and evolutionary forces in peripheral populations. Here, we use mainland–island mathematical models and simulations to explore how the faster rate of epigenetic mutation compared to genetic mutations interacts with migration, selection and genetic drift to affect adaptation in peripheral populations. Our model focuses on cases where epigenetic marks are stably inherited. In a large peripheral population, where the effect of genetic drift is negligible, our analyses suggest that epimutations with random fitness impacts that occur at rates as high as 10^–3 increase local adaptation when migration is strong enough to overwhelm divergent selection. When migration is weak relative to selection and epimutations with random fitness impacts decrease adaptation, we find epigenetic modifications must be highly adaptively biased to enhance adaptation. Finally, in small peripheral populations, where genetic drift is strong, epimutations contribute to adaptation under a wider range of evolutionary conditions. Overall, our results suggest that epimutations can change outcomes of adaptation in peripheral populations, which has implications for understanding conservation and range expansions and contractions, especially of small populations.     

Environmental variance in male mating success modulates the positive versus negative impacts of sexual selection on genetic load

Sexual selection on males is predicted to increase population fitness, and delay population extinction, when mating success negatively covaries with genetic load across individuals. However, such benefits of sexual selection could be counteracted by simultaneous increases in genome-wide drift resulting from reduced effective population size caused by increased variance in fitness. Resulting fixation of deleterious mutations could be greatest in small populations, and when environmental variation in mating traits partially decouples sexual selection from underlying genetic variation. The net consequences of sexual selection for genetic load and population persistence are therefore likely to be context dependent, but such variation has not been examined. We use a genetically explicit individual-based model to show that weak sexual selection can increase population persistence time compared to random mating. However, for stronger sexual selection such positive effects can be overturned by the detrimental effects of increased genome-wide drift. Furthermore, the relative strengths of mutation-purging and drift critically depend on the environmental variance in the male mating trait. Specifically, increasing environmental variance caused stronger sexual selection to elevate deleterious mutation fixation rate and mean selection coefficient, driving rapid accumulation of drift load and decreasing population persistence times. These results highlight an intricate balance between conflicting positive and negative consequences of sexual selection on genetic load, even in the absence of sexually antagonistic selection. They imply that environmental variances in key mating traits, and intrinsic genetic drift, should be properly factored into future theoretical and empirical studies of the evolution of population fitness under sexual selection.     

Model and test in a fungus of the probability that beneficial mutations survive drift

Determining the probability of fixation of beneficial mutations is critically important for building predictive models of adaptive evolution. Despite considerable theoretical work, models of fixation probability have stood untested for nearly a century. However, recent advances in experimental and theoretical techniques permit the development of models with testable predictions. We developed a new model for the probability of surviving genetic drift, a major component of fixation probability, for novel beneficial mutations in the fungus Aspergillus nidulans, based on the life-history characteristics of its colony growth on a solid surface. We tested the model by measuring the probability of surviving drift in 11 adapted strains introduced into wild-type populations of different densities. We found that the probability of surviving drift increased with mutant invasion fitness, and decreased with wild-type density, as expected. The model accurately predicted the survival probability for the majority of mutants, yielding one of the first direct tests of the extinction probability of beneficial mutations.     

Fixation of new alleles and the extinction of small populations: drift load, beneficial alleles, and sexual selection

With a small effective population size, random genetic drift is more important than selection in determining the fate of new alleles. Small populations therefore accumulate deleterious mutations. Left unchecked, the effect of these fixed alleles is to reduce the reproductive capacity of a species, eventually to the point of extinction. New beneficial mutations, if fixed by selection, can restore some of this lost fitness. This paper derives the overall change in fitness due to fixation of new deleterious and beneficial alleles, as a function of the distribution of effects of new mutations and the effective population size. There is a critical effective size below which a population will on average decline in fitness, but above which beneficial mutations allow the population to persist. With reasonable estimates of the relevant parameters, this critical effective size is likely to be a few hundred. Furthermore, sexual selection can act to reduce the fixation probability of deleterious new mutations and increase the probability of fixing new beneficial mutations. Sexual selection can therefore reduce the risk of extinction of small populations.     

Will small population sizes warn us of impending extinctions?

Several models are used to show that population sizes are often relatively insensitive to deteriorating environmental conditions over most of the range of environments that allow population persistence. As conditions continue to worsen in these cases, equilibrium population sizes ultimately decline rapidly toward extinction from sizes similar to or larger than those before environmental decline began. Consumer-resource models predict that equilibrium or average population size can increase with deteriorating environmental conditions over a large part of the range of the environmental parameter that allows persistence. The initial insensitivity or increase in the population of the focal species occurs because changes in the populations of other components of the food web compensate for the decline in one or more fitness components of the focal population. However, the compensatory processes are generally nonlinear and often approach their limits abruptly rather than gradually. When there is steady directional change in the environment, populations lag behind the equilibrium population size specified by current environmental conditions. The environmental variable can then decline below the level required for population persistence while the population size is still close to or greater than its original value. Efficient consumers and self-reproducing resources are especially likely to produce this outcome. More complex models with adaptive behavior, additional consumers, or additional resources often exhibit similar trajectories of population size under environmental deterioration.     

GENETIC SIGNATURE OF ADAPTIVE PEAK SHIFT IN THREESPINE STICKLEBACK

Transition of an evolving population to a new adaptive optimum is predicted to leave a signature in the distribution of effect sizes of fixed mutations. If they affect many traits (are pleiotropic), large effect mutations should contribute more when a population evolves to a farther adaptive peak than to a nearer peak. We tested this prediction in wild threespine stickleback fish (Gasterosteus aculeatus) by comparing the estimated frequency of large effect genetic changes underlying evolution as the same ancestor adapted to two lake types since the end of the ice age. A higher frequency of large effect genetic changes (quantitative trait loci) contributed to adaptive evolution in populations that adapted to lakes representing a more distant optimum than to lakes in which the optimum phenotype was nearer to the ancestral state. Our results also indicate that pleiotropy, not just optimum overshoot, contributes to this difference. These results suggest that a series of adaptive improvements to a new environment leaves a detectable mark in the genome of wild populations. Although not all assumptions of the theory are likely met in natural systems, the prediction may be robust enough to the complexities of natural environments to be useful when forecasting adaptive responses to large environmental changes.     

The temporal distribution of directional gradients under selection for an optimum

Temporal variation in phenotypic selection is often attributed to environmental change causing movements of the adaptive surface relating traits to fitness, but this connection is rarely established empirically. Fluctuating phenotypic selection can be measured by the variance and autocorrelation of directional selection gradients through time. However, the dynamics of these gradients depend not only on environmental changes altering the fitness surface, but also on evolution of the phenotypic distribution. Therefore, it is unclear to what extent variability in selection gradients can inform us about the underlying drivers of their fluctuations. To investigate this question, we derive the temporal distribution of directional gradients under selection for a phenotypic optimum that is either constant or fluctuates randomly in various ways in a finite population. Our analytical results, combined with population‐ and individual‐based simulations, show that although some characteristic patterns can be distinguished, very different types of change in the optimum (including a constant optimum) can generate similar temporal distributions of selection gradients, making it difficult to infer the processes underlying apparent fluctuating selection. Analyzing changes in phenotype distributions together with changes in selection gradients should prove more useful for inferring the mechanisms underlying estimated fluctuating selection.