Selective Sweep at a QTL in a Randomly Fluctuating Environment

Evolutionary and Ecological Processes Determining the Properties of the Matrix

AbstractThe G matrix is the matrix of additive genetic variances and covariances for a vector of phenotypes. Here we apply the classical theory for the balance among selection, genetic drift, and mutations to find the contributions to G from each locus for populations at stasis. The fitness is approximated by a linear function of phenotypes, with coefficients affected by environmental fluctuations. We show that the G matrix can be decomposed into four additive components generated by selection, drift, mutations, and environmental fluctuations. Selection is on average counteracted by the other three processes included in Fisher's concept of deterioration of the environment, generating considerable changes in mean phenotypes. The theory illustrates that neither Fisher's fundamental theorem nor Lande's classical gradient formula is sufficient for assessing adaptive changes through time unless the deteriorations are corrected for. This applies for populations at stasis, but also for populations that are subject to long-term evolutionary changes. The theory also indicates several possible comparative studies for investigations of deteriorating effects. Our analyses also suggest that the factor loadings to the eigenvector of the G matrix with the lowest eigenvalue will rather accurately indicate the relative contributions from different phenotype components to fitness. This is information notoriously difficult to obtain in natural populations.

Polygenic dynamics underlying the response of quantitative traits to directional selection

We study the response of a quantitative trait to exponential directional selection in a finite haploid population, both at the genetic and the phenotypic level. We assume an infinite sites model, in which the number of new mutations per generation in the population follows a Poisson distribution (with mean Θ) and each mutation occurs at a new, previously monomorphic site. Mutation effects are beneficial and drawn from a distribution. Sites are unlinked and contribute additively to the trait. Assuming that selection is stronger than random genetic drift, we model the initial phase of the dynamics by a supercritical Galton-Watson process. This enables us to obtain time-dependent results. We show that the copy-number distribution of the mutant in generation n, conditioned on non-extinction until n, is described accurately by the deterministic increase from an initial distribution with mean 1. This distribution is related to the absolutely continuous part W+ of the random variable, typically denoted W, that characterizes the stochasticity accumulating during the mutant's sweep. A suitable transformation yields the approximate dynamics of the mutant frequency distribution in a Wright-Fisher population of size N. Our expression provides a very accurate approximation except when mutant frequencies are close to 1. On this basis, we derive explicitly the (approximate) time dependence of the expected mean and variance of the trait and of the expected number of segregating sites. Unexpectedly, we obtain highly accurate approximations for all times, even for the quasi-stationary phase when the expected per-generation response and the trait variance have equilibrated. The latter refine classical results. In addition, we find that Θ is the main determinant of the pattern of adaptation at the genetic level, i.e., whether the initial allele-frequency dynamics are best described by sweep-like patterns at few loci or small allele-frequency shifts at many. The number of segregating sites is an appropriate indicator for these patterns. The selection strength determines primarily the rate of adaptation. The accuracy of our results is tested by comprehensive simulations in a Wright-Fisher framework. We argue that our results apply to more complex forms of directional selection.

The genome-wide signature of short-term temporal selection

Despite evolutionary biology's obsession with natural selection, few studies have evaluated multigenerational series of patterns of selection on a genome-wide scale in natural populations. Here, we report on a 10-y population-genomic survey of the microcrustacean Daphnia pulex. The genome sequences of [Formula: see text]800 isolates provide insights into patterns of selection that cannot be obtained from long-term molecular-evolution studies, including the following: the pervasiveness of near quasi-neutrality across the genome (mean net selection coefficients near zero, but with significant temporal variance about the mean, and little evidence of positive covariance of selection across time intervals); the preponderance of weak positive selection operating on minor alleles; and a genome-wide distribution of numerous small linkage islands of observable selection influencing levels of nucleotide diversity. These results suggest that interannual fluctuating selection is a major determinant of standing levels of variation in natural populations, challenge the conventional paradigm for interpreting patterns of nucleotide diversity and divergence, and motivate the need for the further development of theoretical expressions for the interpretation of population-genomic data.

A theory of oligogenic adaptation of a quantitative trait

Rapid phenotypic adaptation is widespread in nature, but the underlying genetic dynamics remain controversial. Whereas population genetics envisages sequential beneficial substitutions, quantitative genetics assumes a collective response through subtle shifts in allele frequencies. This dichotomy of a monogenic and a highly polygenic view of adaptation raises the question of a middle ground, as well as the factors controlling the transition. Here, we consider an additive quantitative trait with equal locus effects under Gaussian stabilizing selection that adapts to a new trait optimum after an environmental change. We present an analytical framework based on Yule branching processes to describe how phenotypic adaptation is achieved by collective changes in allele frequencies at the underlying loci. In particular, we derive an approximation for the joint allele-frequency distribution conditioned on the trait mean as a comprehensive descriptor of the adaptive architecture. Depending on the model parameters, this architecture reproduces the well-known patterns of sequential, monogenic sweeps, or of subtle, polygenic frequency shifts. Between these endpoints, we observe oligogenic architecture types that exhibit characteristic patterns of partial sweeps. We find that a single compound parameter, the population-scaled background mutation rate Θbg, is the most important predictor of the type of adaptation, while selection strength, the number of loci in the genetic basis, and linkage only play a minor role.

Laplace's demon in biology: Models of evolutionary prediction

Our ability to predict natural phenomena can be limited by incomplete information. This issue is exemplified by "Laplace's demon," an imaginary creature proposed in the 18th century, who knew everything about everything, and thus could predict the full nature of the universe forward or backward in time. Quantum mechanics, among other things, has cast doubt on the possibility of Laplace's demon in the full sense, but the idea still serves as a useful metaphor for thinking about the extent to which prediction is limited by incomplete information on deterministic processes versus random factors. Here, we use simple analytical models and computer simulations to illustrate how data limits can be captured in a Bayesian framework, and how they influence our ability to predict evolution. We show how uncertainty in measurements of natural selection, or low predictability of external environmental factors affecting selection, can greatly reduce predictive power, often swamping the influence of intrinsic randomness caused by genetic drift. Thus, more accurate knowledge concerning the causes and action of natural selection is key to improving prediction. Fortunately, our analyses and simulations show quantitatively that reasonable improvements in data quantity and quality can meaningfully increase predictability.

A possible genomic footprint of polygenic adaptation on population divergence in seed beetles?

Efforts to unravel the genomic basis of incipient speciation are hampered by a mismatch between our toolkit and our understanding of the ecology and genetics of adaptation. While the former is focused on detecting selective sweeps involving few independently acting or linked speciation genes, the latter states that divergence typically occurs in polygenic traits under stabilizing selection. Here, we ask whether a role of stabilizing selection on polygenic traits in population divergence may be unveiled by using a phenotypically informed integrative approach, based on genome‐wide variation segregating in divergent populations. We compare three divergent populations of seed beetles (Callosobruchus maculatus) where previous work has demonstrated a prominent role for stabilizing selection on, and population divergence in, key life history traits that reflect rate‐dependent metabolic processes. We derive and assess predictions regarding the expected pattern of covariation between genetic variation segregating within populations and genetic differentiation between populations. Population differentiation was considerable (mean F_ST = 0.23–0.26) and was primarily built by genes showing high selective constraints and an imbalance in inferred selection in different populations (positive Tajima's D_NS in one and negative in one), and this set of genes was enriched with genes with a metabolic function. Repeatability of relative population differentiation was low at the level of individual genes but higher at the level of broad functional classes, again spotlighting metabolic genes. Absolute differentiation (d_XY) showed a very different general pattern at this scale of divergence, more consistent with an important role for genetic drift. Although our exploration is consistent with stabilizing selection on polygenic metabolic phenotypes as an important engine of genome‐wide relative population divergence and incipient speciation in our study system, we note that it is exceedingly difficult to firmly exclude other scenarios.

Negotiating mutualism: A locus for exploitation by rhizobia has a broad effect size distribution and context-dependent effects on legume hosts

In mutualisms, variation at genes determining partner fitness provides the raw material upon which coevolutionary selection acts, setting the dynamics and pace of coevolution. However, we know little about variation in the effects of genes that underlie symbiotic fitness in natural mutualist populations. In some species of legumes that form root nodule symbioses with nitrogen‐fixing rhizobial bacteria, hosts secrete nodule‐specific cysteine‐rich (NCR) peptides that cause rhizobia to differentiate in the nodule environment. However, rhizobia can cleave NCR peptides through the expression of genes like the plasmid‐borne Host range restriction peptidase (hrrP), whose product degrades specific NCR peptides. Although hrrP activity can confer host exploitation by depressing host fitness and enhancing symbiont fitness, the effects of hrrP on symbiosis phenotypes depend strongly on the genotypes of the interacting partners. However, the effects of hrrP have yet to be characterised in a natural population context, so its contribution to variation in wild mutualist populations is unknown. To understand the distribution of effects of hrrP in wild rhizobia, we measured mutualism phenotypes conferred by hrrP in 12 wild Ensifer medicae strains. To evaluate context dependency of hrrP effects, we compared hrrP effects across two Medicago polymorpha host genotypes and across two experimental years for five E. medicae strains. We show for the first time in a natural population context that hrrP has a wide distribution of effect sizes for many mutualism traits, ranging from strongly positive to strongly negative. Furthermore, we show that hrrP effect size varies across host genotypes and experiment years, suggesting that researchers should be cautious about extrapolating the role of genes in natural populations from controlled laboratory studies of single genetic variants.

From genotype to phenotype: Genetic redundancy and the maintenance of an adaptive polymorphism in the context of high gene flow

A central question in evolution is how several adaptive phenotypes are maintained within a species. Theory predicts that the genetic determination of a trait, and in particular the amounts of redundancy in the mapping of genotypes to phenotypes, mediates evolutionary outcomes of phenotypic selection. In Mediterranean wild thyme, numerous discrete chemical phenotypes (chemotypes) occur in close geographic proximity. Chemotypes are defined by the predominant monoterpene produced by individual plants in their essential oil. In this study, we analyze the ecological genetics of six chemotypes nested within two well‐established chemical families (hereafter ecotypes). Ecotypes, and chemotypes within ecotypes, are spatially segregated, and their distributions track local differences in the abiotic environment. By combining population genomic, phenotypic, and environmental data from 700 individuals, we show how the genetics of ecotype determination mediates this evolutionary response. Variation in three terpene‐synthase loci explains variation in ecotype identity, with one single locus accounting for as much as 78% of this variation. Phenotypic selection combined with low segregating genotypic redundancy of ecotypes leaves a clear footprint at the genomic level: alleles associated with ecotype identity track environmental variation despite extensive gene flow. Different chemotypes within each ecotype differentially track environmental variation. Their identity is determined by multiple loci and displays a wider range of genotypic redundancy that dilutes phenotypic selection on their characteristic alleles. Our study thus provides a novel illustration of how genetic redundancy of a phenotype modulates the ability of selection to maintain adaptive differentiation. Identifying the precise genetics of the chemical polymorphism in thyme is the next crucial step for our understanding of the origin and maintenance of a polymorphism that is present in many aromatic plants.

Frequency dependence and the predictability of evolution in a changing environment

Frequency‐dependent (FD) selection, whereby fitness and selection depend on the genetic or phenotypic composition of the population, arises in numerous ecological contexts (competition, mate choice, crypsis, mimicry, etc.) and can strongly impact evolutionary dynamics. In particular, negative frequency‐dependent selection (NFDS) is well known for its ability to potentially maintain stable polymorphisms, but it has also been invoked as a source of persistent, predictable frequency fluctuations. However, the conditions under which such fluctuations persist are not entirely clear. In particular, previous work rarely considered that FD is unlikely to be the sole driver of evolutionary dynamics when it occurs, because most environments are not static but instead change dynamically over time. Here, we investigate how FD interacts with a temporally fluctuating environment to shape the dynamics of population genetic change. We show that a simple metric introduced by Lewontin, the slope of frequency change against frequency near equilibrium, works as a key criterion for distinguishing microevolutionary outcomes, even in a changing environment. When this slope D is between 0 and –2 (consistent with the empirical examples we review), substantial fluctuations would not persist on their own in a large population occupying a constant environment, but they can still be maintained indefinitely as quasi‐cycles fueled by environmental noise or genetic drift. However, such moderate NFDS buffers and temporally shifts evolutionary responses to periodic environments (e.g., seasonality). Stronger FD, with slope D < –2, can produce self‐sustained cycles that may overwhelm responses to a changing environment, or even chaos that fundamentally limits predictability. This diversity of expected outcomes, together with the empirical evidence for both FD and environment‐dependent selection, suggests that the interplay of internal dynamics with external forcing should be investigated more systematically to reach a better understanding and prediction of evolution.

Using singleton densities to detect recent selection in Bos taurus

Many quantitative traits are subject to polygenic selection, where several genomic regions undergo small, simultaneous changes in allele frequency that collectively alter a phenotype. The widespread availability of genome data, along with novel statistical techniques, has made it easier to detect these changes. We apply one such method, the "Singleton Density Score" (SDS), to the Holstein breed of Bos taurus to detect recent selection (arising up to around 740 years ago). We identify several genes as candidates for targets of recent selection, including some relating to cell regulation, catabolic processes, neural-cell adhesion and immunity. We do not find strong evidence that three traits that are important to humans-milk protein content, milk fat content, and stature-have been subject to directional selection. Simulations demonstrate that because B. taurus recently experienced a population bottleneck, singletons are depleted so the power of SDS methods is reduced. These results inform on which genes underlie recent genetic change in B. taurus, while providing information on how polygenic selection can be best investigated in future studies.

Predicting population genetic change in an autocorrelated random environment: Insights from a large automated experiment

Most natural environments exhibit a substantial component of random variation, with a degree of temporal autocorrelation that defines the color of environmental noise. Such environmental fluctuations cause random fluctuations in natural selection, affecting the predictability of evolution. But despite long-standing theoretical interest in population genetics in stochastic environments, there is a dearth of empirical estimation of underlying parameters of this theory. More importantly, it is still an open question whether evolution in fluctuating environments can be predicted indirectly using simpler measures, which combine environmental time series with population estimates in constant environments. Here we address these questions by using an automated experimental evolution approach. We used a liquid-handling robot to expose over a hundred lines of the micro-alga Dunaliella salina to randomly fluctuating salinity over a continuous range, with controlled mean, variance, and autocorrelation. We then tracked the frequencies of two competing strains through amplicon sequencing of nuclear and choloroplastic barcode sequences. We show that the magnitude of environmental fluctuations (determined by their variance), but also their predictability (determined by their autocorrelation), had large impacts on the average selection coefficient. The variance in frequency change, which quantifies randomness in population genetics, was substantially higher in a fluctuating environment. The reaction norm of selection coefficients against constant salinity yielded accurate predictions for the mean selection coefficient in a fluctuating environment. This selection reaction norm was in turn well predicted by environmental tolerance curves, with population growth rate against salinity. However, both the selection reaction norm and tolerance curves underestimated the variance in selection caused by random environmental fluctuations. Overall, our results provide exceptional insights into the prospects for understanding and predicting genetic evolution in randomly fluctuating environments.

Being able to predict evolution under natural selection is important for many applied fields of biology, ranging from agriculture to medicine or conservation. However, this endeavor is complicated by factors that inherently limit our ability to predict the future, such as random fluctuations in the environment. Population genetic theory indicates that probabilistic predictions can still be made in this context, but the extent to which this holds empirically, and whether these predictions can be based on simple measurements, are still open questions. Making progress on answering these questions can be achieved by capitalizing on experiments where the environment is precisely controlled over many generations. Here, we used a pipetting robot to generate random time series of salinities with controlled patterns of fluctuations, which we imposed on a microalga, Dunaliella salina. Tracking the frequencies of two genotypes in a mixture by sequencing two short barcode sequences, we were able to show how patterns of fluctuating selection relate to the fluctuating environment. Interestingly, parts of these responses, but not all, could be predicted by simpler measurements in constant environments, allowing precise characterization the limits and prospects for predicting evolution in fluctuating environments.