Average Selection Coefficient Research Articles

Minimal informational requirements for fitness.

The existing concept of the "fitness value of information" provides a theoretical upper bound on the fitness advantage of using information concerning a fluctuating environment. Using concepts from rate-distortion theory, we develop a theoretical framework to answer a different pair of questions: What is the minimal amount of information needed for a population to achieve a certain growth rate? What is the minimal amount of information gain needed for one subpopulation to achieve a certain average selection coefficient over another? We introduce a correspondence between fitness and distortion and solve for the rate-distortion functions of several systems using analytical and numerical methods. Because accurate information processing is energetically costly, our approach provides a theoretical basis for understanding evolutionary "design principles" underlying information-cost trade-offs.

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.

The mutational decay of male-male and hermaphrodite-hermaphrodite competitive fitness in the androdioecious nematode C. elegans.

Androdioecious Caenorhabditis have a high frequency of self-compatible hermaphrodites and a low frequency of males. The effects of mutations on male fitness are of interest for two reasons. First, when males are rare, selection on male-specific mutations is less efficient than in hermaphrodites. Second, males may present a larger mutational target than hermaphrodites because of the different ways in which fitness accrues in the two sexes. We report the first estimates of male-specific mutational effects in an androdioecious organism. The rate of male-specific inviable or sterile mutations is ⩽5 × 10-4/generation, below the rate at which males would be lost solely due to those kinds of mutations. The rate of mutational decay of male competitive fitness is ~ 0.17%/generation; that of hermaphrodite competitive fitness is ~ 0.11%/generation. The point estimate of ~ 1.5X faster rate of mutational decay of male fitness is nearly identical to the same ratio in Drosophila. Estimates of mutational variance (VM) for male mating success and competitive fitness are not significantly different from zero, whereas VM for hermaphrodite competitive fitness is similar to that of non-competitive fitness. Two independent estimates of the average selection coefficient against mutations affecting hermaphrodite competitive fitness agree to within two-fold, 0.33-0.5%.

Disentangling the effects of selection and loss bias on gene dynamics

We combine mathematical modeling of genome evolution with comparative analysis of prokaryotic genomes to estimate the relative contributions of selection and intrinsic loss bias to the evolution of different functional classes of genes and mobile genetic elements (MGE). An exact solution for the dynamics of gene family size was obtained under a linear duplication-transfer-loss model with selection. With the exception of genes involved in information processing, particularly translation, which are maintained by strong selection, the average selection coefficient for most nonparasitic genes is low albeit positive, compatible with observed positive correlation between genome size and effective population size. Free-living microbes evolve under stronger selection for gene retention than parasites. Different classes of MGE show a broad range of fitness effects, from the nearly neutral transposons to prophages, which are actively eliminated by selection. Genes involved in antiparasite defense, on average, incur a fitness cost to the host that is at least as high as the cost of plasmids. This cost is probably due to the adverse effects of autoimmunity and curtailment of horizontal gene transfer caused by the defense systems and selfish behavior of some of these systems, such as toxin-antitoxin and restriction modification modules. Transposons follow a biphasic dynamics, with bursts of gene proliferation followed by decay in the copy number that is quantitatively captured by the model. The horizontal gene transfer to loss ratio, but not duplication to loss ratio, correlates with genome size, potentially explaining increased abundance of neutral and costly elements in larger genomes.

Determining the factors driving selective effects of new nonsynonymous mutations

The distribution of fitness effects (DFE) of new mutations plays a fundamental role in evolutionary genetics. However, the extent to which the DFE differs across species has yet to be systematically investigated. Furthermore, the biological mechanisms determining the DFE in natural populations remain unclear. Here, we show that theoretical models emphasizing different biological factors at determining the DFE, such as protein stability, back-mutations, species complexity, and mutational robustness make distinct predictions about how the DFE will differ between species. Analyzing amino acid-changing variants from natural populations in a comparative population genomic framework, we find that humans have a higher proportion of strongly deleterious mutations than Drosophila melanogaster. Furthermore, when comparing the DFE across yeast, Drosophila, mice, and humans, the average selection coefficient becomes more deleterious with increasing species complexity. Last, pleiotropic genes have a DFE that is less variable than that of nonpleiotropic genes. Comparing four categories of theoretical models, only Fisher's geometrical model (FGM) is consistent with our findings. FGM assumes that multiple phenotypes are under stabilizing selection, with the number of phenotypes defining the complexity of the organism. Our results suggest that long-term population size and cost of complexity drive the evolution of the DFE, with many implications for evolutionary and medical genomics.

Fifteen Years Later: Hard and Soft Selection Sweeps Confirm a Large Population Number for HIV In Vivo

Fifteen Years Later: Hard and Soft Selection Sweeps Confirm a Large Population Number for HIV In Vivo

Population Growth Inflates the Per-Individual Number of Deleterious Mutations and Reduces Their Mean Effect

This study addresses the question of how purifying selection operates during recent rapid population growth such as has been experienced by human populations. This is not a straightforward problem because the human population is not at equilibrium: population genetics predicts that, on the one hand, the efficacy of natural selection increases as population size increases, eliminating ever more weakly deleterious variants; on the other hand, a larger number of deleterious mutations will be introduced into the population and will be more likely to increase in their number of copies as the population grows. To understand how patterns of human genetic variation have been shaped by the interaction of natural selection and population growth, we examined the trajectories of mutations with varying selection coefficients, using computer simulations. We observed that while population growth dramatically increases the number of deleterious segregating sites in the population, it only mildly increases the number carried by each individual. Our simulations also show an increased efficacy of natural selection, reflected in a higher fraction of deleterious mutations eliminated at each generation and a more efficient elimination of the most deleterious ones. As a consequence, while each individual carries a larger number of deleterious alleles than expected in the absence of growth, the average selection coefficient of each segregating allele is less deleterious. Combined, our results suggest that the genetic risk of complex diseases in growing populations might be distributed across a larger number of more weakly deleterious rare variants.

SnIPRE: selection inference using a Poisson random effects model.

We present an approach for identifying genes under natural selection using polymorphism and divergence data from synonymous and non-synonymous sites within genes. A generalized linear mixed model is used to model the genome-wide variability among categories of mutations and estimate its functional consequence. We demonstrate how the model's estimated fixed and random effects can be used to identify genes under selection. The parameter estimates from our generalized linear model can be transformed to yield population genetic parameter estimates for quantities including the average selection coefficient for new mutations at a locus, the synonymous and non-synynomous mutation rates, and species divergence times. Furthermore, our approach incorporates stochastic variation due to the evolutionary process and can be fit using standard statistical software. The model is fit in both the empirical Bayes and Bayesian settings using the lme4 package in R, and Markov chain Monte Carlo methods in WinBUGS. Using simulated data we compare our method to existing approaches for detecting genes under selection: the McDonald-Kreitman test, and two versions of the Poisson random field based method MKprf. Overall, we find our method universally outperforms existing methods for detecting genes subject to selection using polymorphism and divergence data.

Statistical Inference of Selection and Divergence from a Time-Dependent Poisson Random Field Model

We apply a recently developed time-dependent Poisson random field model to aligned DNA sequences from two related biological species to estimate selection coefficients and divergence time. We use Markov chain Monte Carlo methods to estimate species divergence time and selection coefficients for each locus. The model assumes that the selective effects of non-synonymous mutations are normally distributed across genetic loci but constant within loci, and synonymous mutations are selectively neutral. In contrast with previous models, we do not assume that the individual species are at population equilibrium after divergence. Using a data set of 91 genes in two Drosophila species, D. melanogaster and D. simulans, we estimate the species divergence time (or 1.68 million years, assuming the haploid effective population size years) and a mean selection coefficient per generation . Although the average selection coefficient is positive, the magnitude of the selection is quite small. Results from numerical simulations are also presented as an accuracy check for the time-dependent model.

Clines with partial panmixia in an unbounded unidimensional habitat

In geographically structured populations, global panmixia can be regarded as the limiting case of long-distance migration. The effect of incorporating partial panmixia into diallelic single-locus clines maintained by migration and selection in an unbounded unidimensional habitat is investigated. Migration and selection are both weak. The former is homogenous and isotropic; the latter has no dominance. The population density is uniform. A simple, explicit formula is derived for the maximum value β0 of the scaled panmictic rate β for which a cline exists. The former depends only on the asymptotic values of the scaled selection coefficient. If the two alleles have the same average selection coefficient, there exists a unique, globally asymptotically stable cline for every β≥0. Otherwise, if β≥β0, the allele with the greater average selection coefficient is ultimately fixed. If β<β0, there exists a unique, globally asymptotically stable cline, and some polymorphism is retained even infinitely far from its center. The gene frequencies at infinity are determined by a continuous-time, two-deme migration-selection model. An explicit expression is deduced for the monotone cline in a step-environment. These results differ fundamentally from those for the classical cline without panmixia.

Estimate of effective recombination rate and average selection coefficient for HIV in chronic infection

HIV adaptation to a host in chronic infection is simulated by means of a Monte-Carlo algorithm that includes the evolutionary factors of mutation, positive selection with varying strength among sites, random genetic drift, linkage, and recombination. By comparing two sensitive measures of linkage disequilibrium (LD) and the number of diverse sites measured in simulation to patient data from one-time samples of pol gene obtained by single-genome sequencing from representative untreated patients, we estimate the effective recombination rate and the average selection coefficient to be on the order of 1% per genome per generation (10(-5) per base per generation) and 0.5%, respectively. The adaptation rate is twofold higher and fourfold lower than predicted in the absence of recombination and in the limit of very frequent recombination, respectively. The level of LD and the number of diverse sites observed in data also range between the values predicted in simulation for these two limiting cases. These results demonstrate the critical importance of finite population size, linkage, and recombination in HIV evolution.

Comparing Mutational and Standing Genetic Variability for Fitness and Size inCaenorhabditis briggsaeandC. elegans

The genetic variation present in a species depends on the interplay between mutation, population size, and natural selection. At mutation-(purifying) selection balance (MSB) in a large population, the standing genetic variance for a trait (VG) is predicted to be proportional to the mutational variance for the trait (VM); VM is proportional to the mutation rate for the trait. The ratio VM/VG predicts the average strength of selection (S) against a new mutation. Here we compare VM and VG for lifetime reproductive success (approximately fitness) and body volume in two species of self-fertilizing rhabditid nematodes, Caenorhabditis briggsae and C. elegans, which the evidence suggests have different mutation rates. Averaged over traits, species, and populations within species, the relationship between VG and VM is quite stable, consistent with the hypothesis that differences among groups in standing variance can be explained by differences in mutational input. The average (homozygous) selection coefficient inferred from VM/VG is a few percent, smaller than typical direct estimates from mutation accumulation (MA) experiments. With one exception, the variance present in a worldwide sample of these species is similar to the variance present within a sample from a single locale. These results are consistent with specieswide MSB and uniform purifying selection, but genetic draft (hitchhiking) is a plausible alternative possibility.

Uncovering the Footprint of Positive Selection on the X Chromosome of Drosophila melanogaster

A usual approach to detect the spatial footprint left by recent adaptive events has been to follow up putative candidates emerging from multilocus scans of variation by sequencing additional fragments. We have used a similar experimental and analytical approach to study variation at 15 independently evolving and randomly chosen regions of the X chromosome of Drosophila melanogaster. These incompletely sequenced regions, each extending over approximately 40 kb, were subjected to two tests of positive selection that take into account the spatial distribution of nucleotide variation. Our analysis of variation at these genomic regions in a European population of D. melanogaster has allowed us to uncover a candidate region for positive selection and to empirically evaluate the comparative performance of the two tests of selection under a bottleneck scenario. Moreover, the boundaries here estimated for both the rate of adaptive substitution (delta) and the average selection coefficient (s) would support previous estimates obtained by maximum likelihood that suggest rather strong but uncommon positive selection.

Genetic (Co)Variation for Life Span in Rhabditid Nematodes: Role of Mutation, Selection, and History

The evolutionary mechanisms maintaining genetic variation in life span, particularly post-reproductive life span, are poorly understood. We characterized the effects of spontaneous mutations on life span in the rhabditid nematodes Caenorhabditis elegans and C. briggsae and standing genetic variance for life span and correlation of life span with fitness in C. briggsae. Mutations decreased mean life span, a signature of directional selection. Mutational correlations between life span and fitness were consistently positive. The average selection coefficient against new mutations in C. briggsae was approximately 2% when homozygous. The pattern of phylogeographic variation in life span is inconsistent with global mutation-selection balance (MSB), but MSB appears to hold at the local level. Standing genetic correlations in C. briggsae reflect mutational correlations at a local scale but not at a broad phylogeographic level. At the local scale, results are broadly consistent with predictions of the "mutation accumulation" hypothesis for the evolution of aging.

Model-Based Transition Management

<h3>Abstract</h3> Most natural environments exhibit a substantial component of random variation. Such environmental noise is expected to cause random fluctuations in natural selection, affecting the predictability of evolution. But despite a long-standing theoretical interest for understanding the population genetic consequences of stochastic environments, there has been a dearth of empirical validation and estimation of the underlying parameters of this theory. Indeed, tracking the genetics of a large number of replicate lines under a controlled level of environmental stochasticity is particularly challenging. Here, we tackled this problem by resorting to an automated experimental evolution approach. We used a liquid-handling robot to expose over a hundred lines of the micro-alga <i>Dunaliella salina</i> to randomly fluctuating salinity over a continuous range, with controlled mean, variance, and autocorrelation. We then tracked the frequency of one of two competing strains through amplicon sequencing of a nuclear and choloroplastic barcode sequences. We show that the magnitude of environmental fluctuations (variance), but also their predictability (autocorrelation), have large impacts on the average selection coefficient. Furthermore, the stochastic variance in population genetic change is substantially higher in a fluctuating environment. Reaction norms of selection coefficients and growth rates of single strains against the environment captured the mean response accurately, but failed to explain the high variance induced by environmental stochasticity. Overall, our results provide exceptional insights on the prospects for understanding and predicting genetic evolution in randomly fluctuating environments.

Strength of the purifying selection against different categories of the point mutations in the coding regions of the human genome

Using available Information on the total absolute size of the coding region of the human genome, data on codon usage and pseudogene-derived mutation rates for different single nucleotide substitutions we have estimated, for the human genome, the potential numbers of mutation events capable to produce: (1) nonsense; (2) missense (radical and conservative); (3) silent; (4) splice; and (5) protein-elongating (those changing wild-type stop codon into an amino acid encoding codon) mutations. We used the NCBI dbSNP database to retrieve data on the observed number of polymorphisms of each category. The fraction of polymorphisms in each category among all potential events in the genome depends on the strength of selection: the higher the rate of polymorphism, the weaker the selection. We used nonsense mutations as a referent group. Compared with nonsense mutations, we found that the relative selection coefficient against protein-elongating mutations was 21%, and the relative selection was 12% against missense mutations. Radical missense mutations were found to be four times more deleterious compared to conservative ones. Surprisingly, we found that silent mutations on average are not neutral; with the average harmfulness of 3% of nonsense mutations. Silent mutations may be deleterious when they affect splicing by creating cryptic donor-acceptor sites or by disturbing exonic splicing enhancers (ESESs). The average selection coefficient against splice mutations was 48% of that against nonsense mutations. Converting the relative selection coefficients into absolute ones using data on loss-of-function mutations in Saccharomyces cerevisiae and Caenorhabditis elegans, or by analysis of the expected frequency of mutations in the human genome, suggested that genetic drift could play a role in population dynamics of conservative missense and silent mutations.

Mutations of intermediate effect are responsible for adaptation in evolvingPseudomonas fluorescenspopulations

The fixation of a beneficial mutation represents the first step in adaptation, and the average effect of such mutations is therefore a fundamental property of evolving populations. It is nevertheless poorly characterized because the rarity of beneficial mutations makes it difficult to obtain reliable estimates of fitness. We obtained 68 genotypes each containing a single fixed beneficial mutation from experimental populations of Pseudomonas fluorescens, evolving in medium with serine as the sole carbon source and estimated the selective advantage of each by competition with the ancestor. The distribution of selection coefficients is modal and closely resembles the Weibull distribution. The average selection coefficient (2.1) and beneficial mutation rate (3.8x10(-8)) are high relative to previous studies, possibly because the ancestral population grows poorly in serine-limited medium. Our experiment suggests that the initial stages of adaptation to stressful environments will involve the substitution of mutations with large effect on fitness.

Rapid Evolution of β-Glucuronidase Specificity by Saturation Mutagenesis of an Active Site Loop

Protein engineers have widely adopted directed evolution as a design algorithm, but practitioners have not come to a consensus about the best method to evolve protein molecular recognition. We previously used DNA shuffling to direct the evolution of Escherichia coli beta-glucuronidase (GUS) variants with increased beta-galactosidase activity. Epistatic (synergistic) mutations in amino acids 557, 566, and 568, which are part of an active site loop, were identified in that experiment (Matsumura, I., and Ellington, A. D. (2001) J. Mol. Biol. 305, 331-339). Here we show that site saturation mutagenesis of these residues, overexpression of the resulting library in E. coli, and high throughput screening led to the rapid evolution of clones exhibiting increased activity in reactions with p-nitrophenyl-beta-d-xylopyranoside (pNP-xyl). The xylosidase activities of the 14 fittest clones were 30-fold higher on average than that of the wild-type GUS. The 14 corresponding plasmids were pooled, amplified by long PCR, self-ligated with T4 DNA ligase, and transformed into E. coli. Thirteen clones exhibiting an average of 80-fold improvement in xylosidase activity were isolated in a second round of screening. One of the evolved proteins exhibited a approximately 200-fold improvement over the wild type in reactivity (k(cat)/K(m)) with pNP-xyl, with a 290,000-fold inversion of specificity. Sequence analysis of the 13 round 2 isolates suggested that all were products of intermolecular recombination events that occurred during whole plasmid PCR. Further rounds of evolution using DNA shuffling and staggered extension process (StEP) resulted in modest improvement. These results underscore the importance of epistatic interactions and demonstrate that they can be optimized through variations of the facile whole plasmid PCR technique.

Recombination, Dominance and Selection on Amino Acid Polymorphism in the Drosophila Genome: Contrasting Patterns on the X and Fourth Chromosomes

Surveys of nucleotide polymorphism and divergence indicate that the average selection coefficient on Drosophila proteins is weakly positive. Similar surveys in mitochondrial genomes and in the selfing plant Arabidopsis show that weak negative selection has operated. These differences have been attributed to the low recombination environment of mtDNA and Arabidopsis that has hindered adaptive evolution through the interference effects of linkage. We test this hypothesis with new sequence surveys of proteins lying in low recombination regions of the Drosophila genome. We surveyed >3800 bp across four proteins at the tip of the X chromosome and >3600 bp across four proteins on the fourth chromosome in 24 strains of D. melanogaster and 5 strains of D. simulans. This design seeks to study the interaction of selection and linkage by comparing silent and replacement variation in semihaploid (X chromosome) and diploid (fourth chromosome) environments lying in regions of low recombination. While the data do indicate very low rates of exchange, all four gametic phases were observed both at the tip of the X and across the fourth chromosome. Silent variation is very low at the tip of the X (thetaS = 0.0015) and on the fourth chromosome (thetaS = 0.0002), but the tip of the X shows a greater proportional loss of variation than the fourth shows relative to normal-recombination regions. In contrast, replacement polymorphism at the tip of the X is not reduced (thetaR = 0.00065, very close to the X chromosome average). MK and HKA tests both indicate a significant excess of amino acid polymorphism at the tip of the X relative to the fourth. Selection is significantly negative at the tip of the X (Nes = -1.53) and nonsignificantly positive on the fourth (Nes approximately 2.9), analogous to the difference between mtDNA (or Arabidopsis) and the Drosophila genome average. Our distal X data are distinct from regions of normal recombination where the X shows a deficiency of amino acid polymorphism relative to the autosomes, suggesting more efficient selection against recessive deleterious replacement mutations. We suggest that the excess amino acid polymorphism on the distal X relative to the fourth chromosome is due to (1) differences in the mutation rate for selected mutations on the distal X or (2) a greater relaxation of selection from stronger linkage-related interference effects on the distal X. This relaxation of selection is presumed to be greater in magnitude than the difference in efficiency of selection between X-linked vs. autosomal selection.

MUTATION, SELECTION, AND THE MAINTENANCE OF LIFE-HISTORY VARIATION IN A NATURAL POPULATION.

In an effort to provide insight into the role of mutation in the maintenance of genetic variance for life-history traits, we accumulated spontaneous mutations in 10 sets of clonal replicates of Daphnia pulex for approximately 30 generations and compared the variance generated by mutation with the standing level of variation in the wild population. Mutations for quantitative traits appear to arise at a fairly high rate in this species, on the order of at least 0.6 per character per generation, but have relatively small heterozygous effects, changing the phenotype by less than 2.5% of the mean. The mean persistence time of a new mutation affecting life-history/body-size traits is approximately 40 generations in the natural population, which requires an average selection coefficient against new mutations of approximately 3% in the heterozygous state. These data are consistent with the idea that the vast majority of standing genetic variance for life-history characters may be largely a consequence of the recurrent introduction of transient cohorts of mutations that are at least conditionally deleterious and raise issues about the meaning of conventional measures of standing levels of variation for fitness-related traits.