Stabilizing Selection,Purifying Selection,and Mutational Bias in Finite Populations

Genomic traits such as codon usage and the lengths of noncoding sequences may be subject to stabilizing selection rather than purifying selection. Mutations affecting these traits are often biased in one direction. To investigate the potential role of stabilizing selection on genomic traits, the effects of mutational bias on the equilibrium value of a trait under stabilizing selection in a finite population were investigated, using two different mutational models. Numerical results were generated using a matrix method for calculating the probability distribution of variant frequencies at sites affecting the trait, as well as by Monte Carlo simulations. Analytical approximations were also derived, which provided useful insights into the numerical results. A novel conclusion is that the scaled intensity of selection acting on individual variants is nearly independent of the effective population size over a wide range of parameter space and is strongly determined by the logarithm of the mutational bias parameter. This is true even when there is a very small departure of the mean from the optimum, as is usually the case. This implies that studies of the frequency spectra of DNA sequence variants may be unable to distinguish between stabilizing and purifying selection. A similar investigation of purifying selection against deleterious mutations was also carried out. Contrary to previous suggestions, the scaled intensity of purifying selection with synergistic fitness effects is sensitive to population size, which is inconsistent with the general lack of sensitivity of codon usage to effective population size.     

The classical hitchhiking model with continuous mutational pressure and purifying selection

Detecting selective sweeps driven by strong positive selection and localizing the targets of selection in the genome play a major role in modern population genetics and genomics. Most of these analyses are based on the classical model of genetic hitchhiking proposed by Maynard Smith and Haigh (1974, Genetical Research, 23, 23). Here, we consider extensions of the classical two‐locus model. Introducing mutation at the strongly selected site, we analyze the conditions under which soft sweeps may arise. We identify a new parameter (the ratio of the beneficial mutation rate to the selection coefficient) that characterizes the occurrence of multiple‐origin soft sweeps. Furthermore, we quantify the hitchhiking effect when the polymorphism at the linked locus is not neutral but maintained in a mutation‐selection balance. In this case, we find a smaller relative reduction of heterozygosity at the linked site than for a neutral polymorphism. In our analysis, we use a semi‐deterministic approach; i.e., we analyze the frequency process of the beneficial allele in an infinitely large population when its frequency is above a certain threshold; however, for very small frequencies in the initial phase after the onset of selection we rely on diffusion theory.     

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.     

QUANTITATIVE GENETICS OF BRYOZOAN PHENOTYPIC EVOLUTION. II. ANALYSIS OF SELECTION AND RANDOM CHANGE IN FOSSIL SPECIES USING RECONSTRUCTED GENETIC PARAMETERS

The roles of natural selection and random genetic change in the punctuated phenotypic evolution of eight Miocene-Pliocene tropical American species of the cheilostome bryozoan Metrarabdotos are analyzed by quantitative genetic methods. Trait heritabilities and genetic covariances reconstructed by partitioning within- and among-colony phenotypic variance are similar to those previously obtained for living species of the cheilostome Stylopoma using breeding data. The hypothesis that differences in skeletal morphology between species of Metrarabdotos are entirely due to mutation and genetic drift cannot be rejected for reasonable rates of mutation maintained for periods brief enough to account for the geologically abrupt appearances of these species in the fossil record. Except for one pair of species, separated by the largest morphologic distance, directional selection acting alone would require unrealistically high rates of selective mortality to be maintained for these periods. Thus, directional selection is not strongly implicated in the divergence of Metrarabdotos species. Within species, rates of net phenotypic change are slow enough to require stabilizing selection, but mask large, relatively rapid fluctuations, all of which, however, can be attributed to chance departures from the mean phenotype by mutation and genetic drift, rather than to tracking environmental fluctuation by directional selection. The results are consistent with genetic models involving shifts between multiple adaptive peaks on which phenotypes remain more or less static through long-term stabilizing selection. Regardless of the degree to which directional selection may be involved in peak shifts, phenotypic differentiation is thus related to processes different than the pervasive stabilizing selection acting within species.     

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.     

Population size and the nature of genetic load in Gentianella germanica

Abstract Theory predicts a significant relationship between the size of a population and the magnitude and composition of its genetic load, but few natural populations have been investigated. We examined the magnitude of genetic load due to recessive deleterious alleles (GL) both segregating and fixed within Gentianella germanica populations of varying size by selfing and reciprocally crossing plants within and between natural populations according to a partial diallel design and by comparing the performance of the experimental progeny in a common-garden experiment. The results show that GL for total fitness in small populations (fewer than 200 plants) was mainly due to fixed recessive deleterious alleles, whereas GL for total fitness in larger populations (more than 200 plants) appeared to be mainly due to segregating deleterious recessive alleles. The total fitness of selfed plants increased with decreasing population size, indicating some purging of deleterious alleles associated with declining population sizes. The magnitudes of GL due to fixed deleterious alleles in small populations and segregating deleterious alleles in large populations, however, were overall similar, suggesting that purging selection was an insignificant force when compared to genetic drift in determining the magnitude of GL in small natural populations in this species. The results of this study highlight the importance of population size in determining the dynamics of genetic loads of natural populations and are overall in line with a large body of theoretical work indicating that small populations may face higher extinction risks due to the fixation and accumulation of deleterious alleles of small effect.     

Familial versus mass selection in small populations

We used diffusion approximations and a Markov-chain approach to investigate the consequences of familial selection on the viability of small populations both in the short and in the long term. The outcome of familial selection was compared to the case of a random mating population under mass selection. In small populations, the higher effective size, associated with familial selection, resulted in higher fitness for slightly deleterious and/or highly recessive alleles. Conversely, because familial selection leads to a lower rate of directional selection, a lower fitness was observed for more detrimental genes that are not highly recessive, and with high population sizes. However, in the long term, genetic load was almost identical for both mass and familial selection for populations of up to 200 individuals. In terms of mean time to extinction, familial selection did not have any negative effect at least for small populations (N ≤ 50). Overall, familial selection could be proposed for use in management programs of small populations since it increases genetic variability and short-term viability without impairing the overall persistence times.     

Heterosis in an isolated, effectively small, and self-fertilizing population of the flowering plant Leavenworthia alabamica

Mildly deleterious mutations are thought to play a major role in the extinction of natural populations, especially those that are small, isolated, or inbred. Self-fertilization should reduce the effective size of populations and simultaneously reduce migration between populations. A history of self-fertilization should therefore cause a population to harbor a substantial "local drift load" caused by the fixation of mildly deleterious mutations. This hypothesis was tested in Leavenworthia alabamica, which contains large, self-incompatible populations and smaller self-compatible populations with adaptations for self-fertilization. The fitness of offspring from within- and between-population crosses was compared to quantify heterosis caused by the masking of deleterious alleles in the heterozygous state. Little heterosis was observed in crosses between five large, self-incompatible populations and two of the three small, self-fertilizing populations of L. alabamica. However, the most geographically isolated and genetically divergent self-fertilizing population (Tuscumbia) exhibited a 110.2% increase in germination and a 73.6% increase in fitness, which is consistent with a sizeable local drift load. The finding of substantial heterosis for fitness supports the idea that small effective size, reproductive isolation, and self-fertilization can make populations particularly vulnerable to mutation accumulation.     

Drift load in populations of small size and low density

According to theory, drift load in randomly mating populations is determined by past population size, because enhanced genetic drift in small populations causes accumulation and fixation of recessive deleterious mutations of small effect. In contrast, segregating load due to mutations of low frequency should decline in smaller populations, at least when mutations are highly recessive and strongly deleterious. Strong local selection generally reduces both types of load. We tested these predictions in 13 isolated, outcrossing populations of Arabidopsis lyrata that varied in population size and plant density. Long-term size was estimated by expected heterozygosity at 20 microsatellite loci. Segregating load was assessed by comparing performance of offspring from selfings versus within-population crosses. Drift load was the heterosis effect created by interpopulation outbreeding. Results showed that segregating load was unrelated to long-term size. However, drift load was significantly higher in populations of small effective size and low density. Drift load was mostly expressed late in development, but started as early as germination and accumulated thereafter. The study largely confirms predictions of theory and illustrates that mutation accumulation can be a threat to natural populations.     

Book review of evolutionary genetics: Concepts,analysis, and practice

Recent technological advances have expanded and increased the resolution of studies in evolutionary biology, creating a need for a modern textbook that highlights the latest developments in the field. Evolutionary Genetics: Concepts, Analysis, and Practice, by Glenn‐Peter Sætre and Mark Ravinet (2019), as well as the book's accompanying online tutorials, provide a clear, up‐to‐date, and enjoyable introduction to evolutionary biology and genetics that explains fundamental evolutionary concepts, illustrates recent exciting findings, and offers hands‐on experience in analysing and interpreting genomic data. The book's accessible nature and emphasis on developing practical skills make it a valuable resource for undergraduate courses on evolutionary biology.     

Complexity, pleiotropy, and the fitness effect of mutations

One of the assumptions underlying many theoretical predictions in evolutionary biology concerns the distribution of the fitness effect of mutations. Approximations to this distribution have been derived using various theoretical approaches, of which Fisher's geometrical model is among the most popular ones. Two key concepts in this model are complexity and pleiotropy. Recent studies have proposed different methods for estimating how complexity varies across species, but their results have been contradictory. Here, we show that contradictory results are to be expected when the assumption of universal pleiotropy is violated. We develop a model in which the two key parameters are the total number of traits and the mean number of traits affected by a single mutation. We derive approximations for the distribution of the fitness effect of mutations when populations are either well-adapted or away from the optimum. We also consider drift load in a well-adapted population and show that it is independent of the distribution of the fitness effect of mutations. We show that mutation accumulation experiments can only measure the effect of the mean number of traits affected by mutations, whereas drift load only provides information about the total number of traits. We discuss the plausibility of the model.     

EPISTASIS,PLEIOTROPY, AND THE MUTATION LOAD IN SEXUAL AND ASEXUAL POPULATIONS

Mutation may impose a substantial load on populations, which varies according to the reproductive mode of organisms. Over the past years, various authors used adaptive landscape models to predict the long‐term effect of mutation on mean fitness; however, many of these studies assumed very weak mutation rates, so that at most one mutation segregates in the population. In this article, we derive several simple approximations (confirmed by simulations) for the mutation load at high mutation rate (U), using a general model that allows us to play with the number of selected traits (n), the degree of pleiotropy of mutations, and the shape of the fitness function (which affects the average sign and magnitude of epistasis among mutations). When mutations have strong fitness effects, the equilibrium fitness of sexuals and asexuals is close to ; under weaker mutational effects, sexuals reach a different regime where is a simple function of U and of a parameter describing the shape of the fitness function. Contrarily to weak mutation results showing that is an increasing function of population size and a decreasing function of n, these parameters may have opposite effects in sexual populations at high mutation rate.     

VARIATION IN THE STRENGTH AND SOFTNESS OF SELECTION ON DELETERIOUS MUTATIONS

Deleterious alleles constantly enter populations through mutation. Understanding the nature of selection against such alleles is required to assess their impact on populations. In a subdivided population, two distinct aspects of selection are important: the strength and softness of selection. Using Drosophila melanogaster, we estimated both aspects of selection for each of eight loci across two environments. These data allow us to test conflicting predictions about the factors affecting the softness of selection. First, we show that the softness of selection is not determined by ecological conditions alone. Second, we find that resource limitation makes selection stronger but does not make it softer. Third, we find that wild‐type individuals tend to benefit more than mutants from being reared with competitors of low genetic quality. This means that selection is effectively “harder” on mutants than wild types. A model is presented showing that the sensitivities of mutants and wild types to local competitors differentially affect equilibrium mutation frequency and measures of load.     

The phenotypic variance within plastic traits under migration-mutation-selection balance

How phenotypic variances of quantitative traits are influenced by the heterogeneity in environment is an important problem in evolutionary biology. In this study, both genetic and environmental variances in a plastic trait under migration-mutation-stabilizing selection are investigated. For this, a linear reaction norm is used to approximate the mapping from genotype to phenotype, and a population of clonal inheritance is assumed to live in a habitat consisting of many patches in which environmental conditions vary among patches and generations. The life cycle is assumed to be selection-reproduction-mutation-migration. Analysis shows that phenotypic plasticity is adaptive if correlations between the optimal phenotype and environment have become established in both space and/or time, and it is thus possible to maintain environmental variance (V(E)) in the plastic trait. Under the special situation of no mutation but maximum migration such that separate patches form an effective single-site habitat, the genotype that maximizes the geometric mean fitness will come to fixation and thus genetic variance (V(G)) cannot be maintained. With mutation and/or restricted migration, V(G) can be maintained and it increases with mutation rate but decreases with migration rate; whereas VE is little affected by them. Temporal variation in environmental quality increases V(G) while its spatial variance decreases V(G). Variation in environmental conditions may decrease the environmental variance in the plastic trait.     

Introduction of captive breeders to the wild: Harmful or beneficial?

This work focuses on the consequences on thegenetic load and the risk of extinction when anendangered population is exposed to recurrentintroductions from a captive population whereselection is somewhat relaxed. Our findingssuggest that, although selection pressuresmight be reduced in captivity, which leads tohigher frequency of deleterious alleles innatural populations (Lynch and O'Hely 2001),such a population structure could have positiveeffects on population fitness when threeconditions are met: (i) the time length of thesupplementation program does not exceed areasonable time frame, e.g., 20 generations (ii)introduction of captive individuals is kept ata low level, i.e., one or two individuals pergeneration (iii) the size of the captivepopulation is reasonably large, e.g., more than20 individuals. The positive effect is due tothe fact that the supplementation programdelays the increase of homozygosity of thenatural population. When migration from thewild towards captivity is also allowed, thebenefits with regard to genetic load increasesignificantly even for larger numbers ofcaptive immigrants and a higher number ofgenerations. We also worked out a model withexplicit demographic considerations(fluctuating population sizes, captive migrantsincrease the size of the wild population),which shows that the probability of extinctiondecreases significantly with the number ofintroduced individuals when short-termsupplementation programs are applied (up totwenty generations). Furthermore, anappropriate genetic management of the captivepopulation, such as the equalization of familysizes, could enhance the positive effects ofsuch supplementation programs.     

An estimator of the Opportunity for Selection that is independent of mean fitness

Variation among individuals in number of offspring (fitness, k) sets an upper limit to the evolutionary response to selection. This constraint is quantified by Crow's Opportunity for Selection (I), which is the variance in relative fitness (I = σ²_k/(u_k)²). Crow's I has been widely used but remains controversial because it depends on mean offspring number in a sample (). Here, I used a generalized Wright-Fisher model that allows for unequal probabilities of producing offspring to evaluate behavior of Crow's I and related indices under a wide range of sampling scenarios. Analytical and numerical results are congruent and show that rescaling the sample variance (s²_k) to its expected value at a fixed removes dependence of I on mean offspring number, but the result still depends on choice of . A new index is introduced, Δ_I = Π– E(Î_drift) = Π– 1/, which makes Î independent of sample without the need for variance rescaling. Δ_I has a straightforward interpretation as the component of variance in relative fitness that exceeds that expected under a null model of random reproductive success. Δ_I can be used to directly compare estimates of the Opportunity for Selection for samples from different studies, different sexes, and different life stages.     

Genetic linkage and natural selection

The prevalence of recombination in eukaryotes poses one of the most puzzling questions in biology. The most compelling general explanation is that recombination facilitates selection by breaking down the negative associations generated by random drift (i.e. Hill–Robertson interference, HRI). I classify the effects of HRI owing to: deleterious mutation, balancing selection and selective sweeps on: neutral diversity, rates of adaptation and the mutation load. These effects are mediated primarily by the density of deleterious mutations and of selective sweeps. Sequence polymorphism and divergence suggest that these rates may be high enough to cause significant interference even in genomic regions of high recombination. However, neither seems able to generate enough variance in fitness to select strongly for high rates of recombination. It is plausible that spatial and temporal fluctuations in selection generate much more fitness variance, and hence selection for recombination, than can be explained by uniformly deleterious mutations or species-wide selective sweeps.     

Fisher'S geometrical model of fitness landscape and variance in fitness within a changing environment

The fitness of an individual can be simply defined as the number of its offspring in the next generation. However, it is not well understood how selection on the phenotype determines fitness. In accordance with Fisher's fundamental theorem, fitness should have no or very little genetic variance, whereas empirical data suggest that is not the case. To bridge these knowledge gaps, we follow Fisher's geometrical model and assume that fitness is determined by multivariate stabilizing selection toward an optimum that may vary among generations. We assume random mating, free recombination, additive genes, and uncorrelated stabilizing selection and mutational effects on traits. In a constant environment, we find that genetic variance in fitness under mutation-selection balance is a U-shaped function of the number of traits (i.e., of the so-called "organismal complexity"). Because the variance can be high if the organism is of either low or high complexity, this suggests that complexity has little direct costs. Under a temporally varying optimum, genetic variance increases relative to a constant optimum and increasingly so when the mutation rate is small. Therefore, mutation and changing environment together can maintain high genetic variance. These results therefore lend support to Fisher's geometric model of a fitness landscape.