Quantitative genetics of ovariole number in Drosophila melanogaster. II. Mutational variation and genotype-environment interaction.

The rare alleles model of mutation-selection balance (MSB) hypothesis for the maintenance of genetic variation was evaluated for two quantitative traits, ovariole number and body size. Mutational variances (VM) for these traits, estimated from mutation accumulation lines, were 4.75 and 1.97 x 10(-4) times the environmental variance (VE), respectively. The mutation accumulation lines were studied in three environments to test for genotype x environment interaction (GEI) of new mutations; significant mutational GEI was found for both traits. Mutations for ovariole number have a quadratic relationship with competitive fitness, suggesting stabilizing selection for the trait; there is no significant correlation between mutations for body size and competitive fitness. Under MSB, the ratio of segregating genetic variance, VG, to mutational variance, VM, estimates the inverse of the selection coefficient against a heterozygote for a new mutation. Estimates of VG/VM for ovariole number and body size were both approximately 1.1 x 10(4). Thus, MSB can explain the level of variation, if mutations affecting these traits are under very weak selection, which is inconsistent with the empirical observation of stabilizing selection, or if the estimate of VM is biased downward by two orders of magnitude. GEI is a possible alternative explanation.     

Pleiotropic model of maintenance of quantitative genetic variation at mutation-selection balance

A pleiotropic model of maintenance of quantitative genetic variation at mutation-selection balance is investigated. Mutations have effects on a metric trait and deleterious effects on fitness, for which a bivariate gamma distribution is assumed. Equations for calculating the strength of apparent stabilizing selection (V(s)) and the genetic variance maintained in segregating populations (V(G)) were derived. A large population can hold a high genetic variance but the apparent stabilizing selection may or may not be relatively strong, depending on other properties such as the distribution of mutation effects. If the distribution of mutation effects on fitness is continuous such that there are few nearly neutral mutants, or a minimum fitness effect is assumed if most mutations are nearly neutral, V(G) increases to an asymptote as the population size increases. Both V(G) and V(s) are strongly affected by the shape of the distribution of mutation effects. Compared with mutants of equal effect, allowing their effects on fitness to vary across loci can produce a much higher V(G) but also a high V(s) (V(s) in phenotypic standard deviation units, which is always larger than the ratio V(P)/V(m)), implying weak apparent stabilizing selection. If the mutational variance V(m) is approximately 10(-3)V(e) (V(e), environmental variance), the model can explain typical values of heritability and also apparent stabilizing selection, provided the latter is quite weak as suggested by a recent review.     

Quantitative genetic variation in an island population of the speckled wood butterfly (Pararge aegeria)

Evidence of changes in levels of genetic variation in the field is scarce. Theoretically, selection and a bottleneck may lead to the depletion of additive genetic variance (V(A)) but not of nonadditive, dominance variance (V(D)), although a bottleneck may converse V(D) to V(A). Here we analyse quantitative genetic variation for the Speckled Wood butterfly Pararge aegeria on the island of Madeira about 120 generations after first colonisation. Colonisation of the island involved both a bottleneck and strong natural selection, changing the average value of traits. Several life history and morphological traits with varying levels of change since colonisation were analysed. In accordance with expectations, all traits except one showed relatively low levels of V(A), with an average heritability (h(2)) of 0.078. Levels of V(D) for these traits were relatively high, 20-94% of total variance and on average 80% of V(G). The exception was a morphological trait that probably had not experienced strong natural selection after colonisation, for which a h(2) of 0.27 was found. Another interesting observation is that the population seems resistant to inbreeding effects, which may be the result of purging of deleterious alleles.     

Simultaneous Estimation of Additive and Mutational Genetic Variance in an Outbred Population of Drosophila serrata

How new mutations contribute to genetic variation is a key question in biology. Although the evolutionary fate of an allele is largely determined by its heterozygous effect, most estimates of mutational variance and mutational effects derive from highly inbred lines, where new mutations are present in homozygous form. In an attempt to overcome this limitation, middle-class neighborhood (MCN) experiments have been used to assess the fitness effect of new mutations in heterozygous form. However, because MCN populations harbor substantial standing genetic variance, estimates of mutational variance have not typically been available from such experiments. Here we employ a modification of the animal model to analyze data from 22 generations of Drosophila serrata bred in an MCN design. Mutational heritability, measured for eight cuticular hydrocarbons, 10 wing-shape traits, and wing size in this outbred genetic background, ranged from 0.0006 to 0.006 (with one exception), a similar range to that reported from studies employing inbred lines. Simultaneously partitioning the additive and mutational variance in the same outbred population allowed us to quantitatively test the ability of mutation-selection balance models to explain the observed levels of additive and mutational genetic variance. The Gaussian allelic approximation and house-of-cards models, which assume real stabilizing selection on single traits, both overestimated the genetic variance maintained at equilibrium, but the house-of-cards model was a closer fit to the data. This analytical approach has the potential to be broadly applied, expanding our understanding of the dynamics of genetic variance in natural populations.     

Inbreeding Depression and Inferred Deleterious-Mutation Parameters in Daphnia

DENG and LYNCH recently proposed a method for estimating deleterious genomic mutation parameters from changes in the mean and genetic variance of fitness traits upon inbreeding in outcrossing populations. Such observations are readily acquired in cyclical parthenogens. Selfing and life-table experiments were performed for two such Daphnia populations. We observed a significant inbreeding depression and an increase of genetic variance for all traits analyzed. DENG and LYNCH's original procedures were extended to estimate genomic mutation rate (U), mean dominance coefficient (h), mean selection coefficient (s), and scaled genomic mutational variance (V(m)/V(e)). On average, U, h, s and V(m)/V(e) (^ indicates an estimate) are 0.74, 0.30, 0.14 and 4.6E-4, respectively. For the true values, the U and h are lower bounds, and s and V(m)/V(e) upper bounds. The present U, h and V(m)/V(e) are in general concordance with earlier results. The discrepancy between the present s and that from mutation-accumulation experiments in Drosophila (~0.04) is discussed. It is shown that different reproductive modes do not affect gene frequency at mutation-selection equilibrium if mutational effects on fitness are multiplicative and not completely recessive.     

Multivariate stabilizing selection and pleiotropy in the maintenance of quantitative genetic variation

Abstract. We investigate maintenance of quantitative genetic variation at mutation-selection balance for multiple traits. The intrinsic strength of real stabilizing selection on one of these traits denoted the "target trait" and the observed strength of apparent stabilizing selection on the target trait can be quite different: the latter, which is estimable, is much smaller (i.e., implying stronger selection) than the former. Distinguishing them may enable the mutation load to be relaxed when considering multivariate stabilizing selection. It is shown that both correlations among mutational effects and among strengths of real stabilizing selection on the traits are not important unless they are high. The analysis for independent situations thus provides a good approximation to the case where mutant and stabilizing selection effects are correlated. Multivariate stabilizing selection can be regarded as a combination of stabilizing selection on the target trait and the pleiotropic direct selection on fitness that is solely due to the effects of real stabilizing selection on the hidden traits. As the overall fitness approaches a constant value as the number of traits increases, multivariate stabilizing selection can maintain abundant genetic variance only under quite weak selection. The common observations of high polygenic variance and strong stabilizing selection thus imply that if the mutation-selection balance is the true mechanism of maintenance of genetic variation, the apparent stabilizing selection cannot arise solely by real stabilizing selection simultaneously on many metric traits.     

GENETIC COVARIANCE OF FITNESS CORRELATES: WHAT GENETIC CORRELATIONS ARE MADE OF AND WHY IT MATTERS

The genetic variance-covariance matrix, G, is determined in part by functional architecture, the pathways by which variation in genotype influences phenotype. I develop a simple architectural model for G for two traits under directional selection constrained by their dependence on a common limiting resource. I assume that genetic variance is maintained by mutation-selection balance. The relative numbers of loci that play a role in acquiring versus allocating a limiting resource play a crucial role in determining genetic covariance. If many loci are involved in acquiring a resource, genetic covariance may be either negative or positive at equilibrium, depending on the fitness function and the input of mutational variance. The form of G does not necessarily reveal the constraint on resource acquisition inherent in the system, and therefore studies estimating G do not test for the existence of life-history tradeoffs. Characters may evolve in patterns that are unpredictable from G. Experiments are suggested that would indicate if this model could explain observations of positive genetic covariance.     

Temporal uniformity of the spontaneous mutational variance of quantitative traits in Drosophila melanogaster

Spontaneous mutations were allowed to accumulate over 209 generations in more than 100 lines, all of them independently derived from a completely homozygous population of Drosophila melanogaster and subsequently maintained under strong inbreeding (equivalent to full-sib mating). Traits scored were: abdominal (AB) and sternopleural (ST) bristle number, wing length (WL) and egg-to-adult viability (V). On two occasions--early (generations 93-122) and late (generations 169-209)--ANOVA estimates of the mutational variance and the mutational line x generation interaction variance were obtained. Mutational heritabilities of morphological traits ranged from 2 x 10(-4) to 2 x 10(-3) and the mutational coefficient of variation of viability was 0.01. For AB, WL and V, temporal uniformity of the mutational variance was observed. However, a fluctuation of the mutational heritability of ST was detected and could be ascribed to random genotype x environment interaction.     

Influence of dominance, leptokurtosis and pleiotropy of deleterious mutations on quantitative genetic variation at mutation-selection balance

In models of maintenance of genetic variance (V (G)) it has often been assumed that mutant alleles act additively. However, experimental data show that the dominance coefficient varies among mutant alleles and those of large effect tend to be recessive. On the basis of empirical knowledge of mutations, a joint-effect model of pleiotropic and real stabilizing selection that includes dominance is constructed and analyzed. It is shown that dominance can dramatically alter the prediction of equilibrium V (G). Analysis indicates that for the situations where mutations are more recessive for fitness than for a quantitative trait, as supported by the available data, the joint-effect model predicts a significantly higher V (G) than does an additive model. Importantly, for what seem to be realistic distributions of mutational effects (i.e., many mutants may not affect the quantitative trait substantially but are likely to affect fitness), the observed high levels of genetic variation in the quantitative trait under strong apparent stabilizing selection can be generated. This investigation supports the hypothesis that most V (G) comes from the alleles nearly neutral for fitness in heterozygotes while apparent stabilizing selection is contributed mainly by the alleles of large effect on the quantitative trait. Thus considerations of dominance coefficients of mutations lend further support to our previous conclusion that mutation-selection balance is a plausible mechanism of the maintenance of the genetic variance in natural populations.     

Effects of spontaneous mutation accumulation on sex ratio traits in a parasitoid wasp

Sex allocation theory has proved extremely successful at predicting when individuals should adjust the sex of their offspring in response to environmental conditions. However, we know rather little about the underlying genetics of sex ratio or how genetic architecture might constrain adaptive sex-ratio behavior. We examined how mutation influenced genetic variation in the sex ratios produced by the parasitoid wasp Nasonia vitripennis. In a mutation accumulation experiment, we determined the mutability of sex ratio, and compared this with the amount of genetic variation observed in natural populations. We found that the mutability (h(2)(m)) ranges from 0.001 to 0.002, similar to estimates for life-history traits in other organisms. These estimates suggest one mutation every 5-60 generations, which shift the sex ratio by approximately 0.01 (proportion males). In this and other studies, the genetic variation in N. vitripennis sex ratio ranged from 0.02 to 0.17 (broad-sense heritability, H(2)). If sex ratio is maintained by mutation-selection balance, a higher genetic variance would be expected given our mutational parameters. Instead, the observed genetic variance perhaps suggests additional selection against sex-ratio mutations with deleterious effects on other fitness traits as well as sex ratio (i.e., pleiotropy), as has been argued to be the case more generally.     

Redistribution of gene frequency and changes of genetic variation following a bottleneck in population size

Although the distribution of frequencies of genes influencing quantitative traits is important to our understanding of their genetic basis and their evolution, direct information from laboratory experiments is very limited. In theory, different models of selection and mutation generate different predictions of frequency distributions. When a large population at mutation-selection balance passes through a rapid bottleneck in size, the frequency distribution of genes is dramatically altered, causing changes in observable quantities such as the mean and variance of quantitative traits. We investigate the gene frequency distribution of a population at mutation-selection balance under a joint-effect model of real stabilizing and pleiotropic selection and its redistribution and thus changes of the genetic properties of metric and fitness traits after the population passes a rapid bottleneck and expands in size. If all genes that affect the trait are neutral with respect to fitness, the additive genetic variance (VA) is always reduced by a bottleneck in population size, regardless of their degree of dominance. For genes that have been under selection, VA increases following a bottleneck if they are (partially) recessive, while the dominance variance increases substantially for any degree of dominance. With typical estimates of mutation parameters, the joint-effect model can explain data from laboratory experiments on the effect of bottlenecking on fitness and morphological traits, providing further support for it as a plausible mechanism for maintenance of quantitative genetic variation.     

EMS-induced polygenic mutation rates for nine quantitative characters in Drosophila melanogaster.

Polygenic mutations were induced by treating Drosophila melanogaster adult males with 2.5 mM EMS. The treated second chromosomes, along with untreated controls, were then made homozygous, and five life history, two behavioral, and two morphological traits were measured. EMS mutagenesis led to reduced performance for life history traits. Changes in means and increments in genetic variance were relatively much higher for life history than for morphological traits, implying large differences in mutational target size. Maximum likelihood was used to estimate mutation rates and parameters of distributions of mutation effects, but parameters were strongly confounded with one another. Several traits showed evidence of leptokurtic distributions of effects and mean effects smaller than a few percent of trait means. Distributions of effects for all traits were strongly asymmetrical, and most mutations were deleterious. Correlations between life history mutation effects were positive. Mutation parameters for one generation of spontaneous mutation were predicted by scaling parameter estimates from the EMS experiment, extrapolated to the whole genome. Predicted mutational coefficients of variation were in good agreement with published estimates. Predicted changes in means were up to 0.14% or 0.6% for life history traits, depending on the model of scaling assumed.     

Non-equivalent loci and mutation-selection balance

We consider the implications of mutationally non-equivalent loci for large populations of randomly mating diploid organisms under mutation-selection balance. Variation, across loci, of parameters such as the allelic mutational variance and the mutation rate, is shown to reduce the equilibrium genetic variance. This is proved to follow from the genetic variance contributed by a single locus having an underlying convexity. We give approximate results indicating the way small deviations of the mutational parameters, from their mean values, reduce the genetic variance. Numerical estimates of the size of the effect are given for more general variations of the parameters. Variation in the mutation rates has a significantly smaller effect than variation in the mutational variances. Under accepted parameter values, the reduction in genetic variance can be substantial.     

Spontaneous Mutation Rate of Modifiers of Metabolism in Drosophila

A rigorous test of our understanding of evolutionary quantitative genetics would be to predict accurately the equilibrium distribution of a character from empirical estimates of the relevant parameters in a mutation-selection-drift balance model. an aspect of this problem that is amenable to experimental analysis is the distribution of the effects of new mutations. This study quantifies the divergence among 200 lines of Drosophila melanogaster as they accumulated mutations on the second chromosome and estimates the rate of increase of variation and covariation in metabolic characters. Amounts of stored triacylglycerol and glycogen and the activities of a series of 12 metabolic enzymes were assayed in a subset of lines at generations 0, 11, 22, 33 and 44. Analyses of the rate of increase in the among-line variance in each trait allowed estimation of V(m)/V(e), the ratio of among-line variance added per generation to the environmental variance. Values of V(m)/V(e) for the second chromosome ranged from 0.0004 to 0.0289 per generation. Six of the 16 characters showed significant departure from a normal distribution, and several lines exhibited large changes in more than one character. The covariance of pairs of traits also was partitioned into a within-line component (environmental covariance, Cov(e)) and an among-line component (mutational covariance, Cov(m)). Both variances and covariance among lines increased over time, as assessed by linear regression, whereas environmental covariance showed no such trend. Results indicate that the quantitative genetic parameters describing the variation in metabolic traits are similar to those of other continuous characters.     

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.     

Evolvability of an avian life history trait declines with father's age

Studies of laboratory organisms have suggested that parental age affects the genetic variance of offspring traits. This effect can engender age-specific variance in genetic contributions to evolutionary change in heritable traits under directional selection, particularly in age-structured populations. Using long-term population data of the blue-footed booby (Sula nebouxii), we tested whether genetic variance of recruiting age varies with parental age. Using robust quantitative genetic models fitted to pedigree, we found a significant genotype-by-paternal age interaction for recruiting age. Genetic potential for adaptive change in recruiting age was greater in progeny of young (age 1-6 years) fathers (males: CV(A)=6.68; females: CV(A)=7.59) than those of middle age (7-9 years) fathers (males: CV(A) = 4.64; females: CV(A)=5.08) and old (10-14 years) fathers (CV(A)=0 for both sexes). Therefore, parental age dependence of heritable variance, in addition to age-related variation in survival and fecundity, should affect the strength of natural selection for evolutionary changes. Our results provide rare evidence for the influence of parental age on the evolutionary potential of a life history trait in a wild population.     

灰木莲种源幼苗叶片性状表型多样性分析

以越南收集的12个灰木莲（Manglietia conifera Dandy）种源为材料,对叶片形态性状（叶长、叶宽、叶面积、叶周长、长宽比、叶柄）以及微形态特征（气孔器密度、气孔器长、气孔器宽、气孔器面积、长宽比）进行测定,采用方差分析、变异系数、相关分析和主成分分析等方法进行分析。结果表明：灰木莲不同种源间的叶表型性状存在显著差异;种源中,LC2的叶形态性状的平均变异系数最大（22.09%）,TQ2的变异系数最小（12.76%）;叶表型性状中,叶面积的变异系数最大（28.60%）,气孔器宽的变异系数最小（5.19%）;相关性分析结果表明叶表型性状间存在显著或极显著的相关关系,而地理因素中经度与叶周长显著相关,经纬度与叶长宽比呈显著相关,海拔与叶表型性状间的相关性不显著（P<0.05）;主成分分析表明前3个主成分的累计贡献率达到了89.29%,基本代表原始性状的全部信息。灰木莲12个种源经聚类分析在欧式距离5阈值处可分为4类。灰木莲种源间的叶表型性状存在着丰富的变异,纬度对灰木莲叶形态特征有明显影响,灰木莲种源间和性状间的变异程度存在着差异,本研究为灰木莲遗传改良提供理论依据。     

Deleterious mutations and the genetic variance of male fitness components in Mimulus guttatus

Deleterious mutations are relevant to a broad range of questions in genetics and evolutionary biology. I present an application of the "biometric method" for estimating mutational parameters for male fitness characters of the yellow monkeyflower, Mimulus guttatus. The biometric method rests on two critical assumptions. The first is that experimental inbreeding changes genotype frequencies without changing allele frequencies; i.e., there is no genetic purging during the experiment. I satisfy this condition by employing a breeding design in which the parents are randomly extracted, fully homozygous inbred lines. The second is that all genetic variation is attributable to deleterious mutations maintained in mutation-selection balance. I explicitly test this hypothesis using likelihood ratios. Of the three deleterious mutation models tested, the first two are rejected for all characters. The failure of these models is due to an excess of additive genetic variation relative to the expectation under mutation-selection balance. The third model is not rejected for either of two log-transformed male fitness traits. However, this model imposes only "weak conditions" and is not sufficiently detailed to provide estimates for mutational parameters. The implication is that, if biometric methods are going to yield useful parameter estimates, they will need to consider mutational models more complicated than those typically employed in experimental studies.     

The evolution of male genitalia: patterns of genetic variation and covariation in the genital sclerites of the dung beetle Onthophagus taurus

Three main hypotheses, have been invoked to explain divergent genital evolution, the lock and key, pleiotropy, and sexual selection hypotheses, each of which make different predictions about how genital traits are inherited. Here we used a half-sib breeding design to examine the patterns of genetic variation and covariation between male genital sclerites, and their covariance with general body morphology in the dung beetle Onthophagus taurus. We found CV(A)'s and CV(P)'s were similar for both genital and general morphological traits and that CV(R)'s were large for both trait types. We found that male genital sclerites were negatively genetically correlated with general morphological traits. Variation in male genital morphology has direct implications for a male's fertilization success and the resulting sexual selection acting on male genitalia is predicted to maintain high levels of additive genetic variance. Contrary to this prediction, we found that individual genital sclerites all had low levels of additive genetic variance and large maternal and environmental sources of variation. Our data suggest that the genital sclerites in O. taurus are not inherited independently but as a genetically integrated unit. More importantly, the way the different sclerites function to influence male fertilization success reflects this genetic integration. Even though levels of V(A) in individual genital sclerites may be low, there may still be sufficient V(A) in multivariate trait space for selection to generate evolutionary change in the overall morphology of male genitalia.     

Mutation-selection balance for environmental variance

The role of mutation-selection balance in maintaining environmental variance (V(E)) of quantitative traits is investigated under the assumption that genotypes differ in the magnitude of phenotypic variance, given genotypic value. Thus, V(E) can be regarded as a quantitative trait. As stabilizing selection on phenotype favors genotypes contributing low V(E), mutations that decrease V(E) are more likely to become fixed than those that increase it, and therefore V(E) should decline. If, however, essentially all mutants increase V(E) and overall selection is sufficiently strong that no mutants become fixed, then V(E) can be maintained. The heritability of the trait is determined by the relative sizes of mutational effects on phenotypic mean and residual variance and is independent of mutation rate and pleiotropic effects. This conclusion is not robust for small populations because some mutants may become fixed, which indicates that other selective forces must be involved, such as an intrinsic cost of homogeneity.