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.     

Within-generation mutation variance for litter size in inbred mice

The mutational input of genetic variance per generation (sigma(m)(2)) is the lower limit of the genetic variability in inbred strains of mice, although greater values could be expected due to the accumulation of new mutations in successive generations. A mixed-model analysis using Bayesian methods was applied to estimate sigma(m)(2) and the across-generation accumulated genetic variability on litter size in 46 generations of a C57BL/6J inbred strain. This allowed for a separate inference on sigma(m)(2) and on the additive genetic variance in the base population (sigma(a)(2)). The additive genetic variance in the base generation was 0.151 and quickly decreased to almost null estimates in generation 10. On the other hand, sigma(m)(2) was moderate (0.035) and the within-generation mutational variance increased up to generation 14, then oscillating between 0.102 and 0.234 in remaining generations. This pattern suggested the existence of a continuous uploading of genetic variability for litter size (h(2)=0.045). Relevant genetic drift was not detected in this population. In conclusion, our approach allowed for separate estimation of sigma(a)(2) and sigma(m)(2) within the mixed-model framework, and the heritability obtained highlighted the significant and continuous influence of new genetic variability affecting the genetic stability of inbred strains.     

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.     

Transcriptome‐wide effects of sexual selection on the fate of new mutations

Sexual selection on males is predicted to have widespread effects on genetic variation as a consequence of the pleiotropic allelic effects on sexual and nonsexual traits. We manipulated the opportunity for sexual selection on males during 27 generations of mutation accumulation in inbred lines of Drosophila serrata, and used a microarray platform to investigate the effect of sexual selection on the expression of 2689 genes. While gene expression signal was, on average, higher in the absence of sexual selection, this difference was small (0.1%). In contrast, sexual selection impacted substantially on the mutational variance in gene expression. Over all genes, mutational variance in gene expression was, on average, 42% higher when sexual selection operated than when it was absent. Our results indicate that sexual selection on males can generate widespread effects across the genome. An increase in mutational variance without a corresponding change in mean suggested that most expression traits were unlikely to be under direct sexual selection. Instead, the mutational variance in gene expression traits is consistent with divergence generated by widespread pleiotropic associations with traits affecting male mating success.     

Spontaneous mutational variation for body size in Caenorhabditis elegans

We measured the impact of new mutations on genetic variation for body size in two independent sets of C. elegans spontaneous mutation-accumulation (MA) lines, derived from the N2 strain, that had been maintained by selfing for 60 or 152 generations. The two sets of lines gave broadly consistent results. The change of among-line genetic variation between cryopreserved controls and the MA lines implied that broad sense heritability increased by 0.4% per generation. Overall, MA reduced mean body size by approximately 0.1% per generation. The genome-wide rate for mutations with detectable effects on size was estimated to be approximately 0.0025 per haploid genome per generation, and their mean effects were approximately 20%. The proportion of mutations that increase body size was estimated by maximum likelihood to be no more than 20%, suggesting that the amount of mutational variation available for selection for increased size could be quite small. This hypothesis was supported by an artificial selection experiment on adult body size, started from a single highly inbred N2 individual. We observed a strongly asymmetrical response to selection of a magnitude consistent with the input of mutational variance observed in the MA experiment.     

Polygenic Mutation in Drosophila Melanogaster: Non-Linear Divergence among Unselected Strains

A highly inbred strain of Drosophila melanogaster was subdivided into 20 replicate sublines that were maintained independently with 10 pairs of randomly sampled parents per generation for 180 generations. The variance between lines in abdominal and sternopleural bristle number increased little after 100 generations, in contrast to the neutral expectation of a linear increase; and the covariances of line means between different generations declined with increasing number of generations apart, in contrast to the neutral expectation of constant covariance. Thus, under a neutral model, the estimates of mutational variance were lower than for previous estimates from the first 100 generations of subline divergence. An autoregressive model was fitted to the variance of line means that indicated strong natural selection. There is no single unequivocal explanation for the results. Possible and nonexclusive alternatives include stabilizing selection on bristle number and deleterious effects on fitness of bristle mutations. The inferred strengths of selection on both traits are too high for stabilizing selection alone, and the between-line variance did not continue to increase sufficiently for pleiotropy alone to account for the observations. A third potential explanation that does not invoke selection is duplicate epistasis between mutations affecting bristle number.     

Spontaneous mutational effects on reproductive traits of arabidopsis thaliana

A study of spontaneous mutation in Arabidopsis thaliana was initiated from a single inbred Columbia founder; 120 lines were established and advanced 17 generations by single-seed descent. Here, we report an assay of reproductive traits in a random set of 40 lines from generations 8 and 17, grown together at the same time with plants representing generation 0. For three reproductive traits, mean number of seeds per fruit, number of fruits, and dry mass of the infructescence, the means did not differ significantly among generations. Nevertheless, by generation 17, significant divergence among lines was detected for each trait, indicating accumulation of mutations in some lines. Standardized measures of mutational variance accord with those obtained for other organisms. These findings suggest that the distribution of mutational effects for these traits is approximately symmetric, in contrast to the usual assumption that mutations have predominantly negative effects on traits directly related to fitness. Because distinct generations were grown contemporaneously, each line was represented by three sublines, and seeds were equal in age, these estimates are free of potentially substantial sources of bias. The finding of an approximately symmetric distribution of mutational effects invalidates the standard approach for inferring properties of spontaneous mutation and necessitates further development of more general approaches that avoid restrictions on the distribution of mutational effects.     

POLYGENIC MUTATION IN DROSOPHILA MELANOGASTER: ESTIMATES FROM DIVERGENCE AMONG INBRED STRAINS

A highly inbred line of Drosophila melanogaster was subdivided into 25 replicate sublines, which were independently maintained for 100 generations with 10 pairs of unselected flies per generation. The polygenic mutation rate (V_M) for two quantitative traits, abdominal and sternopleural bristle number, was estimated from divergence among sublines at 10 generation intervals from generations 30-100, and from response of each line to divergent selection after more than 65 generations of mutation accumulation. Estimates of V_M averaged over males and females both from divergence among lines and from response to selection within lines were 3.3 × 10^-3 V_E for abdominal bristles and 1.5 × 10^-3 V_E for sternopleural bristles, where V_E is the environmental variance. The actual rate of production of mutations affecting these traits may be considerably higher if the traits are under stabilizing selection, and if mutations affecting bristle number have deleterious effects on fitness. There was a substantial component of variance for sex × mutant effect interaction and the sublines evolved highly significant mutational variation in sex dimorphism of abdominal bristle number. Pleiotropic effects on sex dimorphism may be a general property of mutations at loci determining bristle number.     

Effects of Multiple Retrovirus Insertions on Quantitative Traits of Mice

To assess the potential to generate quantitative genetic variation by insertional mutagenesis in a vertebrate, lines of mice in which many provirus vector inserts segregated at a low initial frequency on an inbred background (insert lines) were subjected to divergent artificial selection on body weight at 6 weeks and responses and heritability estimates compared to control lines lacking inserts. Heritability estimates were more than 1.5 times greater in the insert lines than in the controls, but because the phenotypic variance was substantially higher in the insert lines the genetic variance was about 3 times greater. Realized heritability estimates tended to be lower than heritabilities estimated by an animal model which utilizes information in covariances between all relatives in the data set. A surprisingly large response to selection occurred in the inbred control line. Insert lines were about 20% less fertile than controls. Division of the selection lines into inbred sublines in the later generations of the experiment revealed substantially greater variation among sublines of the insert lines than among the controls. Heritabilities were similar to typical estimates for the trait in outbred populations. In conclusion, there was clear evidence of extra variation deriving from inserts, which has yet to be attributed to individual genes.     

SPONTANEOUS MUTATION ACCUMULATION IN MULTIPLE STRAINS OF THE GREEN ALGA,CHLAMYDOMONAS REINHARDTII

Estimates of mutational parameters, such as the average fitness effect of a new mutation and the rate at which new genetic variation for fitness is created by mutation, are important for the understanding of many biological processes. However, the causes of interspecific variation in mutational parameters and the extent to which they vary within species remain largely unknown. We maintained multiple strains of the unicellular eukaryote Chlamydomonas reinhardtii, for approximately 1000 generations under relaxed selection by transferring a single cell every ～10 generations. Mean fitness of the lines tended to decline with generations of mutation accumulation whereas mutational variance increased. We did not find any evidence for differences among strains in any of the mutational parameters estimated. The overall change in mean fitness per cell division and rate of input of mutational variance per cell division were more similar to values observed in multicellular organisms than to those in other single‐celled microbes. However, after taking into account differences in genome size among species, estimates from multicellular organisms and microbes, including our new estimates from C. reinhardtii, become substantially more similar. Thus, we suggest that variation in genome size is an important determinant of interspecific variation in mutational parameters.     

Polygenic mutation in Drosophila melanogaster: Mapping spontaneous mutations affecting sensory bristle number

Our ability to predict long-term responses to artificial and natural selection, and understand the mechanisms by which naturally occurring variation for quantitative traits is maintained, depends on detailed knowledge of the properties of spontaneous polygenic mutations, including the quantitative trait loci (QTL) at which mutations occur, mutation rates, and mutational effects. These parameters can be estimated by mapping QTL that cause divergence between mutation-accumulation lines that have been established from an inbred base population and selected for high and low trait values. Here, we have utilized quantitative complementation to deficiencies to map QTL at which spontaneous mutations affecting Drosophila abdominal and sternopleural bristle number have occurred in 11 replicate lines during 206 generations of divergent selection. Estimates of the numbers of mutations were consistent with diploid per-character mutation rates for bristle traits of 0.03. The ratio of the per-character mutation rate to total mutation rate (0.023) implies that >2% of the genome could affect just one bristle trait and that there must be extensive pleiotropy for quantitative phenotypes. The estimated mutational effects were not, however, additive and exhibited dependency on genetic background consistent with diminishing epistasis. However, these inferences must be tempered by the potential for epistatic interactions between spontaneous mutations and QTL affecting bristle number on the deficiency-bearing chromosomes, which could lead to overestimates in numbers of QTL and inaccurate inference of gene action.     

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.     

Mutation accumulation and the effect of copia insertions in Drosophila melanogaster

Repeated efforts to estimate the genomic deleterious mutation rate per generation (U) in Drosophila melanogaster have yielded inconsistent estimates ranging from 0.01 to nearly 1. We carried out a mutation-accumulation experiment with a cryopreserved control population in hopes of resolving some of the uncertainties raised by these estimates. Mutation accumulation (MA) was carried out by brother sister mating of 150 sublines derived from two inbred lines. Fitness was measured under conditions chosen to mimic the ancestral laboratory environment of these genotypes. We monitored the insertions of a transposable element, copia, that proved to accumulate at the unusually high rate of 0.24 per genome per generation in one of our MA lines. Mutational variance in fitness increased at a rate consistent with previous studies, yielding a mutational coefficient of variation greater than 3%. The performance of the cryopreserved control relative to the MA lines was inconsistent, so estimates of mutation rate by the Bateman-Mukai method are suspect. Taken at face value, these data suggest a modest decline in fitness of about 0.3% per generation. The element number of copia was a significant predictor of fitness within generations; on average, insertions caused a 0.76% loss in fitness, although the confidence limits on this estimate are wide.     

The Distribution of Mutation Effects on Viability in Drosophila Melanogaster

Parameters of continuous distributions of effects and rates of spontaneous mutation for relative viability in Drosophila are estimated by maximum likelihood from data of two published experiments on accumulation of mutations on protected second chromosomes. A model of equal mutant effects gives a poor fit to the data of the two experiments; higher likelihoods are obtained with leptokurtic distributions or for models in which there is more than one class of mutation effect. Minimum estimates of mutation rates (events per generation) at polygenes affecting viability on chromosome 2 are 0.14 and 0.068, but estimates are strongly confounded with other parameters in the model. Separate information on rates of molecular divergence between Drosophila species and from rates of movement of transposable elements is used to infer the overall genomic mutation rate in Drosophila, and the viability data are analyzed with mutation rate as a known parameter. If, for example, a mutation rate for chromosome 2 of 0.4 is assumed, maximum likelihood estimates of mean mutant effect on relative viability are 0.4% and 1%, but the majority of mutations have very much smaller effects than these values as distributions are highly leptokurtic. The methodology is applied to estimate viability effects of single P element insertional mutations. The mean effect per insertion is found to be higher, and their distribution is found to be less leptokurtic than for spontaneous mutations. The equilibrium genetic variance of viability predicted by a mutation-selection balance model with parameters estimated from the mutation accumulation experiments is similar to laboratory estimates of genetic variance of viability from natural populations of Drosophila.     

Estimation of additive genetic variance in commercial layer poultry and simulated populations under selection

Changes in genetic parameters over generations for a selected commercial population and simulated populations of poultry with different sizes were studied. The traits analyzed from the commercial population were rate of lay, age at first egg, egg weight, deformation, and body weight. In the simulated population, a trait measured on both sexes and a sex-limited trait, measured only on one sex, each with a heritability of 0.1 and 0.5, were analyzed. In the commercial and simulated populations, males and females were selected on the basis of family selection indexes and data was available only after many generations of selection. Parameters for each generation were estimated by fitting an animal model using derivative free maximum likelihood (DFREML) with different data structures. In structure 1, data included the given (base) generation for which the parameters were to be estimated, and all subsequent generations. In structure 2, only data on birds in the given generation and their progeny were included. In both structures, parents of base-generation birds were assumed unrelated and pedigrees traced back to these parents. With commercial data using structure 1, estimates of _a ² and h² decreased by 14 to 37% across five generations. With structure 2, no trends were observed, though estimates were lower than for structure 1. For simulated data, with a heritability of 0.1, both structures yielded apparently unbiased estimates of the observed additive genetic variances in the (selected) base generation, no matter how many generations of data were utilized, for both sex-limited and normal traits. However, with a heritability of 0.5 the estimated additive genetic variance for both types of trait decreased with a decrease in the number of generations used in the estimation. Estimates based on the first two generations underestimated, while estimates based on five generations of data overestimated, the observed genetic variances in the defined base. The combinations of conditions that lead to varying degrees of bias remain undefined.     

The evolution of age-specific mortality rates in Drosophila melanogaster: genetic divergence among unselected lines.

Age-specific effects of spontaneous mutations on mortality rates in Drosophila are inferred from three large demographic experiments. Data were collected from inbred lines that were allowed to accumulate spontaneous mutations for 10, 19, and 47 generations. Estimates of age-specific mutational variance for mortality were based on data from all three experiments, totalling approximately 225,000 flies, using a model developed for genetic analysis of age-dependent traits (the character process model). Both within- and among-generation analyses suggest that the input of genetic variance is greater for early life mortality rates than for mortality at older ages. In females, age-specific mutational variances ranged over an order of magnitude from 5.96 x 10(-3) at 2 wk posteclosion to 0.02 x 10(-3) at 7 wk. The male data show a similar pattern. Age-specific genetic variances were substantially less at generation 47 than at generation 19-an unexplained observation that is likely due to block effects. Mutational correlations among mortality rates at different ages tend to increase with the accumulation of new mutations. Comparison of the mutation-accumulation lines at generations 19 and 47 with their respective control lines suggests little age-specific mutational bias.     

Polygenic Mutation in Drosophila Melanogaster: Estimates from Response to Selection of Inbred Strains

Replicated divergent artificial selection for abdominal and sternopleural bristle number from a highly inbred strain of Drosophila melanogaster resulted in an average divergence after 125 generations of selection of 12.0 abdominal and 8.2 sternopleural bristles from the accumulation of new mutations affecting bristle number. Responses to selection were highly asymmetrical, with greater responses for low abdominal and high sternopleural bristle numbers. Estimates of V(M), the mutational variance arising per generation, based on the infinitesimal model and averaged over the responses to the first 25 generations of selection, were 4.32 X 10(-3) V(E) for abdominal bristle number and 3.66 X 10(-3) V(E) for sternopleural bristle number, where V(E) is the environmental variance. Based on 10 generations of divergent selection within lines from generation 93, V(M) for abdominal bristle number was 6.75 X 10(-3) V(E) and for sternopleural bristle number was 5.31 X 10(-3) V(E). However, estimates of V(M) using the entire 125 generations of response to selection were lower and generally did not fit the infinitesimal model largely because the observed decelerating responses were not compatible with the predicted increasing genetic variance over time. These decelerating responses, periods of response in the opposite direction to artificial selection, and rapid responses to reverse selection all suggest new mutations affecting bristle number on average have deleterious effects on fitness. Commonly observed periods of accelerated responses followed by long periods of stasis suggest a leptokurtic distribution of mutational effects for bristles.     

GENETIC AND ENVIRONMENTAL VARIATION IN LIFE-HISTORY TRAITS OF A MONOCARPIC PERENNIAL: A DECADE-LONG FIELD EXPERIMENT

Directional and stabilizing selection tend to deplete additive genetic variance. On the other hand, genetic variance in traits related to fitness could be retained through polygenic mutation, spatially varying selection, genotype-environment interaction, or antagonistic pleiotropy. Most estimates of genetic variance in fitness-related traits have come from laboratory studies, with few estimates of heritability made under natural conditions, particularly for longer lived organisms. Here I estimated additive genetic variance in life-history characters of a monocarpic herb, Ipomopsis aggregata, that lives for up to a decade. Experimental crosses yielded 229 full-sibships nested within 32 paternal half-sibships. More than 5000 offspring were planted as seeds into natural field sites and were followed in most cases through their entire life cycle. Survival showed substantial additive genetic variance (genetic coefficient of variation ≈ 54%). Small differences at seedling emergence were magnified over time, such that the genetic variability in survival was only detectable by tracking the success of offspring for several years starting from seed. In contrast to survival, reproductive traits such as flower number, seeds per flower, and age at flowering showed little or no genetic variability. Despite relatively high levels of additive genetic variation for some life-history characters, high environmental variance in survival resulted in very low heritabilities (0–9%) for all of these characters. Maternal effects were evident in seed mass and remained strong throughout the lengthy vegetative period. No negative genetic correlations between major components of female fitness were detected. Mean corolla width for a paternal family was, however, negatively correlated with the finite rate of increase based on female fitness. That negative correlation could help to maintain additive genetic variance in the face of strong selection through male function for wide corollas.     

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.     

A third component causing random variability beside environment and genotype. A reason for the limited success of a 30 year long effort to standardize laboratory animals?

This paper is a review of experiments, performed in our laboratory during the past 20 years, designed to analyse the significance of different components of random variability in quantitative traits in laboratory rats and mice. Reduction of genetic variability by using inbred strains and reduction of environmental variability by highly standardized husbandry in laboratory animals did not remarkably reduce the range of random variability in quantitative biological traits. Neither did a tremendous increase of the environmental variability (i.e., living in a natural setting) increase it. Therefore, the postnatal environment cannot be that important as the source of random variability. Utilizing methods established in twin research, only 20-30% of the range of the body weight in inbred mice were directly estimated to be of environmental origin. The remaining 70-80% were due to a third component creating biological random variability, in addition to the genetic and environmental influences. This third component is effective at or before fertilization and may originate from ooplasmic differences. It is the most important component of the phenotypic random variability, fixing its range and dominating the genetic and the environmental component. The Gaussian distribution of the body weights observed, even in inbred animals, seems to be an arrangement supporting natural selection rather than the consequence of heterogeneous environmental influences. In a group of inbred rats, the males with the highest chance of parenting the next generation were gathered in the central classes of the distribution of the body weight.