Environment dependence of mutational parameters for viability in Drosophila melanogaster

The genomic rate of mildly deleterious mutations (U) figures prominently in much evolutionary and ecological theory. In Drosophila melanogaster, estimates of U have varied widely, from <0.1 to nearly 1 per zygote. The source of this variation is unknown, but could include differences in the conditions used for assaying fitness traits. We examined how assay conditions affect estimates of the rates and effects of viability-depressing mutations in two sets of lines with accumulated spontaneous mutations on the second chromosome. In each set, the among-line variance in egg-to-adult viability was significantly greater when viability was assayed using a high parental density than when it was assayed using a low density. In contrast, the proportional decline in viability due to new mutations did not differ between densities. Two other manipulations, lowering the temperature and adding ethanol to the medium, had no significant effects on either the mean decline or among-line variance. Cross-environment genetic correlations in viability were generally close to one, implying that most mutations reduced viability in all environments. Using data from the low-density, lower-bound estimates of U approached the classic, high values of Mukai and Ohnishi; at the high density, U estimates were similar to recently reported low values. The difference in estimated mutation rates, taken at face value, would imply that many mutations affected fitness at low density but not at high density, but this is shown to be incompatible with the observed high cross-environment correlations. Possible reasons for this discrepancy are discussed. Regardless of the interpretation, the results show that assay conditions can have a large effect on estimates of mutational parameters for fitness traits.     

The genetic analysis of age-dependent traits: modeling the character process

The extension of classical quantitative genetics to deal with function-valued characters (also called infinite-dimensional characters) such as growth curves, mortality curves, and reaction norms, was begun by Kirkpatrick and co-workers. In this theory, the analogs of variance components for single traits are covariance functions for function-valued traits. In the approach presented here, we employ a variety of parametric models for covariance functions that have a number of desirable properties: the functions (1) are positive definite, (2) can be estimated using procedures like those currently used for single traits, (3) have a small number of parameters, and (4) allow simple hypotheses to be easily tested. The methods are illustrated using data from a large experiment that examined the effects of spontaneous mutations on age-specific mortality rates in Drosophila melanogaster. Our methods are shown to work better than a standard multivariate analysis, which assumes the character value at each age is a distinct character. Advantages over existing methods that model covariance functions as a series of orthogonal polynomials are discussed.     

Modeling the evolution of genetic architecture: A continuum of alleles model with pairwise AxA epistasis

A continuum of alleles model with pair-wise AxA epistasis is proposed and its transmission genetic, and variational properties are analysed. The basic idea is that genes control the values of underlying variables, which affect the genotypic value of phenotypic characters proportional to a "scaling factor". Epistasis is the influence of one gene on the average effect of another gene. In this model, epistasis is introduced as a mutational effect of one gene on the scaling factors of another gene. In accordance with empirical results, the model assumes that the average direct effect of mutations is zero, as is the average epistatic effect. The model predicts that, on average, a mutation at one locus increases the expected mutational variance of mutations at another interacting locus. The increase in mutational variance is predicted to be equal to the variance of the pair-wise epistatic effects. This result is consistent with the observation that mutant phenotypes tend to be more variable than the wildtype phenotype. Another generic result of this model is that the frequency of canalizing mutations can at most be equal to the frequency of de-canalizing mutations. Furthermore, it is predicted that the mutational variance of a character increases at least linearly with the size of the character; hence this model is scale variant. In the case of two characters it is shown that the dimensionality of the locus-specific mutational effect distribution is invariant, i.e. the rank of the mutational covariance matrix M is invariant. While in additive models the mutational covariance matrix is always and entirely invariant, the invariance in the case of epistatic models is unexpected. Epistatic interactions can change the magnitude of the mutational (co)variances at a locus and can thus influence the structure of the mutational covariance matrix. However, in the present model the dimensionality of the mutational effect distribution remains the same. A consequence of this result is that, in this model, the genetic architecture of a set of characters is always evolvable i.e. no hard constraints can evolve.     

Effects of P Element Insertions on Quantitative Traits in Drosophila Melanogaster

P element mutagenesis was used to construct 94 third chromosome lines of Drosophila melanogaster which contained on average 3.1 stable P element inserts, in an inbred host strain background previously free of P elements. The homozygous and heterozygous effects of the inserts on viability and abdominal and sternopleural bristle number were ascertained by comparing the chromosome lines with inserts to insert-free control lines of the inbred host strain. P elements reduced average homozygous viability by 12.2% per insert and average heterozygous viability by 5.5% per insert, and induced recessive lethal mutations at a rate of 3.8% per insert. Mutational variation for the bristle traits averaged over both sexes was 0.03Ve per homozygous P insert and 0.003Ve per heterozygous P insert, where Ve is the environmental variance. Mutational variation was greater for the sexes considered separately because inserts had large pleiotropic effects on sex dimorphism of bristle characters. The distributions of homozygous effects of inserts on the bristle traits were asymmetrical, with the largest effects in the direction of reducing bristle number; and highly leptokurtic, with most of the increase in variance contributed by a few lines with large effects. The inserts had partially recessive effects on the bristle traits. Insert lines with extreme bristle effects had on average greatly reduced viability.     

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.     

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.     

The Nature and Extent of Mutational Pleiotropy in Gene Expression of Male Drosophila serrata

The nature and extent of mutational pleiotropy remain largely unknown, despite the central role that pleiotropy plays in many areas of biology, including human disease, agricultural production, and evolution. Here, we investigate the variation in 11,604 gene expression traits among 41 mutation accumulation (MA) lines of Drosophila serrata. We first confirmed that these expression phenotypes were heritable, detecting genetic variation in 96% of them in an outbred, natural population of D. serrata. Among the MA lines, 3385 (29%) of expression traits were variable, with a mean mutational heritability of 0.0005. In most traits, variation was generated by mutations of relatively small phenotypic effect; putative mutations with effects of greater than one phenotypic standard deviation were observed for only 8% of traits. With most (71%) traits unaffected by any mutation, our data provide no support for universal pleiotropy. We further characterized mutational pleiotropy in the 3385 variable traits, using sets of 5, randomly assigned, traits. Covariance among traits chosen at random with respect to their biological function is expected only if pleiotropy is extensive. Taking an analytical approach in which the variance unique to each trait in the random 5-trait sets was partitioned from variance shared among traits, we detected significant (at 5% false discovery rate) mutational covariance in 21% of sets. This frequency of statistically supported covariance implied that at least some mutations must pleiotropically affect a substantial number of traits (>70; 0.6% of all measured traits).     

Comparing Mutational Variabilities

We have reviewed the available data on V(M), the amount of genetic variation in phenotypic traits produced each generation by mutation. We use these data to make several qualitative tests of the mutation-selection balance hypothesis for the maintenance of genetic variance (MSB). To compare V(M) values, we use three dimensionless quantities: mutational heritability, V(M)/V(E); the mutational coefficient of variation, CV(M); and the ratio of the standing genetic variance to V(M), V(G)/V(M). Since genetic coefficients of variation for life history traits are larger than those for morphological traits, we predict that under MSB, life history traits should also have larger CV(M). This is confirmed; life history traits have a median CV(M) value more than six times higher than that for morphological traits. V(G)/V(M) approximates the persistence time of mutations under MSB in an infinite population. In order for MSB to hold, V(G)/V(M) must be small, substantially less than 1000, and life history traits should have smaller values than morphological traits. V(G)/V(M) averages about 50 generations for life history traits and 100 generations for morphological traits. These observations are all consistent with the predictions of a mutation-selection balance model.     

Genetic variability and fluctuating asymmetry of morphological signs of Drosophila melanogaster during development in a pesticide-containing environment

The effects of chlorine-organic insecticide endosulfane (thiodan) on phenotypic and genetic variation in four morphological traits of Drosophila melanogaster (wing length, thorax length, the number of orbital bristles and the number of sternopleural bristles) were examined. In addition, the effect of this pesticide on stability of development measured as fluctuating asymmetry of bilateral traits was estimated. On the medium with endosulfane, phenotypic variation of morphometric traits was significantly higher. No difference in fluctuating asymmetry between the stressed and the control samples was found. The among-line variance of morphometric traits of flies reared on the endosulfane-containing medium was significantly higher as compared to the corresponding variance under control conditions. The efficiency of using fluctuating asymmetry and phenotypic variation of morphometric and meristic traits as indicators of environmental stress in insect populations is discussed.     

Genetic Variability and Fluctuating Asymmetry of Morphological Traits in Drosophila melanogasterReared on a Pesticide-Containing Medium

The effects of chlorine-organic insecticide endosulfane (thiodan) on phenotypic and genetic variation in four morphological traits of Drosophila melanogaster(wing length, thorax length, the number of orbital bristles and the number of sternopleural bristles) were examined. In addition, the effect of this pesticide on stability of development measured as fluctuating asymmetry of bilateral traits was estimated. On the medium with endosulfane, phenotypic variation of morphometric traits was significantly higher. No difference in fluctuating asymmetry between the stressed and the control samples was found. The among-line variance of morphometric traits of flies reared on the endosulfane-containing medium was significantly higher as compared to the corresponding variance under control conditions. The efficiency of using fluctuating asymmetry and phenotypic variation of morphometric and meristic traits as indicators of environmental stress in insect populations is discussed.     

SPONTANEOUS MUTATIONAL GENOTYPE-ENVIRONMENT INTERACTION FOR FITNESS-RELATED TRAITS IN DROSOPHILA MELANOGASTER

Spontaneous mutations were allowed to accumulate for 104–161 generations in 113–176 inbred lines, independently maintained by a single brother-sister mating per generation, all of them derived from a completely homozygous population of Drosophila melanogaster. In each of two to three consecutive generations, all lines were scored for fecundity, egg-to-pupa and pupa-to-adult viabilities, both in the standard laboratory culture medium (ST) and in three harsh media differing from the former by a single factor: higher temperature (HT), higher NaCl concentration (HSC), or a much reduced concentration of nutrients (D). Relative to the standard medium, productivity (fecundity × viability) decreased by 25% (HT), 66% (HSC), and 80% (D). In each medium, mutational variances of those traits and mutational covariances between all possible pairs were calculated from the between-line divergence (codivergence). Mutational correlations between character states in different media were also obtained. Because we used inbred lines, those estimates were mainly due to the accumulation of mildly detrimental mutations, deleterious mutations of large effect being underrepresented. For all traits, mutational heritabilities ranged from 1.41 × 10^–4 to 11.24 × 10^–4, and did not increase with intensified environmental harshness. Mutational correlations between character states in different media were usually not large (average absolute value 0.31), reflecting a high degree of environmental specificity of the mutations involved. In our results, mutations quasi-neutral in ST conditions and mildly detrimental in more stressful media were not, as a class, important. Mutational correlations between fecundity and egg-to-pupa viability were small and positive in all media. Those involving pupa-to-adult viability were positive in HT, nonsignificant in HSC, and negative in ST and D, showing how the genetic covariance structure of quantitative traits in populations may change in variable environments.     

The Quantitative Genetic Consequences of Pleiotropy under Stabilizing and Directional Selection

The independence of two phenotypic characters affected by both pleiotropic and nonpleiotropic mutations is investigated using a generalization of M. Slatkin's stepwise mutation model of 1987. The model is used to determine whether predictions of either the multivariate normal model introduced in 1980 by R. Lande or the house-of-cards model introduced in 1985 by M. Turelli can be regarded as typical of models that are intermediate between them. We found that, under stabilizing selection, the variance of one character at equilibrium may depend on the strength of stabilizing selection on the other character (as in the house-of-cards model) or not (as in the multivariate normal model) depending on the types of mutations that can occur. Similarly, under directional selection, the genetic covariance between two characters may increase substantially (as in the house-of-cards model) or not (as in the multivariate normal model) depending on the kinds of mutations that are assumed to occur. Hence, even for the simple model we consider, neither the house-of-cards nor the multivariate normal model can be used to make predictions, making it unlikely that either could be used to draw general conclusions about more complex and realistic models.     

The effect of a population bottleneck on the evolution of genetic variance/covariance structure

It is well known that standard population genetic theory predicts decreased additive genetic variance (V(a) ) following a population bottleneck and that theoretical models including interallelic and intergenic interactions indicate such loss may be avoided. However, few empirical data from multicellular model systems are available, especially regarding variance/covariance (V/CV) relationships. Here, we compare the V/CV structure of seventeen traits related to body size and composition between control (60 mating pairs/generation) and bottlenecked (2 mating pairs/generation; average F = 0.39) strains of mice. Although results for individual traits vary considerably, multivariate analysis indicates that V(a) in the bottlenecked populations is greater than expected. Traits with patterns and amounts of epistasis predictive of enhanced V(a) also show the largest deviations from additive expectations. Finally, the correlation structure of weekly weights is not significantly different between control and experimental lines but correlations between necropsy traits do differ, especially those involving the heart, kidney and tail length.     

Spontaneous mutational correlations for life-history, morphological and behavioral characters in Caenorhabditis elegans

The pattern of mutational covariance among traits plays a central, but largely untested, role in many theories in evolutionary genetics. Here we estimate the pattern of phenotypic, environmental, and mutational correlations for a set of life-history, behavioral, and morphological traits using 67 self-fertilizing lines of Caenorhabditis elegans, each having independently experienced an average of 370 generations of spontaneous mutation accumulation. Bivariate relationships of mutational effects indicate the existence of extensive pleiotropy. We find that mutations may tend to produce manifold effects on suites of functionally related traits; however, our data do not support the idea of completely parcelated pleiotropy, in which functional units are separately affected by mutations. Positive net phenotypic and mutational correlations are common for life-history traits, with environmental correlations being comparatively smaller and of the same sign for most pairs of traits. Observed mutational correlations are shown to be higher than those produced by the chance accumulation of nonpleiotropic mutations in the same lines.     

The genetic variance but not the genetic covariance of life‐history traits changes towards the north in a time‐constrained insect

Seasonal time constraints are usually stronger at higher than lower latitudes and can exert strong selection on life‐history traits and the correlations among these traits. To predict the response of life‐history traits to environmental change along a latitudinal gradient, information must be obtained about genetic variance in traits and also genetic correlation between traits, that is the genetic variance‐covariance matrix, G . Here, we estimated G for key life‐history traits in an obligate univoltine damselfly that faces seasonal time constraints. We exposed populations to simulated native temperatures and photoperiods and common garden environmental conditions in a laboratory set‐up. Despite differences in genetic variance in these traits between populations (lower variance at northern latitudes), there was no evidence for latitude‐specific covariance of the life‐history traits. At simulated native conditions, all populations showed strong genetic and phenotypic correlations between traits that shaped growth and development. The variance–covariance matrix changed considerably when populations were exposed to common garden conditions compared with the simulated natural conditions, showing the importance of environmentally induced changes in multivariate genetic structure. Our results highlight the importance of estimating variance–covariance matrixes in environments that mimic selection pressures and not only trait variances or mean trait values in common garden conditions for understanding the trait evolution across populations and environments.     

The quantitative genetics of maximal and basal rates of oxygen consumption in mice

A positive genetic correlation between basal metabolic rate (BMR) and maximal (VO(2)max) rate of oxygen consumption is a key assumption of the aerobic capacity model for the evolution of endothermy. We estimated the genetic (V(A), additive, and V(D), dominance), prenatal (V(N)), and postnatal common environmental (V(C)) contributions to individual differences in metabolic rates and body mass for a genetically heterogeneous laboratory strain of house mice (Mus domesticus). Our breeding design did not allow the simultaneous estimation of V(D) and V(N). Regardless of whether V(D) or V(N) was assumed, estimates of V(A) were negative under the full models. Hence, we fitted reduced models (e.g., V(A) + V(N) + V(E) or V(A) + V(E)) and obtained new variance estimates. For reduced models, narrow-sense heritability (h(2)(N)) for BMR was <0.1, but estimates of h(2)(N) for VO(2)max were higher. When estimated with the V(A) + V(E) model, the additive genetic covariance between VO(2)max and BMR was positive and statistically different from zero. This result offers tentative support for the aerobic capacity model for the evolution of vertebrate energetics. However, constraints imposed on the genetic model may cause our estimates of additive variance and covariance to be biased, so our results should be interpreted with caution and tested via selection experiments.     

Changes in genetic variances with increased inbreeding of beef cattle

Data on performance traits from a herd of Hereford cattle composed of inbred lines and linecross groups were analyzed to estimate within- and among-line genetic variances and to evaluate how these variances changed with increased inbreeding. Within-line variances were highly erratic while among-line variances tended to be somewhat more consistent. Changes in variances with increased inbreeding did not generally follow the theoretical expectations for the redistribution of genetic variances.     

Quantifying natural seasonal variation in mutation parameters with mutation accumulation lines

Mutations create novel genetic variants, but their contribution to variation in fitness and other phenotypes may depend on environmental conditions. Furthermore, natural environments may be highly heterogeneous. We assessed phenotypes associated with survival and reproductive success in over 30,000 plants representing 100 mutation accumulation lines of Arabidopsis thaliana across four temporal environments at a single field site. In each of the four assays, environmental variance was substantially larger than mutational variance. For some traits, whether mutational variance was significantly varied between seasons. The founder genotype had mean trait values near the mean of the distribution of the mutation accumulation lines in all field experiments. New mutations also contributed more phenotypic variation than would be predicted, given phenotypic and sequence‐level divergence among natural populations of A. thaliana. The combination of large environmental variance with a mean effect of mutation near zero suggests that mutations could contribute substantially to standing genetic variation.     

On the quantitative genetics of mixture characters

Finite mixture models are helpful for uncovering heterogeneity due to hidden structure. Quantitative genetics issues of continuous characters having a finite mixture of Gaussian components as statistical distribution are explored in this article. The partition of variance in a mixture, the covariance between relatives under the supposition of an additive genetic model, and the offspring-parent regression are derived. Formulas for assessing the effect of mass selection operating on a mixture are given. Expressions for the genetic and phenotypic correlations between mixture and Gaussian traits and between two mixture traits are presented. It is found that, if there is heterogeneity in a population at the genetic or environmental level, then genetic parameters based on theory treating distributions as homogeneous can lead to misleading interpretations. Some peculiarities of mixture characters are: heritability depends on the mean values of the component distributions, the offspring-parent regression is nonlinear, and genetic or phenotypic correlations cannot be interpreted devoid of the mixture proportions and of the parameters of the distributions mixed.     

Quantifying the decanalizing effects of spontaneous mutations in rhabditid nematodes

The evolution of canalization, the robustness of the phenotype to environmental or genetic perturbation, has attracted considerable recent interest. A key step toward understanding the evolution of any phenotype is characterizing the rate at which mutation introduces genetic variation for the trait (the mutational variance, V(M)) and the average directional effects of mutations on the trait mean (DeltaM). In this study, the mutational parameters for canalization of productivity and body volume are quantified in two sets of mutation accumulation lines of nematodes in the genus Caenorhabditis and are compared with the mutational parameters for the traits themselves. Four results emerge: (1) spontaneous mutations consistently decanalize the phenotype; (2) the mutational parameters for decanalization, V(M) (quantified as mutational heritability) and DeltaM, are of the same order of magnitude as the same parameters for the traits themselves; (3) the mutational parameters for canalization are roughly correlated with the parameters for the traits themselves across taxa; and (4) there is no evidence that residual segregating overdominant loci contribute to the decay of canalization. These results suggest that canalization is readily evolvable and that any evolutionary factor that causes mutations to accumulate will, on average, decanalize the phenotype.