Accounting for bias in estimates of the rate of polygenic mutation

Causes of variability in estimates of mutational variance from mutation accumulation experiments

Characteristics of the new phenotypic variation introduced via mutation have broad implications in evolutionary and medical genetics. Standardized estimates of this mutational variance, V_M, span 2 orders of magnitude, but the causes of this remain poorly resolved. We investigated estimate heterogeneity using 2 approaches. First, meta-analyses of ∼150 estimates of standardized V_M from 37 mutation accumulation studies did not support a difference among taxa (which differ in mutation rate) but provided equivocal support for differences among trait types (life history vs morphology, predicted to differ in mutation rate). Notably, several experimental factors were confounded with taxon and trait, and further empirical data are required to resolve their influences. Second, we analyzed morphological data from an experiment in Drosophila serrata to determine the potential for unintentional heterogeneity among environments in which phenotypes were measured (i.e. among laboratories or time points) or transient segregation of mutations within mutation accumulation lines to affect standardized V_M. Approximating the size of an average mutation accumulation experiment, variability among repeated estimates of (accumulated) mutational variance was comparable to variation among published estimates of standardized V_M. This heterogeneity was (partially) attributable to unintended environmental variation or within line segregation of mutations only for wing size, not wing shape traits. We conclude that sampling error contributed substantial variation within this experiment, and infer that it will also contribute substantially to differences among published estimates. We suggest a logistically permissive approach to improve the precision of estimates, and consequently our understanding of the dynamics of mutational variance of quantitative traits.

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.

Joint allelic effects on fitness and metric traits

Theoretical explanations of empirically observed standing genetic variation, mutation, and selection suggest that many alleles must jointly affect fitness and metric traits. However, there are few direct demonstrations of the nature and extent of these pleiotropic associations. We implemented a mutation accumulation (MA) divergence experimental design in Drosophila serrata to segregate genetic variants for fitness and metric traits. By exploiting naturally occurring MA line extinctions as a measure of line-level total fitness, manipulating sexual selection, and measuring productivity we were able to demonstrate genetic covariance between fitness and standard metric traits, wing size, and shape. Larger size was associated with lower total fitness and male sexual fitness, but higher productivity. Multivariate wing shape traits, capturing major axes of wing shape variation among MA lines, evolved only in the absence of sexual selection, and to the greatest extent in lines that went extinct, indicating that mutations contributing wing shape variation also typically had deleterious effects on both total fitness and male sexual fitness. This pleiotropic covariance of metric traits with fitness will drive their evolution, and generate the appearance of selection on the metric traits even in the absence of a direct contribution to fitness.

Mutations and quantitative genetic variation: lessons from Drosophila

A central issue in evolutionary quantitative genetics is to understand how genetic variation for quantitative traits is maintained in natural populations. Estimates of genetic variation and of genetic correlations and pleiotropy among multiple traits, inbreeding depression, mutation rates for fitness and quantitative traits and of the strength and nature of selection are all required to evaluate theoretical models of the maintenance of genetic variation. Studies in Drosophila melanogaster have shown that a substantial fraction of segregating variation for fitness-related traits in Drosophila is due to rare deleterious alleles maintained by mutation-selection balance, with a smaller but significant fraction attributable to intermediate frequency alleles maintained by alleles with antagonistic pleiotropic effects, and late-age-specific effects. However, the nature of segregating variation for traits under stabilizing selection is less clear and requires more detailed knowledge of the loci, mutation rates, allelic effects and frequencies of molecular polymorphisms affecting variation in suites of pleiotropically connected traits. Recent studies in D. melanogaster have revealed unexpectedly complex genetic architectures of many quantitative traits, with large numbers of pleiotropic genes and alleles with sex-, environment- and genetic background-specific effects. Future genome wide association analyses of many quantitative traits on a common panel of fully sequenced Drosophila strains will provide much needed empirical data on the molecular genetic basis of quantitative traits.

Drosophila bristles and the nature of quantitative genetic variation

Numbers of Drosophila sensory bristles present an ideal model system to elucidate the genetic basis of variation for quantitative traits. Here, we review recent evidence that the genetic architecture of variation for bristle numbers is surprisingly complex. A substantial fraction of the Drosophila genome affects bristle number, indicating pervasive pleiotropy of genes that affect quantitative traits. Further, a large number of loci, often with sex- and environment-specific effects that are also conditional on background genotype, affect natural variation in bristle number. Despite this complexity, an understanding of the molecular basis of natural variation in bristle number is emerging from linkage disequilibrium mapping studies of individual candidate genes that affect the development of sensory bristles. We show that there is naturally segregating genetic variance for environmental plasticity of abdominal and sternopleural bristle number. For abdominal bristle number this variance can be attributed in part to an abnormal abdomen-like phenotype that resembles the phenotype of mutants defective in catecholamine biosynthesis. Dopa decarboxylase (Ddc) encodes the enzyme that catalyses the final step in the synthesis of dopamine, a major Drosophila catecholamine and neurotransmitter. We found that molecular polymorphisms at Ddc are indeed associated with variation in environmental plasticity of abdominal bristle number.

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.

The genetic architecture of Drosophila sensory bristle number

We have mapped quantitative trait loci (QTL) for Drosophila mechanosensory bristle number in six recombinant isogenic line (RIL) mapping populations, each of which was derived from an isogenic chromosome extracted from a line selected for high or low, sternopleural or abdominal bristle number and an isogenic wild-type chromosome. All RILs were evaluated as male and female F(1) progeny of crosses to both the selected and the wild-type parental chromosomes at three developmental temperatures (18 degrees, 25 degrees, and 28 degrees ). QTL for bristle number were mapped separately for each chromosome, trait, and environment by linkage to roo transposable element marker loci, using composite interval mapping. A total of 53 QTL were detected, of which 33 affected sternopleural bristle number, 31 affected abdominal bristle number, and 11 affected both traits. The effects of most QTL were conditional on sex (27%), temperature (14%), or both sex and temperature (30%). Epistatic interactions between QTL were also common. While many QTL mapped to the same location as candidate bristle development loci, several QTL regions did not encompass obvious candidate genes. These features are germane to evolutionary models for the maintenance of genetic variation for quantitative traits, but complicate efforts to understand the molecular genetic basis of variation for complex traits.

Patterns of genetic variation in Mendelian and complex traits

This review discusses the prospects for understanding the genetic basis of complex traits in humans. We take the view that work done on Drosophila melanogaster can serve as a model for understanding complex traits in humans, and the literature on this model system, as well as on humans, is reviewed. The prospects for success in understanding the genetic basis of complex traits depend, in part, on the nature of the forces acting on genetic variation. We suggest that different experimental approaches should be undertaken for traits caused by common genetic variants versus those arising from rare genetic variants.

Genotype-environment interaction at quantitative trait loci affecting sensory bristle number in Drosophila melanogaster

The magnitude of segregating variation for bristle number in Drosophila melanogaster exceeds that predicted from models of mutation-selection balance. To evaluate the hypothesis that genotype-environment interaction (GEI) maintains variation for bristle number in nature, we quantified the extent of GEI for abdominal and sternopleural bristles among 98 recombinant inbred lines, derived from two homozygous laboratory strains, in three temperature environments. There was considerable GEI for both bristle traits, which was mainly attributable to changes in rank order of line means. We conducted a genome-wide screen for quantitative trait loci (QTLs) affecting bristle number in each sex and temperature environment, using a dense (3.2-cM) marker map of polymorphic insertion sites of roo transposable elements. Nine sternopleural and 11 abdominal bristle number QTLs were detected. Significant GEI was exhibited by 14 QTLs, but there was heterogeneity among QTLs in their sensitivity to thermal and sexual environments. To further evaluate the hypothesis that GEI maintains variation for bristle number, we require estimates of allelic effects across environments at genetic loci affecting the traits. This level of resolution may be achievable for Drosophila bristle number because candidate loci affecting bristle development often map to the same location as bristle number QTLs.

Candidate quantitative trait loci and naturally occurring phenotypic variation for bristle number in Drosophila melanogaster: the Delta-Hairless gene region

Delta (Dl) and Hairless (H) are two chromosome 3 candidate neurogenic loci that might contribute to naturally occurring quantitative variation for sensory bristle number. To evaluate this hypothesis, we assessed quantitative genetic variation in abdominal and sternopleural bristle numbers among homozygous isogenic third chromosomes sampled from nature and substituted into the Samarkand (Sam) inbred chromosome 1 and 2 background; among homozygous lines in which the wild-derived Dl-H gene region was introgressed into the Sam chromosome 3 background; and among Dl-H region introgression lines as heterozygotes against the Sam wild-type strain and derivatives of Sam into which mutant Dl and H alleles had been introgressed. Variation among the Dl-H region introgression lines accounted for 36% (8.3%) of the total chromosome 3 among line variance in abdominal (sternopleural) bristle number and for 53% of the chromosome 3 sex x line variance in abdominal bristle number. Naturally occurring alleles in the Dl-H region failed to complement a Dl mutant allele for female abdominal bristle number and sternopleural bristle number in both sexes, and an H mutant allele for both bristle traits in males and females. These results are consistent with the hypothesis that naturally occurring alleles at Dl and H contribute to quantitative genetic variation in sensory bristle number.

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.

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.

Sex-specific quantitative trait loci affecting longevity in Drosophila melanogaster

Senescence, the decline in survivorship and fertility with increasing age, is a near-universal property of organisms. Senescence and limited lifespan are thought to arise because weak natural selection late in life allows the accumulation of mutations with deleterious late-age effects that are either neutral (the mutation accumulation hypothesis) or beneficial (the antagonistic pleiotropy hypothesis) early in life. Analyses of Drosophila spontaneous mutations, patterns of segregating variation and covariation, and lines selected for late-age fertility have implicated both classes of mutation in the evolution of aging, but neither their relative contributions nor the properties of individual loci that cause aging in nature are known. To begin to dissect the multiple genetic causes of quantitative variation in lifespan, we have conducted a genome-wide screen for quantitative trait loci (QTLs) affecting lifespan that segregate among a panel of recombinant inbred lines using a dense molecular marker map. Five autosomal QTLs were mapped by composite interval mapping and by sequential multiple marker analysis. The QTLs had large sex-specific effects on lifespan and age-specific effects on survivorship and mortality and mapped to the same regions as candidate genes with fertility, cellular aging, stress resistance and male-specific effects. Late age-of-onset QTL effects are consistent with the mutation accumulation hypothesis for the evolution of senescence, and sex-specific QTL effects suggest a novel mechanism for maintaining genetic variation for lifespan.

The lack of mutational variance for fluctuating and directional asymmetry in Drosophila melanogaster

Starting from a completely homozygous population of Drosophila melanogaster, lines were derived and independently maintained by a single brother-sister mating in each generation. Two bilateral traits--sternopleural bristle number and wing length--were individually scored on the right-(R) and left-hand (L) sides. Directional (DA) and fluctuating (FA) asymmetries were represented by the signed (R-L) and unsigned magnitude of R-L difference, respectively. Mutational variances (the mutational rate of input of genetic variation) and heritabilities (the mutational variance scaled by the environmental variance) of R, L, (R-L) and magnitude of R-L were calculated from the between-line divergence after a number of generations of mutation accumulation (bristle number: 171 lines, 122 generations; wing length: 148 lines, 170 generations). Mutational heritabilities of R and L were all significant, ranging from 0.73 x 10(-3)-2.10 x 10(-3). Those of (R-L) and magnitude of R-L were two orders of magnitude smaller and nonsignificant, ranging from -1.95 x 10(-5)-5.49 x 10(-5). These results imply that mutations affecting the DA or FA of bristle number and wing length have not been fixed in the lines or alternatively, that their effects were too small to be detected. In the population under study, the data strongly suggest that FA reflects only developmental noise due to non-genetic processes.

Genetic variation for total fitness in Drosophila melanogaster

We measured the heterozygous effects on net fitness of a sample of 12 wild-type third chromosomes in D. melanogaster. Effects on fitness were assessed by competing the wild-type chromosomes against balancer chromosomes, to prevent the production of recombinants. The measurements were carried out in the population cage environment in which the life history had been evolving, in an undisturbed population with overlapping generations, and replicated measurements were made on each chromosome to control for confounding effects such as mutation accumulation. We found significant variation among the wild type chromosomes in their additive genetic effect on net fitness. The system provides an opportunity to obtain an accurate estimate of the distribution of heterozygous effects on net fitness, the contribution of different fitness components including male mating success, and the role of intra-chromosomal epistasis in fitness variation.

Positive association between copia transposition rate and copy number in Drosophila melanogaster

Rates of copia transposition were determined directly, by cytological in situ hybridization analysis of sites of copia insertion in progeny of males from sublines of an inbred strain with different genomic copia copy numbers. Copia transposition rate was positively and nonlinearly associated with copia copy number. This relation cannot be simply explained by mutations in a single host factor that normally suppresses transposition, or by mutations in copia elements themselves. We postulate that the number of copia virus-like particles, necessary for copia transposition, could depend nonlinearly on copia copy number. Deleterious side-effects of the transposition process may be an important force controlling copia copy number in natural populations.

Response to selection from new mutation and effective size of partially inbred populations. II. Experiments with Drosophila melanogaster

Divergent artificial selection for abdominal bristle number in Drosophila melanogaster has been carried out starting from a genetically homogeneous base population. Lines with two different systems of mating, random (P lines) or between full sibs whenever possible (about 50%), random otherwise (I lines) were compared. Responses after 40 generations of selection were mostly due to one or two mutations of large effect (0.2 to 2 phenotypic standard deviations) per line. Ten mutations affecting the selected trait were individually studied (five lethal and five non-lethal, these being predominantly additive). These mutations satisfactorily explain the response attained, although some minor mutations may also be involved. No evidence of epistasis for bristle number was found. The average final divergence was 57% larger in the P lines, but it was mostly due to lethals or highly deleterious mutations. Thus, after relaxation of selection, the ranking reversed and the mean divergence became significantly larger in the I lines (14%). Analysis of inbreeding showed that the very small amount of variation created by spontaneous mutations (a heritability for the selected trait of about 3%) was responsible for a reduction in the effective size of about 50% in the I lines (relative to the case with random selection), but only about 10% in the P lines. Mutational heritabilities estimated from the response to selection (0.05-0.18%) were within the range usually found for this trait in previous experiments. REML estimates account for correlations between relatives, and were much larger in those lines where the response was due to lethal mutations, as these do not contribute to response after reaching maximum frequency.

Accumulation of mutations affecting body weight in inbred mouse lines

The variation from spontaneous mutations for 6-week body weight in the mouse was estimated by selection from a cross of two inbred sublines, C57BL/6 and C57BL/10, separated about 50 years previously from the same inbred line. Selection was practised high and low for 12 generations from the F2, followed by one generation of relaxation. The lines diverged by approximately 1.7 g or 0.7 sd. The additive genetic variance was estimated in the F2 by restricted maximum likelihood and from the selection response, and from this variance the mutational heritability hM2 was estimated using the number of generations since divergence. Estimates of hM2 range from 0.08 to 0.10% depending on the method of analysis. These estimates are similar to those found for other species, but lower than other estimates for the mouse. It is concluded that substantial natural and, perhaps, artificial selection operated during the maintenance of the sublines.