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

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 Variation↗

Associations between environmental stress, selection history, and quantitative genetic variation in Drosophila melanogaster.

Stressful environments may increase quantitative genetic variation in populations by promoting the expression of genetic variation that has not previously been eliminated or canalized by natural selection. This "selection history" hypothesis predicts that novel stressors will increase quantitative genetic variation, and that the magnitude of this effect will decrease following continued stress exposure. We tested these predictions using Drosophila melanogaster and sternopleural bristle number as a model system. In particular, we examined the effect of high temperature stress (31 degrees Celsius) on quantitative genetic variation before and after our study population had been reared at 31 degrees Celsius for 15 generations. High temperature stress was found to increase both additive genetic variance and heritability, but contrary to the selection history hypothesis prediction, the magnitude of this effect significantly increased after the study population had been reared for 15 generations under high temperature stress. These results demonstrate that high temperature stress increases quantitative genetic variation for bristle number, but do not support the selection history hypothesis as an explanation for this effect.

Adaptation, Biological↗

Mutation models and quantitative genetic variation.

Analyses of evolution and maintenance of quantitative genetic variation depend on the mutation models assumed. Currently two polygenic mutation models have been used in theoretical analyses. One is the random walk mutation model and the other is the house-of-cards mutation model. Although in the short term the two models give similar results for the evolution of neutral genetic variation within and between populations, the predictions of the changes of the variation are qualitatively different in the long term. In this paper a more general mutation model, called the regression mutation model, is proposed to bridge the gap of the two models. The model regards the regression coefficient, gamma, of the effect of an allele after mutation on the effect of the allele before mutation as a parameter. When gamma = 1 or 0, the model becomes the random walk model or the house-of-cards model, respectively. The additive genetic variances within and between populations are formulated for this mutation model, and some insights are gained by looking at the changes of the genetic variances as gamma changes. The effects of gamma on the statistical test of selection for quantitative characters during macroevolution are also discussed. The results suggest that the random walk mutation model should not be interpreted as a null hypothesis of neutrality for testing against alternative hypotheses of selection during macroevolution because it can potentially allocate too much variation for the change of population means under neutrality.

Biological Evolution↗

Multipoint analysis of human quantitative genetic variation.

A unique method of partitioning human quantitative genetic variation into effects due to specific chromosomal regions is presented. This method is based on estimating the proportion of genetic material, R, shared identical by descent (IBD) by sibling pairs in a specified chromosomal region, on the basis of their marker genotypes at a set of marker loci spanning the region. The mean and variance of the distribution of R conditional on IBD status and recombination pattern between two marker loci are derived as a function of the distance between the two loci. The distribution of the estimates of R is exemplified using data on 22 loci on chromosome 7. A method of using the estimated R values and observed values of a quantitative trait in a set of sibships to estimate the proportion of total genetic variance explained by loci in the region of interest is presented. Monte Carlo simulation techniques are used to show that this method is more powerful than existing methods of quantitative linkage analysis based on sib pairs. It is also shown through simulation studies that the proposed method is sensitive to genetic variation arising from both a single locus of large effect as well as from several loosely linked loci of moderate phenotypic effect.

Chromosomes, Human, Pair 7↗

The molecular basis of quantitative genetic variation in central and secondary metabolism in Arabidopsis.

To find the genes controlling quantitative variation, we need model systems where functional information on physiology, development, and gene regulation can guide evolutionary inferences. We mapped quantitative trait loci (QTLs) influencing quantitative levels of enzyme activity in primary and secondary metabolism in Arabidopsis. All 10 enzymes showed highly significant quantitative genetic variation. Strong positive genetic correlations were found among activity levels of 5 glycolytic enzymes, PGI, PGM, GPD, FBP, and G6P, suggesting that enzymes with closely related metabolic functions are coregulated. Significant QTLs were found influencing activity of most enzymes. Some enzyme activity QTLs mapped very close to known enzyme-encoding loci (e.g., hexokinase, PGI, and PGM). A hexokinase QTL is attributable to cis-acting regulatory variation at the AtHXK1 locus or a closely linked regulatory locus, rather than polypeptide sequence differences. We also found a QTL on chromosome IV that may be a joint regulator of GPD, PGI, and G6P activity. In addition, a QTL affecting PGM activity maps within 700 kb of the PGM-encoding locus. This QTL is predicted to alter starch biosynthesis by 3.4%, corresponding with theoretical models, suggesting that QTLs reflect pleiotropic effects of mutant alleles.

Analysis of Variance↗

Simple sequence repeats as a source of quantitative genetic variation.

Most traits in biological populations appear to be under stabilizing selection, which acts to eliminate quantitative genetic variation. Yet, virtually all measured traits in biological populations continue to show significant quantitative genetic variation. The paradox can be resolved by postulating the existence of an abundant, though unspecified, source of mutations that has quantitative effects on phenotype, but does not reduce fitness. Does such a source actually exist? We propose that it does, in the form of repeat-number variation in SSRs (simple sequence repeats, of which the triplet repeats of human neurodegenerative diseases are a special case). Viewing SSRs as a major source of quantitative mutation has broad implications for understanding molecular processes of evolutionary adaptation, including the evolutionary control of the mutation process itself.

Animals↗

The nature of quantitative genetic variation revisited: lessons from Drosophila bristles.

Most characters that distinguish one individual from another, like height or weight, vary continuously in populations. Continuous variation of these 'quantitative' traits is due to the simultaneous segregation of multiple quantitative trait loci (QTLs) as well as environmental influences. A major challenge in human medicine, animal and plant breeding and evolutionary genetics is to identify QTLs and determine their genetic properties. Studies of the classic quantitative traits, abdominal and sternopleural bristle numbers of Drosophila, have shown that: (1) many loci have small effects on bristle number, but a few have large effects and cause most of the genetic variation; (2) 'candidate' loci involved in bristle development often have large quantitative effects on bristle number; and (3) alleles at QTLs affecting bristle number have variable degrees of dominance, interact with each other, and affect other quantitative traits, including fitness. Lessons learned from this model system will be applicable to studies of the genetic basis of quantitative variation in other species.

Animals↗

Quantitative genetic variation in an ecological setting.

The machinery was developed to investigate the behavior of quantitative genetic variation in an ecological model of a finite number of islands of finite size, with migration rate m and extinction rate e, for a quantitative genetic model general for numbers of alleles and loci and additive, dominance, and additive by additive epistatic effects. It was necessary to reckon with seven quadratic genetic components, whose coefficients in the genotypic variance components within demes, sigma Gw2, between demes within populations, sigma s2, and between replicate populations, sigma r2, are given by descent measures. The descent measures at any time are calculated with the use of transition equations which are determined by the parameters of the ecological model. Numerical results were obtained for the coefficients of the quadratic genetic components in each of the three genotypic variance components in the early phase of differentiation. The general effect of extinction is to speed up the time course leading to fixation, to increase sigma r2, and to decrease sigma s2 (with a few exceptions) in comparison with no extinction. The general effect of migration is to slow down the time course leading to fixation, to increase sigma Gw2, at least in the later generations, and to decrease sigma s2 (with a few exceptions) in comparison with no migration. Except for these, the effects of migration and extinction on the variance components are complex, depending on the genetic model, and sometimes involve interaction of migration and extinction. Sufficient details are given for an investigator to evaluate numerically the results for variations in the quantitative genetic and ecological models.

Alleles↗

Quantitative genetic variation and developmental clocks.

It is well-known that most genetic variation affects quantitative traits, and natural or artificial selection can act to change quantitative features of organisms more rapidly than qualitative ones. Surprisingly, variability is not confined to outbred species, but also occurs in inbred mice at a much higher rate than expected from known mutation rates. The size and shape of organisms and their constituent parts are, at least in part, controlled by the number of cell divisions, and there is published evidence for the existence of developmental clocks, which may count cell divisions. A molecular model for a developmental clock was previously proposed. It depends on the DNA methylation of repeated sequences of DNA, where the methylation of each additional sequence is tied to DNA synthesis and therefore cell division. The number of repeats specifies the number of divisions which will occur before a signal is produced which can activate or inactivate one or more genes. It is known that crossing over occurs between sister chromatids, and where tandemly repeated sequences occur unequal exchange can generate a larger or smaller number of repeats. An example of this is seen in the well-known variability of "minisatellite" sequences in human DNA. Unequal sister chromatid exchange can occur in mitotic and meiotic cells in the germ line, and in the case of developmental clock sequences could generate variation in clock length which in turn would directly affect quantitative traits. These events can be regarded as a special case of molecular drive during evolution.

Animals↗

From micro- to macroevolution through quantitative genetic variation: positive evidence from field crickets.

Quantitative genetics has been introduced to evolutionary biologists with the suggestion that microevolution could be directly linked to macroevolutionary patterns using, among other parameters, the additive genetic variance/ covariance matrix (G) which is a statistical representation of genetic constraints to evolution. However, little is known concerning the rate and pattern of evolution of G in nature, and it is uncertain whether the constraining effect of G is important over evolutionary time scales. To address these issues, seven species of field crickets from the genera Gryllus and Teleogryllus were reared in the laboratory, and quantitative genetic parameters for morphological traits were estimated from each of them using a nested full-sibling family design. We used three statistical approaches (T method, Flury hierarchy, and Mantel test) to compare G matrices or genetic correlation matrices in a phylogenetic framework. Results showed that G matrices were generally similar across species, with occasional differences between some species. We suggest that G has evolved at a low rate, a conclusion strengthened by the consideration that part of the observed across-species variation in G can be explained by the effect of a genotype by environment interaction. The observed pattern of G matrix variation between species could not be predicted by either morphological trait values or phylogeny. The constraint hypothesis was tested by comparing the multivariate orientation of the reconstructed ancestral G matrix to the orientation of the across-species divergence matrix (D matrix, based on mean trait values). The D matrix mainly revealed divergence in size and, to a much smaller extent, in a shape component related to the ovipositor length. This pattern of species divergence was found to be predictable from the ancestral G matrix in agreement with the expectation of the constraint hypothesis. Overall, these results suggest that the G matrix seems to have an influence on species divergence, and that macroevolution can be predicted, at least qualitatively, from quantitative genetic theory. Alternative explanations are discussed.

Analysis of Variance↗

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.

Genetic Variation↗

Quantitative genetic variation of odor-guided behavior in a natural population of Drosophila melanogaster.

Quantitative genetic variation in behavioral response to the odorant, benzaldehyde, was assessed among a sample of 43 X and 35 third chromosomes extracted from a natural population and substituted into a common inbred background. Significant genetic variation among chromosome lines was detected. Heritability estimates for olfactory response, however, were low, as is typical for traits under natural selection. Furthermore, the loci affecting naturally occurring variation in olfactory response to benzaldehyde were not the same in males and females, since the genetic correlation between the sexes was low and not significantly different from zero for the chromosome 3 lines. Competitive fitness, viability and fertility of the chromosome 3 lines were estimated using the balancer equilibrium technique. Genetic correlations between fitness and odor-guided behavior were not significantly different from zero, suggesting the number of loci causing variation in olfactory response is small relative to the number of loci causing variation in fitness. Since different genes affect variation in olfactory response in males and females, genetic variation for olfactory response could be maintained by genotype x sex environment interaction. This unusual genetic architecture implies that divergent evolutionary trajectories for olfactory behavior may occur in males and females.

Animals↗

Joint effects of pleiotropic selection and stabilizing selection on the maintenance of quantitative genetic variation at mutation-selection balance.

In quantitative genetics, there are two basic "conflicting" observations: abundant polygenic variation and strong stabilizing selection that should rapidly deplete that variation. This conflict, although having attracted much theoretical attention, still stands open. Two classes of model have been proposed: real stabilizing selection directly on the metric trait under study and apparent stabilizing selection caused solely by the deleterious pleiotropic side effects of mutations on fitness. Here these models are combined and the total stabilizing selection observed is assumed to derive simultaneously through these two different mechanisms. Mutations have effects on a metric trait and on fitness, and both effects vary continuously. The genetic variance (V(G)) and the observed strength of total stabilizing selection (V(s,t)) are analyzed with a rare-alleles model. Both kinds of selection reduce V(G) but their roles in depleting it are not independent: The magnitude of pleiotropic selection depends on real stabilizing selection and such dependence is subject to the shape of the distributions of mutational effects. The genetic variation maintained thus depends on the kurtosis as well as the variance of mutational effects: All else being equal, V(G) increases with increasing leptokurtosis of mutational effects on fitness, while for a given distribution of mutational effects on fitness, V(G) decreases with increasing leptokurtosis of mutational effects on the trait. The V(G) and V(s,t) are determined primarily by real stabilizing selection while pleiotropic effects, which can be large, have only a limited impact. This finding provides some promise that a high heritability can be explained under strong total stabilizing selection for what are regarded as typical values of mutation and selection parameters.

Genetic Variation↗

Understanding quantitative genetic variation.

Until recently, it was impracticable to identify the genes that are responsible for variation in continuous traits, or to directly observe the effects of their different alleles. Now, the abundance of genetic markers has made it possible to identify quantitative trait loci (QTL)--the regions of a chromosome or, ideally, individual sequence variants that are responsible for trait variation. What kind of QTL do we expect to find and what can our observations of QTL tell us about how organisms evolve? The key to understanding the evolutionary significance of QTL is to understand the nature of inherited variation, not in the immediate mechanistic sense of how genes influence phenotype, but, rather, to know what evolutionary forces maintain genetic variability.

Animals↗

Quantitative genetic variation photoinduced by 8-methoxypsoralen in yeast.

The variation in cell mass production within cultured populations of Saccharomyces cerevisiae derived from untreated cells and from cells treated with 8-methoxypsoralen plus near-UV light (8MOP-NUV) was determined. Spontaneous mutation was not significant source of variation, since no genetic component of variance was detected in the untreated population. Following mutagenesis significant levels of genetic variation were found, showing that 8MOP-NUV was effective in inducing quantitative genetic variation among clonal populations of the yeast. The magnitudes of the estimates of the heritability and of the genetic coefficient of variation, indicate that, in phenotypic selection, greater genetic progress can be expected after mutagenic treatment than with untreated populations. The highest estimate of genetic gain was obtained at the intermediate survival level.

Analysis of Variance↗

Quantitative genetic variation in the hematopoietic stem cell and progenitor cell compartment and in lifespan are closely linked at multiple loci in BXD recombinant inbred mice.

The number of bone marrow hematopoietic stem and progenitor cells as defined by the lineage(-), Sca1(++), c-kit(+) (LSK) phenotype and their proliferative capacity in vitro are subject to quantitative genetic variation, and several quantitative trait loci (QTL) have been identified in young mice. Because some traits affecting hematopoiesis also change with age in a mouse strain-dependent fashion, we performed quantitative trait analysis in aged BXD recombinant inbred (RI) mice for the number and frequency of LSK cells, and for their proliferative capacity in vitro. Several novel QTL were identified. The number and frequency of LSK cells in old mice correlated inversely with lifespan. Furthermore, 4 of 7 lifespan QTL overlap with QTL contributing to the number, frequency, or proliferative capacity of LSK cells in young or old mice. Taken together, these data establish a close genetic, and perhaps functional, link between genetic variation in lifespan and characteristics of stem and progenitor cells.

Aging↗

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.

Genes, Dominant↗

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.

Animals↗