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PubMed1984

Pleiotropic overdominance and the maintenance of genetic variation in polygenic characters.

A model of selection is described in which optimizing phenotypic selection is combined with pleiotropic overdominance. Thus, the role that mutation commonly plays in models of phenotypic evolution is replaced by balancing selection. Expressions are provided for the equilibrium genetic variance in phenotype and for the heterozygosity. An approximate analysis of the transient properties of the model shows that, in certain circumstances, the behavior is quite similar to that of models based on the interaction of mutation and selection.

Genes, Dominant↗
PubMed1992

Estimating polygenic models for multivariate data on large pedigrees.

We have developed algorithms for the likelihood estimation of additive genetic models for quantitative traits on large pedigrees. The approach uses the expectation L-maximization (EM) algorithm, but avoids intensive computation. In this paper, we focus on extensions of previous work to the case of multivariate data. We exemplify the approach by analyses of bivariate data on a four-generation, 949-member pedigree of the snail Lymnaea elodes, and on a three-generation pedigree of the guppy Poecilia reticulata containing about 400 individuals.

Algorithms↗
PubMed1994

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 VM, 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) VE for abdominal bristle number and 3.66 x 10(-3) VE for sternopleural bristle number, where VE is the environmental variance. Based on 10 generations of divergent selection within lines from generation 93, VM for abdominal bristle number was 6.75 x 10(-3) VE and for sternopleural bristle number was 5.31 x 10(-3) VE. However, estimates of VM 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.

Animals↗
PubMed1994

Analysis of autosomal polygenic variation for the expression of Haldane's rule in flour beetles.

Haldane's rule states that, in interspecific crosses, when hybrid viability or fertility is diminished more in one sex of the hybrids than in the other, the heterogametic sex is more adversely affected. We used quantitative genetic methods to investigate the genetic basis of variation for the expression of the viability aspect of Haldane's rule when Tribolium castaneum males are crossed to Tribolium freemani females. Using a half-sib design, we found significant genetic variance for the expression of Haldane's rule, i.e., variation among T. castaneum sires in the hybrid sex ratios produced by their sons. We also derived 23 independent lineages from the same base population by 8 generations of brother-sister mating. From the same experiments, we also found heritable variation among surviving hybrid males in the incidence of antennal deformities. Upon inbreeding, the variance of both traits (hybrid sex ratio and proportion deformities) increased substantially but the means changed little. Because fitness within T. castaneum lineages declined substantially with inbreeding, we infer that hybrid male viability may have a different genetic basis than viability fitness within species. Deleterious recessive alleles held within species by mutation/selection balance appear not to be a major contributor to hybrid incompatibility.

Animals↗
PubMed1995

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.

Analysis of Variance↗
PubMed1995

Polygenic mutation in Drosophila melanogaster: the causal relationship of bristle number to fitness.

The association between sternopleural and abdominal bristle number and fitness in Drosophila melanogaster was determined for sublines of an initially highly inbred strain that were maintained by divergent artificial selection for 150 generations or by random mating for 180 generations. Replicate selection lines had more extreme bristle numbers than those that were maintained without artificial selection at the same census size for approximately the same number of generations. The average fitness, estimated by a single generation of competition against a compound autosome strain, was 0.17 for lines selected for high and low abdominal bristle numbers and 0.19 for lines selected for high and low sternopleural bristle number. The average fitness of unselected lines, 0.46, was significantly higher than that of the selection lines. The fitnesses and the relationships of bristle number to fitness in progeny of all possible crosses of high x high (H x H), high x low (H x L) and low x low (L x L) selection lines were examined to determine whether the observed intermediate optima were caused by direct stabilizing selection on bristle number or by apparent stabilizing selection mediated through deleterious pleiotropic fitness effects of mutations affecting bristle number. Although bristle number was nearly additive for progeny of H x H, H x L and L x L crosses among sternopleural bristle selection lines, their mean fitnesses were not significantly different from each other, or from the mean fitness of the unselected lines, suggesting partly or completely recessive pleiotropic fitness effects cause apparent stabilizing selection. The average fitness of the progeny of H x H abdominal bristle selection lines was not significantly different from the fitness of unselected lines, but the mean fitness of the progeny of L x L crosses was not significantly different from that of the pure low lines. This is consistent with direct selection against low but not high abdominal bristle number, but the interpretation is confounded by variation in average degree of dominance for fitness (on average recessive in the high abdominal bristle selection lines and additive in the low abdominal bristle selection lines). Neither direct stabilizing selection nor pleiotropy, therefore, can account for all the observations.

Animals↗
PubMed1995

Polygenic mutation in Drosophila melanogaster: genetic analysis of selection lines.

We have conducted genetic analyses of 12 long-term selection lines of Drosophila melanogaster derived from a highly inbred base population, containing new mutations affecting abdominal and sternopleural bristle number. Biometric analysis of the number of effective factors differentiating the selected lines from the base inbred indicated that with the exception of the three lines selected for increased number of abdominal bristles, three or more mutations contributed to the responses of the selection lines. Analysis of the chromosomal distribution of effects revealed that mutations affecting abdominal bristle number occurred on all three major chromosomes. In addition, Y-linked mutations with effects ranging from one to three bristles occurred in all three lines selected for decreased number of abdominal bristles, as well as in one line selected for increased abdominal bristle number. Mutations affecting sternopleural bristle number were mainly on the X and third chromosomes. One abdominal and one sternopleural selection line showed evidence of a segregating lethal with large effects on bristle number. As an indirect test for allelism of mutations occurring in different selection lines, the three lines selected in the same direction for the same trait were crossed in all possible combinations, and selection continued from the F2 hybrids. Responses of the hybrid lines usually did not exceed those of the most extreme parental lines, indicating that the responses of the parental lines may have been partly due to mutations at the same loci, although other interpretations are possible.

Abdomen↗
PubMed1996

Polygenic mutation in Drosophila melanogaster: genetic interactions between selection lines and candidate quantitative trait loci.

We have investigated genetic interactions between spontaneous mutations affecting abdominal and sternopleural bristle number that have accumulated in 12 long-term selection lines derived from an inbred strain, and mutations at 14 candidate bristle number quantitative trait loci. The quantitative test for complementation was to cross the selection lines to an inbred wild-type strain (the control cross) and to a derivative of the control strain into which the mutant allele at the candidate locus to be tested was substituted (the tester strain). Genetic interactions between spontaneous mutations affecting bristle number and the candidate locus mutations were common, and in several cases the interaction effects were different in males and females. Analyses of variance of the (tester- control) differences among and within groups of replicate lines selected in the same direction for the same trait showed significant group effects for several candidate loci. Genetically, the interactions could be caused by allelism of, and/ or epistasis between, spontaneous mutations in the selection lines and the candidate locus mutations. It is possible that much of the response to selection was from new mutations at candidate bristle number quantitative trait loci, and that for some of these loci, mutation rates were high.

Analysis of Variance↗
PubMed1999

An analysis of polygenes affecting wing shape on chromosome 3 in Drosophila melanogaster.

Loci on the third chromosome of Drosophila melanogaster that affect an index of wing shape were mapped, using recombinant isogenic lines, with transposable elements as markers. Many genes with small subequal effects are dispersed along the whole chromosome. Their alleles act nearly additively in heterozygotes. They have small correlated effects on leg shape, but no detectable effects on halteres. Small negative net interactions occur over most of the chromosome. The data set of 519 recombinant isogenic lines can be explained reasonably well by two models. One model posits an indefinitely large number of loci with no interactions. The other model posits 11 loci with additive effects whose sum equals the total phenotypic range and with large positive and negative interactions that nearly cancel each other.

Animals↗
PubMed2001

An analysis of polygenes affecting wing shape on chromosome 2 in Drosophila melanogaster.

Genetic effects on an index of wing shape on chromosome 2 of Drosophila melanogaster were mapped using isogenic recombinants with transposable element markers. At least 10 genes with small additive effects are dispersed evenly along the chromosome. Many interactions exist, with only small net effects in homozygous recombinants and little effect on phenotypic variance. Heterozygous chromosome segments show almost no dominance. Pleiotropic effects on leg shape are only minor. At first view, wing shape genes form a rather homogeneous class, but certain complexities remain unresolved.

Alleles↗
PubMed2003

Estimating polygenic effects using markers of the entire genome.

Molecular markers have been used to map quantitative trait loci. However, they are rarely used to evaluate effects of chromosome segments of the entire genome. The original interval-mapping approach and various modified versions of it may have limited use in evaluating the genetic effects of the entire genome because they require evaluation of multiple models and model selection. Here we present a Bayesian regression method to simultaneously estimate genetic effects associated with markers of the entire genome. With the Bayesian method, we were able to handle situations in which the number of effects is even larger than the number of observations. The key to the success is that we allow each marker effect to have its own variance parameter, which in turn has its own prior distribution so that the variance can be estimated from the data. Under this hierarchical model, we were able to handle a large number of markers and most of the markers may have negligible effects. As a result, it is possible to evaluate the distribution of the marker effects. Using data from the North American Barley Genome Mapping Project in double-haploid barley, we found that the distribution of gene effects follows closely an L-shaped Gamma distribution, which is in contrast to the bell-shaped Gamma distribution when the gene effects were estimated from interval mapping. In addition, we show that the Bayesian method serves as an alternative or even better QTL mapping method because it produces clearer signals for QTL. Similar results were found from simulated data sets of F(2) and backcross (BC) families.

Bayes Theorem↗