REGRESSION ANALYSIS OF NATURAL SELECTION: STATISTICAL INFERENCE AND BIOLOGICAL INTERPRETATION

Recent theoretical work in quantitative genetics has fueled interest in measuring natural selection in the wild. We discuss statistical and biological issues that may arise in applications of Lande and Arnold's (1983) multiple-regression approach to measuring selection. We review assumptions involved in estimation and hypothesis testing in regression problems, and we note difficulties that frequently arise as a result of violation of these assumptions. In particular, multicollinearity (extreme intercorrelation of characters) and extrinsic, unmeasured factors affecting fitness may seriously complicate inference regarding selection. Further, violation of the assumption that residuals are normally distributed vitiates tests of significance. For this situation, we suggest applications of recently developed jackknife tests of significance. While fitness regression permits direct assessment of selection in a form suitable for predicting selection response, we suggest that the aim of inferring causal relationships about the effects of phenotypic characters on fitness is greatly facilitated by manipulative experiments. Finally, we discuss alternative definitions of stabilizing and disruptive selection.     

The quantitative genetic basis of polyandry in the parasitoid wasp, Nasonia vitripennis

Understanding the evolution of female multiple mating (polyandry) is crucial for understanding sexual selection and sexual conflict. Despite this interest, little is known about its genetic basis or whether genetics influences the evolutionary origin or maintenance of polyandry. Here, we explore the quantitative genetic basis of polyandry in the parasitoid wasp Nasonia vitripennis, a species in which female re-mating has been observed to evolve in the laboratory. We performed a quantitative genetic experiment on a recently collected population of wasps. We found low heritabilities of female polyandry (re-mating frequency after 18 h), low heritability of courtship duration and a slightly higher heritability of copulation duration. However, the coefficients of additive genetic variance for these traits were all reasonably large (CV(A)>7.0). We also found considerable dam effects for all traits after controlling for common environment, suggesting either dominance or maternal effects. Our work adds to the evidence that nonadditive genetic effects may influence the evolution of mating behaviour in Nasonia vitripennis, and the evolution of polyandry more generally.     

Comparing sire and dam estimates of heritability: jackknife and likelihood approaches

Three estimates of heritability are available from the half-sib pedigree design: the sire, dam and genotypic estimates. Because of its significantly smaller standard error, the genotypic estimate is preferred provided that there are no non-additive effects that inflate the estimate. I present two methods to test for such effects: these are a t-test of the paired sire and dam pseudovalues from the jackknife procedure and the likelihood ratio test from the animal model. Both methods are shown to be valid tests for significant dominance and/or maternal effects. SPLUS coding for the implementation of the jackknife method is provided. Unless sample sizes are very large, the power of the tests is low and hence caution is advised in the use of the genotypic estimate following a nonsignificant test. An approximate power analysis can be done using the data from the jackknife method but the estimated power is typically a substantial underestimate of the true power and its use is not recommended.     

Quantitative genetics of functional characters in<Emphasis Type="Italic">Drosophila melanogaster</Emphasis> populations subjected to laboratory selection

What are the genetics of phenotypes other than fitness, in outbred populations? To answer this question, the quantitative-genetic basis of divergence was characterized for outbredDrosophila melanogaster populations that had previously undergone selection to enhance characters related to fitness. Line-cross analysis using first-generation and second-generation hybrids from reciprocal crosses was conducted for two types of cross, each replicated fivefold. One type of cross was between representatives of the ancestral population, a set of five populations maintained for several hundred generations on a two-week discrete-generation life cycle and a set of five populations adapted to starvation stress. The other type of cross was between the same set of ancestral-representative populations and another set of five populations selected for accelerated development from egg to egg. Developmental time from egg to eclosion, starvation resistance, dry body weight and fecundity at day 14 from egg were fit to regression models estimating single-locus additive and dominant effects, maternal and paternal effects, and digenic additive and dominance epistatic effects. Additive genetic variation explained most of the differences between populations, with additive maternal and cytoplasmic effects also commonly found. Both within-locus and between-locus dominance effects were inferred in some cases, as well as one instance of additive epistasis. Some of these effects may have been caused by linkage disequilibrium. We conclude with a brief discussion concerning the relationship of the genetics of population differentiation to adaptation.     

Quantitative Genetics of Postponed Aging in Drosophila Melanogaster. I. Analysis of Outbred Populations

Selection has been used to create replicated outbred stocks of Drosophila melanogaster with increased longevity, increased later fecundity, and increased levels of physiological performance at later ages. The present study analyzed the quantitative transmission patterns of such stocks, employing extensive replication in numbers of stocks, individuals, and assayed characters. The populations used derived from five lines with postponed aging and five control lines, all created in 1980 from the same founding base population. The following characters were studied: early 24-hr fecundity, early ovary weight, early female starvation resistance, early male starvation resistance, female longevity and male longevity. Numerous crosses were performed to test for non-Mendelian inheritance, average dominance, maternal effects, sex-linkage and between-line heterogeneity. There was only slight evidence for any of these phenomena arising reproducibly in the characters studied. These findings suggest the value of this set of stocks for studies of the physiological basis of postponed aging.     

Quantitative Genetics of Postponed Aging in Drosophila Melanogaster. II. Analysis of Selected Lines

Quantitative genetic analyses of Drosophila melanogaster stocks with postponed aging have suffered from the problem of a lack of certainty concerning patterns of allelic differentiation. The present experiments were designed to alleviate this difficulty by selecting for enhanced levels of characters known to be related to postponed aging. Selection successfully increased the degree of differentiation of postponed aging stocks with respect to starvation resistance and fecundity, but persistent additive genetic variance suggested that selection did not result in fixation of alleles. The artificially selected stocks were subjected to crosses to test for patterns of dominance and maternal effects. There was little evidence for these effects in the inheritance of the characters underlying postponed aging, even with the increased differentiation of the selected stocks.     

An analysis of genetic variation in sugar beet (Beta vulgaris L. using an augmented biparental (ABIP) mating design

An augmented biparental (ABIP) mating design was used to investigate the quantitative variation, particularly the dominance variation, for morphological and chemical characters in sugar beet. Diploid O-type plants were both crossed and selfed and the progeny were grown in a single-plant randomised field trial. A comparison of the two kinds of family provided tests for both dominance variation and directional dominance effects. Estimates of the narrow heritability were also obtained for each character. Germination problems reduced the size of the final analysis but evidence was obtained of dominance variation and positive directional dominance effects for leaf length, root weight and potassium concentration and, to a lesser extent, sugar concentration. Genetic control of sodium and alpha-amino nitrogen concentrations appeared to be mostly additive. Hybrid varieties of sugar beet should exploit these directional dominance effects and the more closely varieties approach true F, hybrids the more they will capitalise on these advantages. It is possible that other factors such as epistasis, contamination, competition and seed effects may cause us to under- or overestimate the importance of dominance.     

昆虫的母代效应

母代效应,由于其特殊的作用方式,引起了许多进化生态学家的极大兴趣。近年来,随着研究的不断深入,特别是数量遗传学的引入,使该领域的研究取得了令人瞩目的成绩。该文就这几十年来对母代效应研究进行综述,论述昆虫生活史中的母代效应及其适应意义,阐明以下几个问题：（1）母代效应影响昆虫哪些特征;（2）环境因素对母代效应的影响;（3）母代对环境刺激的敏感期;（4）子代受母代效应调控的敏感期;（5）母代效应调控子代生长发育的生化机制;（6）种群内和种群间母代效应的基因差异。     

The ecology and genetics of fitness in forest plants. IV. Quantitative genetics of fitness components in Impatiens pallida (Balsaminaceae)

Genetic and environmental variances were estimated for a number of characters in the annual plant Impatiens pallida by planting seed obtained through controlled crosses into their native field site or pots maintained in the greenhouse. Significant additive genetic variance was detected for three of 11 characters studied—germination date, cotyledon area, and date of first flower production. Significant dominance and/or maternal variance was found for seed weight, proportion of seeds germinating, cotyledon area, plant height, and number of leaves produced. Environmental variance was greater in the field compared with the greenhouse. Characters found to be under strong directional selection in a previous study showed no detectable additive genetic variance. While these populations exhibit conditions that in theory could contribute to the maintenance of genetic variation (limited pollen and seed dispersal distances and small-scale variation for edaphic characteristics influencing plant growth), levels of additive genetic variance for most characters were not significantly different from zero.     

Influence of mom and dad: quantitative genetic models for maternal effects and genomic imprinting

The expression of an imprinted gene is dependent on the sex of the parent it was inherited from, and as a result reciprocal heterozygotes may display different phenotypes. In contrast, maternal genetic terms arise when the phenotype of an offspring is influenced by the phenotype of its mother beyond the direct inheritance of alleles. Both maternal effects and imprinting may contribute to resemblance between offspring of the same mother. We demonstrate that two standard quantitative genetic models for deriving breeding values, population variances and covariances between relatives, are not equivalent when maternal genetic effects and imprinting are acting. Maternal and imprinting effects introduce both sex-dependent and generation-dependent effects that result in differences in the way additive and dominance effects are defined for the two approaches. We use a simple example to demonstrate that both imprinting and maternal genetic effects add extra terms to covariances between relatives and that model misspecification may over- or underestimate true covariances or lead to extremely variable parameter estimation. Thus, an understanding of various forms of parental effects is essential in correctly estimating quantitative genetic variance components.     

籼稻糙米厚度的发育遗传研究

应用包括３套遗传体系基因效应的数量性状发育遗传模型,分析了１２个籼稻亲本在４个不同稻米发育时期的糙米厚性状。结果表明,三倍体胚乳、二倍体母体植株基因的加性和显性效应以及细胞质效应均可以明显影响各个稻米发育时期的糙米厚度,其中灌浆始期以二倍体母体植株效应为主,灌浆中后期以三倍体胚乳效应为主,成熟期则以细胞质效应为主。在４个不同发育时期中,控制糙米厚的基因加性效应和显性效应交替为主。胚乳显性方差和母体     

Mapping quantitative trait Loci interactions from the maternal and offspring genomes

The expression of most developmental or behavioral traits involves complex interactions between quantitative trait loci (QTL) from the maternal and offspring genomes. The maternal-offspring interactions play a pivotal role in shaping the direction and rate of evolution in terms of their substantial contribution to quantitative genetic (co)variation. To study the genetics and evolution of maternal-offspring interactions, a unifying statistical framework that embraces both the direct and indirect genetic effects of maternal and offspring QTL on any complex trait is developed. This model is derived for a simple backcross design within the maximum-likelihood context, implemented with the EM algorithm. Results from extensive simulations suggest that this model can provide reasonable estimation of additive and dominant effects of the QTL at different generations and their interaction effects derived from the maternal and offspring genomes. Although our model is framed to characterize the actions and interactions of maternal and offspring QTL affecting offspring traits, the idea can be readily extended to decipher the genetic machinery of maternal traits, such as maternal care. Our model provides a powerful means for studying the evolutionary significance of indirect genetic effects in any sexually reproductive organisms.     

The nature of quantittative 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.     

Genetic Correlations and Maternal Effect Coefficients Obtained from Offspring-Parent Regression

Additive genetic variances and covariances of quantitative characters are necessary to predict the evolutionary response of the mean phenotype vector in a population to natural or artificial selection. Standard formulas for estimating these parameters, from the resemblance between relatives in one or two characters at a time, are biased by natural selection on the parents and by maternal effects. We show how these biases can be removed using a multivariate analysis of offspring-parent regressions. A dynamic model of maternal effects demonstrates that, in addition to the phenotypic variance-covariance matrix of the characters, sufficient parameters for predicting the response of the mean phenotype vector to weak selection are the additive genetic variance-covariance matrix and a set of causal coefficients for maternal effects. These can be simultaneously estimated from offspring-parent regressions alone, in some cases just from the daughter-mother regressions, if all of the important selected and maternal characters have been measured and included in the analysis.     

A method for identification of the expression mode and mapping of QTL underlying embryo-specific characters

Embryos of crop seeds are one of the major sources of the plant protein and lipid for human nutrition. The genetic expression for embryo-specific characters in crop seeds can be controlled exclusively by the embryo or the maternal genotypes and sometimes by both simultaneously. However, current methods for mapping quantitative trait loci (QTLs) underlying characters of maternal plants have not been effective in dealing with the QTL analysis of embryo characters. On the basis of the expression feature of embryo, a statistical method was proposed for the identification of expression mode and mapping of QTL controlling embryo traits. The maximum likelihood method implemented via the expectation maximization algorithm was used to estimate parameters of a putative embryo-specific QTL. The QTL expression mode was identified by the likelihood ratio test statistic. Statistical power and other properties of the proposed method were investigated under a variety of scenarios through simulation studies. The results showed that the mapping method neglecting the effects of embryo genotype or maternal effects could neither identify the expression mode of QTL nor estimate its genetic effects accurately, whereas the proposed method could effectively map the embryo-specific QTL of various expression modes.     

The correlation of substitution effects across populations and generations in the presence of nonadditive functional gene action

Allele substitution effects at quantitative trait loci (QTL) are part of the basis of quantitative genetics theory and applications such as association analysis and genomic prediction. In the presence of nonadditive functional gene action, substitution effects are not constant across populations. We develop an original approach to model the difference in substitution effects across populations as a first order Taylor series expansion from a “focal” population. This expansion involves the difference in allele frequencies and second-order statistical effects (additive by additive and dominance). The change in allele frequencies is a function of relationships (or genetic distances) across populations. As a result, it is possible to estimate the correlation of substitution effects across two populations using three elements: magnitudes of additive, dominance, and additive by additive variances; relationships (Nei’s minimum distances or Fst indexes); and assumed heterozygosities. Similarly, the theory applies as well to distinct generations in a population, in which case the distance across generations is a function of increase of inbreeding. Simulation results confirmed our derivations. Slight biases were observed, depending on the nonadditive mechanism and the reference allele. Our derivations are useful to understand and forecast the possibility of prediction across populations and the similarity of GWAS effects.     

The quantitative genetics of fluctuating asymmetry

Fluctuating asymmetry (subtle departures from identical expression of a trait across an axis of symmetry) in many taxa is under stabilizing selection for reduced asymmetry. However, lack of reliable estimates of genetic parameters for asymmetry variation hampers our ability to predict the evolutionary outcome of this selection. Here we report on a study, based on analysis of variation within and between isofemale lines and of generation means (line-cross analysis), designed to dissect in detail the quantitative genetics of positional fluctuating asymmetry (PFA) in bristle number in natural populations of Drosophila falleni. PFA is defined as the difference between the two sides of the body in the placement or position of components of a meristic trait. Heritability (measured at 25 degrees C) of two related measures of PFA were 13% and 21%, both of which differed significantly from zero. In contrast, heritability estimates for fluctuating asymmetry in the total number of anterior (0.7%) and transverse (2.4%) sternopleural bristles were smaller, not significant, and in quantitative agreement with previously published estimates. Heritabilities for bristle number (trait size) were considerably greater than that for any asymmetry measure. The experimental design controlled for the potentially confounding effects of common familial environment, and repeated testing revealed that PFA differences between lines were genetically stable for up to 16 generations in the laboratory at 25 degrees C. We performed line cross analysis between strains at the extremes of the PFA distribution (highest and lowest values); parental strains, F1, F1r (reciprocal), F2, backcross, and backcross reciprocal generations were represented. The inheritance of PFA was described best by additive and dominance effects localized to the X-chromosomes, whereas autosomal dominance effects were also detected. Epistatic, maternal, and cytoplasmic effects were not detected. The inheritance of trait size was notably more complex and involved significant autosomal additive, dominance, and epistatic effects; maternal dominance effects; and additive and dominance effects localized to the X-chromosomes. The additive genetic correlation between PFA and its associated measure of trait size was negative (-0.049), but not statistically significant, indicating that the loci contributing additive genetic effects to these traits are probably different. It is suggested that PFA may be a sensitive measure of developmental instability because PFA taps the ability of an organism to integrate interconnected developmental pathways.     

Analysis of cytoplasmic and maternal effects. II. Genetic models for triploid endosperms

Genetic models for quantitative traits of triploid endosperms are proposed for the analysis of direct gene effects, cytoplasmic effects, and maternal gene effects. The maternal effect is partitioned into maternal additive and dominance components. In the full genetic model, the direct effect is partitioned into direct additive and dominance components and high-order dominance component, which are the cumulative effects of three-allele interactions. If the high-order dominance effects are of no importance, a reduced genetic model can be used. Monte Carlo simulations were conducted in this study for demonstrating unbiasedness of estimated variance and covariance components from the MINQUE (0/1) procedure, which is a minimum norm quadratic unbiased estimation (MINQUE) method setting 0 for all the prior covariances and 1 for all the prior variances. Robustness of estimating variance and covariance components for the genetic models was tested by simulations. Both full and reduced genetic models are shown to be robust for estimating variance and covariance components under several situations of no specific effects. Efficiency of predicting random genetic effects for the genetic models by the MINQUE (0/1) procedure was compared with the best linear unbiased prediction (BLUP). A worked example is given to illustrate the use of the reduced genetic model for kernel growth characteristics in corn (Zea mays L.).     

作物数量性状研究进展

作物主要农艺性状和经济性状大多属于数量性状。传统数量遗传学采用数理统计方法,把控制数量性状的多基因系统作为一个整体进行研究。DNA分子标记技术的出现和发展,为数量性状研究提供了重要工具。自20世纪80年代以来,QTL定位的统计分析方法发展很快,先后提出单标记分析法、区间作图法及复合区间作图法等。目前,作物QTL研究取得了重要进展,一些重要作物、重要农艺性状的主效QTL基因已被相继克隆成功,作物数量性状的研究已经成为一个具有勃勃生机的热门领域。     

Mixed Model Methods for Genomic Prediction and Variance Component Estimation of Additive and Dominance Effects Using SNP Markers

We established a genomic model of quantitative trait with genomic additive and dominance relationships that parallels the traditional quantitative genetics model, which partitions a genotypic value as breeding value plus dominance deviation and calculates additive and dominance relationships using pedigree information. Based on this genomic model, two sets of computationally complementary but mathematically identical mixed model methods were developed for genomic best linear unbiased prediction (GBLUP) and genomic restricted maximum likelihood estimation (GREML) of additive and dominance effects using SNP markers. These two sets are referred to as the CE and QM sets, where the CE set was designed for large numbers of markers and the QM set was designed for large numbers of individuals. GBLUP and associated accuracy formulations for individuals in training and validation data sets were derived for breeding values, dominance deviations and genotypic values. Simulation study showed that GREML and GBLUP generally were able to capture small additive and dominance effects that each accounted for 0.00005–0.0003 of the phenotypic variance and GREML was able to differentiate true additive and dominance heritability levels. GBLUP of the total genetic value as the summation of additive and dominance effects had higher prediction accuracy than either additive or dominance GBLUP, causal variants had the highest accuracy of GREML and GBLUP, and predicted accuracies were in agreement with observed accuracies. Genomic additive and dominance relationship matrices using SNP markers were consistent with theoretical expectations. The GREML and GBLUP methods can be an effective tool for assessing the type and magnitude of genetic effects affecting a phenotype and for predicting the total genetic value at the whole genome level.