Genetic analysis of agronomic characters in chickpea. II. Estimates of genetic variances from line × tester mating designs

Summary Thirty line x tester experiments involving diverse chickpea (Cicer arietinum L.) germplasm were conducted over 8 years and three locations to determine the nature of the genetic variance for grain yield and related characters, and the effects of generation and environment on these genetic parameters. Days-to-flowering, 100-seed mass, and seeds per pod were predominantly under the control of additive genetic variance, while both additive and non-additive genetic components of variance were important for days-to-maturity, plant height, primary and secondary branches, pods per plant, and seed yield. The F₁ and F₂ generations were found equally useful in estimating the genetic variances for different characters because the generation did not significantly interact with genetic parameters in the majority of cases. Sites or seasons, on the other hand, showed significant interaction with genetic components of variances; additive variance showed a larger interaction with environments than non-additive variance. This indicated the importance of more than one site and/ or season for unbiased estimation of the genetic components of variance. The results were compared with previous findings from diallel analyses.ICRISAT Journal Article No. 1200     

The races of maize: III. choices of appropriate characters for racial classification

Analyses of variance for 111 characters from 55 races and subraces of maize from eastern South America grown at Piracicaba, S. P., Brazil, between 1960 and 1965, indicated that those characters which were least affected by environmental factors and interactions were reproductive characters. In particular, the component of variance due to differences among races for certain ear and kernel characters was greater than the sum of the corresponding components due to differences among years and race by year interactions. The converse was true for all vegetative characters. Tassel characters tended to be intermediate between ear and plant characters. While some indices had larger components of variance attributable to racial differences than to the effects of environment and/or environmental interaction, some commonly used ones, such as cob/rachis and rachilla/kernel indices, proved to be quite susceptible to environmental influences. Again, indices based upon solely vegetative characters were consistently influenced more strongly by environmental factors and interaction than were those based on reproductive characters.     

Statistical Genetics of an Annual Plant, Impatiens Capensis. I. Genetic Basis of Quantitative Variation

Analysis of quantitative genetics in natural populations has been hindered by computational and methodological problems in statistical analysis. We developed and validated a jackknife procedure to test for existence of broad sense heritabilities and dominance or maternal effects influencing quantitative characters in Impatiens capensis. Early life cycle characters showed evidence of dominance and/or maternal effects, while later characters exhibited predominantly environmental variation. Monte Carlo simulations demonstrate that these jackknife tests of variance components are extremely robust to heterogeneous error variances. Statistical methods from human genetics provide evidence for either a major locus influencing germination date, or genes that affect phenotypic variability per se. We urge explicit consideration of statistical behavior of estimation and testing procedures for proper biological interpretation of statistical results.     

On the Applicability of Multidimensional Classification Procedures

An example from the EEG-analysis shows that particularly in using the R-error estimation the variance analysis and discrimination might indicate contradictory results. Therefore the use of results of MANOVA for a subsequent discrimination appears not to be advisable as a rule. If the number of test persons per class does not amount to at least the five-fold of the number of characters, the error estimation according to the R-method is not applicable. Since the feature selection by the methods investigated in this paper only pretend an improvement of the classification, producing even misleading results in single cases, it should not be used, at least not with smaller random samples.     

Rosetta error model for gene expression analysis

MOTIVATION: In microarray gene expression studies, the number of replicated microarrays is usually small because of cost and sample availability, resulting in unreliable variance estimation and thus unreliable statistical hypothesis tests. The unreliable variance estimation is further complicated by the fact that the technology-specific variance is intrinsically intensity-dependent. RESULTS: The Rosetta error model captures the variance-intensity relationship for various types of microarray technologies, such as single-color arrays and two-color arrays. This error model conservatively estimates intensity error and uses this value to stabilize the variance estimation. We present two commonly used error models: the intensity error-model for single-color microarrays and the ratio error model for two-color microarrays or ratios built from two single-color arrays. We present examples to demonstrate the strength of our error models in improving statistical power of microarray data analysis, particularly, in increasing expression detection sensitivity and specificity when the number of replicates is limited.     

Variance component estimation techniques compared for two mating designs with forest genetic architecture through computer simulation

Computer simulation was used to compare minimum variance quadratic estimation (MIVQUE), minimum norm quadratic unbiased estimation (MINQUE), restricted maximum likelihood (REML), maximum likelihood (ML), and Henderson's Method 3 (HM3) on the basis of variance among estimates, mean square error (MSE), bias and probability of nearness for estimation of both individual variance components and three ratios of variance components. The investigation also compared three procedures for dealing with negative estimates and included the use of both individual observations and plot means as the experimental unit of the analysis. The structure of data simulated (field design, mating designs, genetic architecture and imbalance) represented typical analysis problems in quantitative forest genetics. Results of comparing the estimation techniques demonstrated that: estimates of probability of nearness did not discriminate among techniques; bias was discriminatory among procedures for dealing with negative estimates but not among estimation techniques (except ML); sampling variance among estimates was discriminatory among procedures for dealing with negative estimates, estimation techniques and unit of observation; and MSE provided no additional information to variance of the estimates. HM3 and REML were the closest competitors under these criteria; however, REML demonstrated greater robustness to imbalance. Of the three negative estimate procedures, two are of practical significance and guidelines for their application are presented. Estimates from individual observations were always preferable to those from plot means over the experimental levels of this study.This is Journal Series NO. R-03768 of the Institute of Food and Agricultural Sciences     

Methodologies for segregation analysis and QTL mapping in plants

Most characters of biological interest and economic importance are quantitative traits. To uncover the genetic architecture of quantitative traits, two approaches have become popular in China. One is the establishment of an analytical model for mixed major-gene plus polygenes inheritance and the other the discovery of quantitative trait locus (QTL). Here we review our progress employing these two approaches. First, we proposed joint segregation analysis of multiple generations for mixed major-gene plus polygenes inheritance. Second, we extended the multilocus method of Lander and Green (1987), Jiang and Zeng (1997) to a more generalized approach. Our methodology handles distorted, dominant and missing markers, including the effect of linked segregation distortion loci on the estimation of map distance. Finally, we developed several QTL mapping methods. In the Bayesian shrinkage estimation (BSE) method, we suggested a method to test the significance of QTL effects and studied the effect of the prior distribution of the variance of QTL effect on QTL mapping. To reduce running time, a penalized maximum likelihood method was adopted. To mine novel genes in crop inbred lines generated in the course of normal crop breeding work, three methods were introduced. If a well-documented genealogical history of the lines is available, two-stage variance component analysis and multi-QTL Haseman-Elston regression were suggested; if unavailable, multiple loci in silico mapping was proposed.     

MAXIMUM-LIKELIHOOD APPROACHES APPLIED TO QUANTITATIVE GENETICS OF NATURAL POPULATIONS

Growing interest in adaptive evolution in natural populations has spurred efforts to infer genetic components of variance and covariance of quantitative characters. Here, I review difficulties inherent in the usual least-squares methods of estimation. A useful alternative approach is that of maximum likelihood (ML). Its particular advantage over least squares is that estimation and testing procedures are well defined, regardless of the design of the data. A modified version of ML, REML, eliminates the bias of ML estimates of variance components. Expressions for the expected bias and variance of estimates obtained from balanced, fully hierarchical designs are presented for ML and REML. Analyses of data simulated from balanced, hierarchical designs reveal differences in the properties of ML, REML, and F-ratio tests of significance. A second simulation study compares properties of REML estimates obtained from a balanced, fully hierarchical design (within-generation analysis) with those from a sampling design including phenotypic data on parents and multiple progeny. It also illustrates the effects of imposing nonnegativity constraints on the estimates. Finally, it reveals that predictions of the behavior of significance tests based on asymptotic theory are not accurate when sample size is small and that constraining the estimates seriously affects properties of the tests. Because of their great flexibility, likelihood methods can serve as a useful tool for estimation of quantitative-genetic parameters in natural populations. Difficulties involved in hypothesis testing remain to be solved.     

Population structure and quantitative characters

A migration matrix model is used to investigate the behavior of neutral polygenic characters in subdivided populations. It is shown that gametic disequilibrium has a large effect on the variance among groups but none at all on its expectation. The variance of among-group variance is substantial and does not depend on the number of loci contributing to variance in the character. It is just as large for polygenic characters as for single loci with the same additive variance. This implies that one polygenic character contains exactly as much information about population relationships as one single-locus marker. The theory is compared with observed differentiation of dermatoglyphic and anthropometric characters among Bougainville islanders.     

Spontaneous Mutation Rate of Modifiers of Metabolism in Drosophila

A rigorous test of our understanding of evolutionary quantitative genetics would be to predict accurately the equilibrium distribution of a character from empirical estimates of the relevant parameters in a mutation-selection-drift balance model. an aspect of this problem that is amenable to experimental analysis is the distribution of the effects of new mutations. This study quantifies the divergence among 200 lines of Drosophila melanogaster as they accumulated mutations on the second chromosome and estimates the rate of increase of variation and covariation in metabolic characters. Amounts of stored triacylglycerol and glycogen and the activities of a series of 12 metabolic enzymes were assayed in a subset of lines at generations 0, 11, 22, 33 and 44. Analyses of the rate of increase in the among-line variance in each trait allowed estimation of V(m)/V(e), the ratio of among-line variance added per generation to the environmental variance. Values of V(m)/V(e) for the second chromosome ranged from 0.0004 to 0.0289 per generation. Six of the 16 characters showed significant departure from a normal distribution, and several lines exhibited large changes in more than one character. The covariance of pairs of traits also was partitioned into a within-line component (environmental covariance, Cov(e)) and an among-line component (mutational covariance, Cov(m)). Both variances and covariance among lines increased over time, as assessed by linear regression, whereas environmental covariance showed no such trend. Results indicate that the quantitative genetic parameters describing the variation in metabolic traits are similar to those of other continuous characters.     

Comparative analysis of methods for estimating arm segment parameters and joint torques from inverse dynamics

A common problem in the analyses of upper limb unfettered reaching movements is the estimation of joint torques using inverse dynamics. The inaccuracy in the estimation of joint torques can be caused by the inaccuracy in the acquisition of kinematic variables, body segment parameters (BSPs), and approximation in the biomechanical models. The effect of uncertainty in the estimation of body segment parameters can be especially important in the analysis of movements with high acceleration. A sensitivity analysis was performed to assess the relevance of different sources of inaccuracy in inverse dynamics analysis of a planar arm movement. Eight regression models and one water immersion method for the estimation of BSPs were used to quantify the influence of inertial models on the calculation of joint torques during numerical analysis of unfettered forward arm reaching movements. Thirteen subjects performed 72 forward planar reaches between two targets located on the horizontal plane and aligned with the median plane. Using a planar, double link model for the arm with a floating shoulder, we calculated the normalized joint torque peak and a normalized root mean square (rms) of torque at the shoulder and elbow joints. Statistical analyses quantified the influence of different BSP models on the kinetic variable variance for given uncertainty on the estimation of joint kinematics and biomechanical modeling errors. Our analysis revealed that the choice of BSP estimation method had a particular influence on the normalized rms of joint torques. Moreover, the normalization of kinetic variables to BSPs for a comparison among subjects showed that the interaction between the BSP estimation method and the subject specific somatotype and movement kinematics was a significant source of variance in the kinetic variables. The normalized joint torque peak and the normalized root mean square of joint torque represented valuable parameters to compare the effect of BSP estimation methods on the variance in the population of kinetic variables calculated across a group of subjects with different body types. We found that the variance of the arm segment parameter estimation had more influence on the calculated joint torques than the variance of the kinematics variables. This is due to the low moments of inertia of the upper limb, especially when compared with the leg. Therefore, the results of the inverse dynamics of arm movements are influenced by the choice of BSP estimation method to a greater extent than the results of gait analysis.     

Age-dependent genetic variance in a life-history trait in the mute swan

Genetic variance in characters under natural selection in natural populations determines the way those populations respond to that selection. Whether populations show temporal and/or spatial constancy in patterns of genetic variance and covariance is regularly considered, as this will determine whether selection responses are constant over space and time. Much less often considered is whether characters show differing amounts of genetic variance over the life-history of individuals. Such age-specific variation, if present, has important potential consequences for the force of natural selection and for understanding the causes of variation in quantitative characters. Using data from a long-term study of the mute swan Cygnus olor, we report the partitioning of phenotypic variance in timing of breeding (subject to strong natural selection) into component parts over 12 different age classes. We show that the additive genetic variance and heritability of this trait are strongly age-dependent, with higher additive genetic variance present in young and, particularly, old birds, but little evidence of any genetic variance for birds of intermediate ages. These results demonstrate that age can have a very important influence on the components of variation of characters in natural populations, and consequently that separate age classes cannot be assumed to be equivalent, either with respect to their evolutionary potential or response.     

The natural variability of morphogenesis: a tool for exploring the mechanics of gastrulation movements in amphibian embryos

The investigation of natural variability of metric morphological characters in frog gastrulation revealed that in genetically and environmentally homogeneous samples of embryos their variability is of a higher order of magnitude than that known for quantitative metric characters in adult organisms. Matching the coefficients of variation of characters under consideration to the specific rates of their changes in normal development revealed a strong positive correlation between the rates of morphological change and the amount of morphological variance. The increase in the variance is mainly in characters concerned with shaping of moving embryonic areas and arises as a result of a positive feedback between the movement of a given area and recruitment of cells from surrounding areas into the movement. The account of natural variation suggests a new model of amphibian gastrulation whose essential feature is the intimate connection between the movement and shaping of the dorsal blastopore lip of the gastrula.     

具有亲缘关系矩阵的混合模型的方差组分迭代估计——应用于计算BLUP的方差比值和遗传参数

论述的是来自非均街资料的混合模型中具有亲缘关系矩阵时利用迭代法估计方差组分问题。这篇文章表明计算程序是可行的,只要能够按照混合模型中固定效应的结构矩阵和Henderson方法3的固定效应的假设条件正确地计算二次型约化平方和,就可获得较为精确的方差组分估计值;而且表明方差初始比值k偏高或偏低,不影响迭代求解的最后结果,这是因为在迭代过程中可以通过结构矩阵x'x和x'x的控制而自行调整。这些方差组分不仅可应用于选种种畜用的BLUP计算,还可用来估计遗传参数。     

Exponential decontamination models for count data

Several models are developed for the estimation of the rate of exponential die-off from decontamination data. Calculations with illustrative data are reported which indicate that the estimation of this rate and its variance are sensitive to changes in modelling assumptions. Since extrapolation using this estimated rate is used in the specification of planetary quarantine standards, special care should be taken in the selection of an appropriate model and corresponding estimation procedure for the analysis of each set of decontamination data to be used for this purpose.     

Efficient Estimators for the verianoe of a Finite Population

For the estimation of finite population variance of a character, DAS and TRIPATHI (1978) proposed some efficient estimators when population mean of variance of some other character (associated with main character) is known. We propose here some estimators for population variance using same information and compare with those given by DAS and TRIPATHI (1978). Some examples are given for illustration.     

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.     

An epistatic genetic basis for fluctuating asymmetry of tooth size and shape in mice

Although there typically is little additive genetic variation for fluctuating asymmetry (FA), or variation in nondirectional differences between left and right sides of bilateral characters, several investigators have hypothesized that FA may have an epistatic genetic basis. We tested this hypothesis by conducting a whole genome scan of FA of size and shape of the mandibular molars in house mice from an F2 intercross population generated from crossing the Large (LG/J) and Small (SM/J) inbred strains. Although no individual genes (QTLs=quantitative trait loci) on any of the 19 autosomes significantly affected FA for centroid size, and only two affected shape FA, a number of pairwise combinations of QTLs exhibited significant epistasis for FA in both molar size and shape. The QTLs involved in these interactions differed for FA in molar size versus FA in molar shape, but their epistatic contributions to the total variance was nearly the same (about 20%) for FA in both molar characters. It was noted that the genetic architecture of FA in the molar characters, consisting of little or no additive genetic variance but an abundance of epistatic genetic variance, is consistent with that of other typical fitness components such as litter size.     

A Simple Illustration of the Failure of PQL,IRREML and APHL as Approximate ML Methods for Mixed Models for Binary Data

Evaluation of the likelihood in mixed models for non-normal data, e.g. dependent binary data, involves high dimensional integration, which offers severe numerical problems. Penalized quasi-likelihood, iterative re-weighted restricted maximum likelihood and adjusted profile h-likelihood estimation are methods which avoid numerical integration. They will be derived by approximation of the maximum likelihood equations. For binary data, these estimation procedures may yield seriously biased estimates for components of variance, intra-class correlation or heritability. An analytical evaluation of a simple example illustrates how very critical the approximations can be for the performance of the variance component estimators.     

Borrowing information across genes and experiments for improved error variance estimation in microarray data analysis

Statistical inference for microarray experiments usually involves the estimation of error variance for each gene. Because the sample size available for each gene is often low, the usual unbiased estimator of the error variance can be unreliable. Shrinkage methods, including empirical Bayes approaches that borrow information across genes to produce more stable estimates, have been developed in recent years. Because the same microarray platform is often used for at least several experiments to study similar biological systems, there is an opportunity to improve variance estimation further by borrowing information not only across genes but also across experiments. We propose a lognormal model for error variances that involves random gene effects and random experiment effects. Based on the model, we develop an empirical Bayes estimator of the error variance for each combination of gene and experiment and call this estimator BAGE because information is Borrowed Across Genes and Experiments. A permutation strategy is used to make inference about the differential expression status of each gene. Simulation studies with data generated from different probability models and real microarray data show that our method outperforms existing approaches.