A TEST OF THE CONJECTURE THAT G‐MATRICES ARE MORE STABLE THAN B‐MATRICES

The G‐matrix occupies an important position in evolutionary biology both as a summary of the inheritance of quantitative traits and as an ingredient in predicting how those traits will respond to selection and drift. Consequently, the stability of G has an important bearing on the accuracy of predicted evolutionary trajectories. Furthermore, G should evolve in response to stable features of the adaptive landscape and their trajectories through time. Although the stability and evolution of G might be predicted from knowledge of selection in natural populations, most empirical comparisons of G‐matrices have been made in the absence of such a priori predictions. We present a theoretical argument that within‐sex G‐matrices should be more stable than between‐sex B‐matrices because they are more powerfully exposed to multivariate stabilizing selection. We tested this conjecture by comparing estimates of B‐ and within‐sex G‐matrices among three populations of the garter snake Thamnophis elegans. Matrix comparisons using Flury's hierarchical approach revealed that within‐sex G‐matrices had four principal components in common (full CPC), whereas B‐matrices had only a single principal component in common and eigenvalues that were more variable among populations. These results suggest that within‐sex G is more stable than B , as predicted by our theoretical argument.     

Multiple-trait genome-wide association study based on principal component analysis for residual covariance matrix

Given the drawbacks of implementing multivariate analysis for mapping multiple traits in genome-wide association study (GWAS), principal component analysis (PCA) has been widely used to generate independent ‘super traits'' from the original multivariate phenotypic traits for the univariate analysis. However, parameter estimates in this framework may not be the same as those from the joint analysis of all traits, leading to spurious linkage results. In this paper, we propose to perform the PCA for residual covariance matrix instead of the phenotypical covariance matrix, based on which multiple traits are transformed to a group of pseudo principal components. The PCA for residual covariance matrix allows analyzing each pseudo principal component separately. In addition, all parameter estimates are equivalent to those obtained from the joint multivariate analysis under a linear transformation. However, a fast least absolute shrinkage and selection operator (LASSO) for estimating the sparse oversaturated genetic model greatly reduces the computational costs of this procedure. Extensive simulations show statistical and computational efficiencies of the proposed method. We illustrate this method in a GWAS for 20 slaughtering traits and meat quality traits in beef cattle.     

Selection Indices and Multivariate Analysis Show Similar Results in the Evaluation of Growth and Carcass Traits in Beef Cattle

This research evaluated a multivariate approach as an alternative tool for the purpose of selection regarding expected progeny differences (EPDs). Data were fitted using a multi-trait model and consisted of growth traits (birth weight and weights at 120, 210, 365 and 450 days of age) and carcass traits (longissimus muscle area (LMA), back-fat thickness (BF), and rump fat thickness (RF)), registered over 21 years in extensive breeding systems of Polled Nellore cattle in Brazil. Multivariate analyses were performed using standardized (zero mean and unit variance) EPDs. The k mean method revealed that the best fit of data occurred using three clusters (k = 3) (P < 0.001). Estimates of genetic correlation among growth and carcass traits and the estimates of heritability were moderate to high, suggesting that a correlated response approach is suitable for practical decision making. Estimates of correlation between selection indices and the multivariate index (LD1) were moderate to high, ranging from 0.48 to 0.97. This reveals that both types of indices give similar results and that the multivariate approach is reliable for the purpose of selection. The alternative tool seems very handy when economic weights are not available or in cases where more rapid identification of the best animals is desired. Interestingly, multivariate analysis allowed forecasting information based on the relationships among breeding values (EPDs). Also, it enabled fine discrimination, rapid data summarization after genetic evaluation, and permitted accounting for maternal ability and the genetic direct potential of the animals. In addition, we recommend the use of longissimus muscle area and subcutaneous fat thickness as selection criteria, to allow estimation of breeding values before the first mating season in order to accelerate the response to individual selection.     

基于主成分分析法的墨兰品种观赏价值评价

以福州地区栽培多年的30个墨兰品种为材料,对其植株高、花色、瓣型等20个观赏性状进行测定和观察,分析墨兰品种观赏性状的变异范围、性状间的相关性以及主成分因子,并利用主成分分析法对30个墨兰品种的观赏价值进行评价。结果表明,不同品种间的16个数量性状均存在不同程度的变异,花部形态存在较大差异,叶片形态和数量变异小;4个质量性状中,花色和叶艺的遗传多样性较高。叶部形态和花部形态的观赏性状间存在显著相关性。20个观赏性状指标可以分为7个主成分因子,分别为株高因子、瓣型因子、花色因子、叶片数因子、花径因子、叶宽因子和叶艺因子,7个主成分因子的方差贡献率累计达全部性状信息的87.35%。通过计算30个品种的重要主成分值并对其进行排序,筛选出4个观赏性状优良的品种,分别为‘白墨’、‘宝山爪’、‘龙梅’和‘金华山’。     

Estimates of heritability and correlations of morphometric traits in Clarkia (Onagraceae)

Summary Interspecific heritability values were estimated using parent-offspring regression analyses for 11 morphological traits differentiating Clarkia nitens and C. speciosa subsp. polyantha. Estimates ranged from near 0 for anther color and germination percentage, to 0.8 for calyx length and petal tip color. Phenotypic, genetic, and environmental correlation matrices were computed to determine the extent of interspecific correlations of traits. Cluster analyses of the genetic and environmental correlation matrices each resulted in three clusters of correlated traits; however, the clusters derived from the two matrices were different. The clusters produced by analysis of the environmental correlation matrix were similar to the factors obtained from principal component analysis of the phenotypic correlation matrix. Genetic correlations may result from strong linkage due to interspecific chromosomal differences.     

A simple stepwise procedure of deriving selection index with restrictions

Summary A simplified alternative procedure was derived for computing selection indices with various restrictions. The procedure involved construction of a sub-index for the unrestricted traits by the conventional methods (Smith-Hazel index approach) and construction of a sub-index for the restricted traits based on the restrospective index approach. The two subindices were then combined to obtain the desired index which met the prespecified restriction. The formulation is straightforward and easy to compute and does not involve the complicated formula as does the derivation of restricted index by the use of the Lagrange multiplier method. As a consequence of simplification, the proposed procedure is approximate in terms of optimal gain in net merit. The procedure presented can also be extended to derive an index with simultaneous imposition of multiple restrictions. Numerical examples were given to illustrate the use of this alternative approach.Animal Research Centre Contribution No. 1251     

15份多花黑麦草优良引进种质的表型变异分析

多花黑麦草(Lolium multiflorum Lam.)是世界栽培牧草中的优良禾本科牧草。为更好地利用多花黑麦草种质资源,本研究对引自国外的15份多花黑麦草种质的15个形态性状和农艺性状进行了变异系数、相关性分析、主成分分析和聚类分析。结果表明:15份材料间存在较大变异,除单株干重外,其余性状在供试材料间均表现出显著性差异,变异系数范围为10.28%~39.15%,变异系数平均值为19.49%,从小到大依次为小穗数小穗长株高分蘖数千粒重花序长倒二叶长小花数茎粗第一节间长倒二叶宽旗叶宽旗叶长单株干重单株鲜重。主成分结果表明,前5个主成分累积贡献率达到84.51%,第1主成分以株高为主要特征;第2主成分以旗叶和倒二叶长、宽为主要特征;第3主成分以花序长和小花数为主要特征;第4主成分以千粒重为主要特征;第5主成分以产草量为主要特征。15份种质材料经基于欧氏距离的UPGMA聚类分析被划分为3大类,类别间存在较显著的差异,其中第2类因其植株高大、叶片宽大的特点,具备选育高产种质的潜力。     

湿加松无性系表型遗传多样性研究

以35个湿加松（Pinus elliottii×P.caribaea Morelet var.hondurensis）无性系为试验材料,对其8个表型性状进行相关性分析、聚类分析及主成分分析研究,并深入探讨了遗传多样性水平,为湿加松无性系利用及良种选育提供科学依据。结果表明：（1）生长性状变异系数介于12.31~29.28%,均值为22.90%;多样性指数介于1.61~1.80,均值为1.69。形质性状变异系数介于13.34~47.25%,均值为26.86%;多样性指数介于1.50~1.94,均值为1.77。表明湿加松无性系遗传变异较为丰富,遗传多样性水平较高。（2）8对表型性状两两间有11对呈极显著正相关,5对呈显著正相关。选定材积为该材料育种选择的主要指标,其次为树高。（3）采用系统聚类法在欧式距离为12的时候将35个无性系分为6大类群,部分来源相同或父本相同的聚为一类,说明它们在表型上的变异较小。（4）针对8个表型性状做主成分分析提取了3个主成分,累积贡献率达86.00%,主要代表了6个性状,以此来表达所有供试材料的综合变异情况。     

Index selection with nonlinear profit function as a tool to achieve simultaneous genetic gain

Summary Simultaneous improvement of several, and often negatively correlated, traits is frequently a desired objective in forest tree breeding. A profit function that includes a combination of both linear weights and weights for the cross-products of trait combinations facilitates the construction of a linear index, with an attractive response in all traits. A detailed algorithm for finding the index coefficients is provided, along with three examples of applications in tree breeding. The index is also a powerful tool in optimizing the selection for a ratio of two traits. It is argued that a more equal progress in several traits provides a safetey net when faced with economic uncertainties. The provided algorithm eliminates the need for direct search techniques. Existence of a dual set of linear weights means that the statistical properties of the index based on nonlinear profit functions are identical to those of the classical Smith-Hazel type of index.     

76株薄壳山核桃实生单株的果实品质差异及综合评价

对南京地区种植的76株薄壳山核桃〔Carya illinoinensis(Wangenh.)K.Koch〕实生单株的8项果实性状和种仁中5种脂肪酸含量的差异以及各指标的相关性进行分析,并筛选出单项性状优良的单株;在此基础上,结合主成分分析结果,对供试76株单株的果实品质进行综合评价.结果显示:8项果实性状(包括坚果质量、种仁鲜质量、坚果壳厚度、坚果纵径、坚果横径、果形指数、出仁率和含油率)以及种仁中5种脂肪酸(包括棕榈酸、硬脂酸、油酸、亚油酸和亚麻酸)的含量均有较大变异,变异系数为663%~2899%,其中,出仁率的变异系数最小,亚麻酸含量的变异系数最大,8项果实性状的变异系数总体上小于5种脂肪酸含量的变异系数.部分果实性状间极显著或显著正相关,少数果实性状间极显著或显著负相关,而5种脂肪酸含量间均极显著正相关,但脂肪酸含量与果实性状间总体上无显著相关性.主成分分析结果表明:在8项果实性状中,与坚果大小有关的性状较为重要;而5种脂肪酸含量均同等重要.对果实性状和脂肪酸含量的主成分分析结果显示:第1主成分的决定指标包括含油率以及棕榈酸、硬脂酸、油酸、亚油酸和亚麻酸的含量,第2主成分的决定指标包括坚果质量、种仁鲜质量、坚果壳厚度和坚果横径,说明薄壳山核桃果实评价的首要指标为种仁中脂肪酸含量,其次为果实大小.在利用坚果质量、种仁鲜质量、坚果壳厚度、出仁率、含油率、果形指数、油酸含量和不饱和脂肪酸含量8个单项指标优选单株的基础上,结合主成分分析结果,71号单株的综合得分较高,其种仁鲜质量、含油率以及油酸和不饱和脂肪酸的含量均较高,可作为优良品种选育的首选候选单株.根据上述研究结果,建议在薄壳山核桃不同育种目标的优良品种选育工作中,将主成分分析法作为单项性状筛选法的有效补充方法.     

The search for Pleiades in trait constellations: functional integration and phenotypic selection in the complex flowers of Morrenia brachystephana (Apocynaceae)

Pollinator‐mediated natural selection on single traits, such as corolla tube or spur length, has been well documented. However, flower phenotypes are usually complex, and selection is expected to act on several traits that functionally interact rather than on a single isolated trait. Despite the fact that selection on complex phenotypes is expectedly widespread, multivariate selection modelling on such phenotypes still remains under‐explored in plants. Species of the subfamily Asclepiadoideae (Apocynaceae) provide an opportunity to study such complex flower contrivances integrated by fine‐scaled organs from disparate developmental origin. We studied the correlation structure among linear floral traits (i) by testing a priori morphological, functional or developmental hypotheses among traits and (ii) by exploring the organization of flower covariation, considering alternative expectations of modular organization or whole flower integration through conditional dependence analysis (CDA) and integration matrices. The phenotypic selection approach was applied to determine whether floral traits involved in the functioning of the pollination mechanism were affected by natural selection. Floral integration was low, suggesting that flowers are organized in more than just one correlation pleiad; our hypothetical functional correlation matrix was significantly correlated with the empirical matrix, and the CDA revealed three putative modules. Analyses of phenotypic selection showed significant linear and correlational gradients, lending support to expectations of functional interactions between floral traits. Significant correlational selection gradients found involved traits of different floral whorls, providing evidence for the existence of functional integration across developmental domains.     

60Coγ射线辐射诱变大杯香菇的营养价值效应的主成分分析

应用多元统计成分分析法,对不同剂量60Coγ射线辐射大杯香菇诱发的蛋白质营养价值的6个主要营养指标进行了相关及主成分分析.结果表明,大杯香菇的大部分营养指标间存在极显著或显著相关.主成分分析显示,可将原6个营养指标综合为2个主成分,其累积贡献率可达96.20%.根据主成分对原性状的综合能力,进行营养价值分析,2个主成分可分别解释为生物价和必需氨基酸指数效应因子和营养指数效应因子,并建立了主成分方程,各处理组的主成分得分、综合得分计算排序第一为1.25 kGy处理组,所以为较适宜的辐射剂量.     

Morphological and molecular characterization of sweet,grain and forage sorghum (Sorghum bicolor L.) genotypes grown under temperate climatic conditions

Abstract

In the present study, we used 12 genotypes of sorghum originated from different countries (five sweet, four grain and three forage). These different genotypes and types of sorghum were evaluated for the agro-morphological traits that are associated with the estimated sugar and bioethanol yield to estimate their phenotypic diversity. Analysis of variance showed significant differences between different types of sorghum for all the evaluated traits. Sweet sorghum genotypes, however, showed better performance with respect to all studied traits than the other genotypes. A positive significant correlation was observed between plant height, leaf number, leaf area, biomass yield, cane and bagasse yields, and the predicted bioethanol yield. Both, cluster and principal component analysis were performed to group the genotypes according to their agro-morphological and molecular similarity coefficients. For analytical approaches, the Iranian grain and forage genotypes clustered separately from the other genotypes. The clustering patterns obtained from the molecular dominant markers had higher discriminatory power than using morphological characters to separate sweet genotypes from the forage and grain sorghum ones. The results clearly indicated that sweet sorghum can be grown in Germany and maintains its superiority in biomass production and sugar yield over grain and forage sorghum types.     

Multivariate QST-FST comparisons: a neutrality test for the evolution of the g matrix in structured populations

Neutrality tests in quantitative genetics provide a statistical framework for the detection of selection on polygenic traits in wild populations. However, the existing method based on comparisons of divergence at neutral markers and quantitative traits (Q(st)-F(st)) suffers from several limitations that hinder a clear interpretation of the results with typical empirical designs. In this article, we propose a multivariate extension of this neutrality test based on empirical estimates of the among-populations (D) and within-populations (G) covariance matrices by MANOVA. A simple pattern is expected under neutrality: D = 2F(st)/(1 - F(st))G, so that neutrality implies both proportionality of the two matrices and a specific value of the proportionality coefficient. This pattern is tested using Flury's framework for matrix comparison [common principal-component (CPC) analysis], a well-known tool in G matrix evolution studies. We show the importance of using a Bartlett adjustment of the test for the small sample sizes typically found in empirical studies. We propose a dual test: (i) that the proportionality coefficient is not different from its neutral expectation [2F(st)/(1 - F(st))] and (ii) that the MANOVA estimates of mean square matrices between and among populations are proportional. These two tests combined provide a more stringent test for neutrality than the classic Q(st)-F(st) comparison and avoid several statistical problems. Extensive simulations of realistic empirical designs suggest that these tests correctly detect the expected pattern under neutrality and have enough power to efficiently detect mild to strong selection (homogeneous, heterogeneous, or mixed) when it is occurring on a set of traits. This method also provides a rigorous and quantitative framework for disentangling the effects of different selection regimes and of drift on the evolution of the G matrix. We discuss practical requirements for the proper application of our test in empirical studies and potential extensions.     

光皮树不同无性系主要农艺性状多样性分析

依据光皮树(Cornus wilsoniana)丰产育种目标,对7个光皮树优良无性系的28个农艺性状进行观测,并进行方差、主成分、聚类及相关性分析。方差分析结果显示28个农艺性状的变异系数为804%~9430%,其中叶形态（叶形、叶色、叶缘）的变异系数最高;表型分化系数为4527%~9640%,即各性状的遗传较为稳定;主成分分析结果显示花序、果实、含油率以及果穗果数因子是主要的遗传因子,是光皮树无性系性状遗传的主要来源;依据主成分因子得分将7个光皮树优良无性系聚为4个类群,其中第Ⅱ类群与第Ⅲ类群杂交可以获得高产高含油率的目标资源。     

Multitrait index based on factor analysis and ideotype‐design: proposal and application on elephant grass breeding for bioenergy

This study proposes a new multitrait index based on factor analysis and ideotype‐design (FAI‐BLUP index), and validates its potential on the selection of elephant grass genotypes for energy cogeneration. Factor analysis was carried out, and afterwards, factorial scores of each ideotype were designed according to the desirable and undesirable factors, and the spatial probability was estimated based on genotype‐ideotype distance, enabling genotype ranking. In order to quantify the potential of the FAI‐BLUP index, genetic gains were predicted and compared with the Smith‐Hazel classical index. The FAI‐BLUP index allows ranking the genotypes based on multitrait, free from multicollinearity, and it does not require assigning weights, as in the case of the Smith‐Hazel classical index and its derived indices. Furthermore, the genetic correlation ‐ positive or negative ‐ within each factor was taken into account, preserving their traits relationship, and giving biological meaning to the ideotypes. The FAI‐BLUP index indicated the 15 elephant grass with the highest performance for conversion to bioenergy via combustion, and predicted balanced and desirable genetic gains for all traits. In addition, the FAI‐BLUP index predicted gains of approximately 62% of direct selection, simultaneously for all traits that are desired to be increased, and approximately 33% for traits which are desired to be decreased. The genotypes selected by the FAI‐BLUP index have potential to improve all traits simultaneously, while the Smith‐Hazel classical index predicted gains of 66% for traits that are desired to be increased, and ?32% for traits that are desired to be decreased, and it does not have potential to improve all traits simultaneously. The FAI‐BLUP index provides an undoubtable selection process and can be used in any breeding programme aiming at selection based on multitrait.     

杜鹃红山茶叶片主要性状的遗传多样性分析

为有效评价和利用杜鹃红山茶基因资源、挖掘其优良性状,以37个杜鹃红山茶无性系为研究材料,对14个叶片的表型性状进行测定,分析各性状的变异系数、不同性状间的相关关系,并进行主成分分析和聚类分析研究。结果显示：14个叶片表型性状的变异系数为5.30%～47.00%,平均变异系数为18.52%,表明杜鹃红山茶叶片主要数量性状的变异较大,遗传多样性较丰富。叶长与叶形指数间的相关性系数达0.967,叶面积与叶片干重的相关性系数为0.942,叶柄长和叶柄长/叶长的相关性系数为0.828。14个性状可以综合为5个主成分,前5个主成分累计贡献率达80%,表明这些性状具有较强的代表性。根据系统聚类将37个杜鹃红山茶无性系划分为5个组。     

黄土塬地区集雨窖水水源地优选

为提高黄土塬地区窖水水质,保证窖水饮用安全,集雨水源地的选择势在必行。本文通过应用主成分分析法,研究了优质集雨水源地和决定水质的控制指标。结果表明,在不同类型集雨水源地中,水泥地面和瓦屋面的综合主成分得分分别为-3.350和-1.945,污染程度分级结果为轻度,是集雨的最佳场地;COD、NH4+-N、TP、SS和粪大肠菌群在主成分中具有高荷载值;集雨水受有机物质、地表尘土、人畜粪便污染明显,与人为活动密切相关。最后,就集雨水源地在政策法规、水质保护技术体系、水质检测和保护等方面提出了改善措施和建议。     

基于表型性状和SSR标记的57份辣椒种质遗传多样性分析

为了解辣椒(Capsicum annuum)种质资源的遗传多样性,以57份辣椒种质资源为材料,对34个表型性状进行变异度、多样性及主成分分析,分别基于表型性状和SSR分子标记进行聚类分析。结果表明,种质间的34个表型性状存在差异,平均变异系数为40.67%,平均Shannon-Weiner多样性指数为1.20;提取的10个主成分可以代表辣椒种质表型性状75.972%的遗传信息,其中第1主成分占比22.317%,主要由果实横径、单果重、果肩形状和果顶性状所组成;19对SSR引物的平均Nei’s基因多样性指数及香农信息指数分别为0.48和0.80;基于表型性状和SSR标记均将57份辣椒分为4类,但2种聚类结果间的相关性不显著(r=-0.175 9)。这为辣椒育种的亲本选配及种质资源评价提供理论依据。     

Multiple-trait breeding values for parental selection in self-pollinating crops

Using breeding values in parental selection of self-pollinating crops seems to be superior to conventional selection strategies, where selection is often based on several traits which are correlated among each other. However, analysing each trait separately can bias estimates of breeding values. This study examined responses to selection for total merit indices based on breeding values resulting from single- and multiple-trait best linear unbiased prediction (BLUP). We generated data for a multi-environment trial of a “virtual” parental population in which the phenotypic value of inbred lines was influenced by additive, additive-by-additive epistatic, year, location, block and genotype-by-environment interaction effects. Two traits with heritabilities of 0.7 and 0.3 and nine different correlation scenarios between traits (estimated phenotypic correlation ranging from −0.39 to +0.36) were simulated. Gain in selection response was greater for multiple-trait than for single-trait breeding values, especially if traits were negatively correlated. For all correlation scenarios, the overall standard errors of difference of multiple-trait predictors were lower than those of single-trait analysis.