Rejoinder to Use of Principal Component Analysis and the GE -Biplot for the Graphical Exploration of Gene Expression Data

Summary This note is in response to Wouters et al. (2003, Biometrics 59, 1131–1139) who compared three methods for exploring gene expression data. Contrary to their summary that principal component analysis is not very informative, we show that it is possible to determine principal component analyses that are useful for exploratory analysis of microarray data. We also present another biplot representation, the GE‐biplot (Gene Expression biplot), that is a useful method for exploring gene expression data with the major advantage of being able to aid interpretation of both the samples and the genes relative to each other.     

Determining environmental covariates which explain genotype environment interaction in winter wheat through probe genotypes and biadditive factorial regression

Genotype-environment interaction has been analyzed in a winter-wheat breeding network using bi-additive factorial regression models. This family of models generalizes both factorial regression and biadditive (or AMMI) models; it fits especially well when abundant external information is available on genotypes and/or environments. Our approach, focused on environmental characterization, was performed with two kinds of covariates: (1) deviations of yield components measured on four probe genotypes and (2) usual indicators of yield-limiting factors. The first step was based on the analysis of a crop diagnosis on four probe genotypes. Difference of kernel number to a threshold number (DKN) and reduction of thousand-kernel weight from a potential value (RTKW) were used to characterize the grain-number formation and the grain-filling periods, respectively. Grain yield was analyzed according to a biadditive factorial regression model using eight environmental covariates (DKN and RTKW measured on each of four probe genotypes). In the second step, the usual indicators of yield-limiting factors were too numerous for the analysis of grain yield. Thus a selection of a subset of environmental covariates was performed on the analysis of DKN and RTKW for the four probe genotypes. Biadditive factorial regression models involved environmental covariates related to each deviation and included environmental main effect, sum of water deficits, an indicator of nitrogen stress, sum of daily radiation, high temperature, pressure of powdery mildew and lodging. The correlations of each environmental covariate to the synthetic variates helped to discard those poorly involved in interaction (with | correlation | <0.3). The grain yield of 12 genotypes was interpreted with the retained covariates using biadditive factorial regression. The models explained about 75% of the interaction sums of squares. In addition, the biadditive factorial regression biplot gave relevant information about the interaction of the genotypes (interaction pattern and sensitivities to environmental covariates) with respect to the environmental covariates and proved to be interesting for such an approach. Received: 8 March 1999 / Accepted: 29 July 1999     

THE DUAL ROLE OF SELECTION AND EVOLUTIONARY HISTORY AS REFLECTED IN GENETIC CORRELATIONS

The patterns of genetic correlations between a series of eye and antenna characters were compared among two sets of spring-dwelling and cave-dwelling populations of Gammarus minus. The two sets of populations originate from different drainages and represent two separate invasions of cave habitats from surface-dwelling populations. Matrix correlations, using permutation tests, indicated significant correlations both between populations in the same basin and from the same habitat. The technique of biplot, which allows for the simultaneous consideration of relationships between different genetic correlations and different populations, was used to further analyze the correlation structure. A rank-3 biplot indicated that spring and cave populations were largely differentiated by eye-antennal correlations, whereas basins were differentiated by both eye-antennal and antennal-antennal correlations. Eye-antennal correlations, which are likely to be subject to selection, were most similar within habitats, which are likely to have similar selective regimes.     

Calibration of multivariate scatter plots for exploratory analysis of relations within and between sets of variables in genomic research

The scatter plot is a well known and easily applicable graphical tool to explore relationships between two quantitative variables. For the exploration of relations between multiple variables, generalisations of the scatter plot are useful. We present an overview of multivariate scatter plots focussing on the following situations. Firstly, we look at a scatter plot for portraying relations between quantitative variables within one data matrix. Secondly, we discuss a similar plot for the case of qualitative variables. Thirdly, we describe scatter plots for the relationships between two sets of variables where we focus on correlations. Finally, we treat plots of the relationships between multiple response and predictor variables, focussing on the matrix of regression coefficients. We will present both known and new results, where an important original contribution concerns a procedure for the inclusion of scales for the variables in multivariate scatter plots. We provide software for drawing such scales. We illustrate the construction and interpretation of the plots by means of examples on data collected in a genomic research program on taste in tomato.     

甘蓝型油菜油酸配合力的双标图分析

用GGE双标图法对甘蓝型油菜8×8完全双列杂交试验的脂肪酸组分进行分析,以期得到配合力高的亲本,为高油酸材料的转育和配组奠定基础。结果显示:(1)一般配合力(GCA)较高的亲本是父本Y511、Y539和母本Y511、Y520、Y539,而特殊配合力(SCA)较高的亲本是父本L308、Y511、Y539和母本L121、L307、L331、Y539。从GCA和SCA综合来看,Y511、Y520和Y539是配合力较高的父本,L307、L331、Y539是配合力较高的母本,父本L121和母本L308的配合力相对最低;(2)Y539是母本L121、L307、L308、L332、Y511、Y520、Y539的最佳组配父本,Y511是L331的最佳组配父本;Y520是父本L121、L307、L331、L332、Y511的最佳组配母本,Y539是L308、Y520、Y539的最佳组配母本;(3)SCA较高的组合有L307×L308、L331×L332、L332×Y511、Y520×Y511、Y539×L121等;(4)在芥酸含量为0、二十碳烯酸含量趋近于0(0.87%左右)、硬脂酸含量变幅不大(1.36%~1.75%)的遗传背景下,父本脂肪酸组分中油酸与棕榈酸、硬脂酸、亚油酸和亚麻酸均呈负相关;母本中油酸与硬脂酸呈正相关,与棕榈酸、亚油酸、亚麻酸呈负相关;(5)各杂交种脂肪酸组分的表型关系中,与油酸含量呈正相关的是硬脂酸,呈负相关的是棕榈酸,而与亚油酸、亚麻酸呈极显著负相关,这与母本脂肪酸组分之间的关系基本一致。     

关中地区'陕253'品质与氮、磷、钾配比间关系的研究

选用强筋小麦品种‘陕253’,在关中东、西和中部采取不同的氮(N)、磷(P)、钾(K)肥配比处理,用GGE Bi-plot叠图软件分析肥料配比对不同地区籽粒品质性状的效应。研究结果表明:不同N、P、K配比对强筋小麦品质性状的效应与生态区有关。关中西部蛋白质含量、容重、硬度、稳定时间之间呈显著正相关,蛋白质含量、容重和硬度的最优N、P、K配比是N 135 kg/hm2、P2O5225 kg/hm2、K2O 120 kg/hm2,降落值、出粉率、湿面筋含量和稳定时间是N 225 kg/hm2、P2O5225 kg/hm2、K2O 120 kg/hm2;关中中部蛋白质含量、稳定时间、沉淀值、容重之间呈显著正相关,其最优N、P、K配比为N 225 kg/hm2、P2O5225 kg/hm2、K2O 120 kg/hm2,降落值和吸水率最优N、P、K配比为N 135 kg/hm2、P2O5225 kg/hm2、K2O 180 kg/hm2;关中东部籽粒蛋白质含量与吸水率之间显著正相关,其最优N、P、K配比为N 225 kg/hm2、P2O5225 kg/hm2、K2O 180 kg/hm2,湿面筋含量、降落值、沉淀值、容重、出粉率和硬度间表现极限著的正相关关系,最优N、P、K配比是N 135 kg/hm2、P2O5120 kg/hm2、K2O 120 kg/hm2。