Consensus Principal Components

From the polar forms of the principal components corresponding with each of a set of covariance (or correlation) matrices, a linear combination based on their inner products is defined as the polar form of the consensus. The corresponding eigenvectors form an orthogonal matrix which rotates each of the covariance matrices to approximate diagonal form. From the norms of the polar forms, these eigenvectors can be used to estimate a common covariance matrix. These procedures are illustrated by a numerical example.     

大蒜种质产量和品质性状主成分聚类分析与综合评价

以40个大蒜品种为供试材料,依据数值分类学的性状选择原则,分别于大蒜生长期和采收后进行农艺性状指标的采集。估算40个大蒜品种16个农艺性状及4个品质指标的主成分,并以前3个主成分和遗传相似性系数为基础,分别作二维散点图和系统聚类分析。40份大蒜品种前7个主成分累计贡献率达85%。根据品种性状主成分表现,评选出性状优良的大蒜品种共10个。在聚类图中,在0.14的遗传相似性水平上可以把40份品种分成4类,即由5份种质组成的类群Ⅰ;由28份种质聚成的类群Ⅱ;由改良蒜等4份种质组成的类群Ⅲ,及苏联蒜等3份种质组成的类群Ⅳ。全部种质的遗传相似性系数在0.07～0.64之间,很好地揭示了品种类群间存在的亲缘关系。     

Factor and principal component analyses as alternatives to index selection

Summary Selections from factor and principal component analyses were compared with those from the Smith-Hazel index when selecting for several switchgrass (Panicum virgatum L.) traits. The objective of this study was to examine several alternatives to index selection. Such procedures would potentially eliminate problems of selection associated with Smith-Hazel indices, including errors in genetic parameter estimates and difficulty in assigning relative economic weights to traits. Selection was performed on 1,280 plants that were evaluated over 2 years at 1 location, in a randomized complete block design with 4 replicates. The plants were evaluated for forage yield and several forage quality traits. The comparisons of index selection with principal factor analysis, maximum-likelihood factor analysis and principal component analysis were made for three sets of traits (five traits per set) to estimate repeatability for the comparisons. Multivariate analyses were performed on both simple and genotypic correlation matrices. Comparisons were made by computing Spearman's rank correlations between selection index plant scores and scores computed from multivariate analysis and by determining the number of plants selected in common for the selection methods. Among the three multivariate analysis methods evaluated in this study, principal component analysis had the highest correlation with index selection. The high correlation for principal component analysis of simple correlation matrices indicates the potential for using this statistical method for selection purposes. This would permit the breeder to reduce field costs (e.g., time, labor, equipment) required to obtain the genetic parameter estimates necessary to construct selection indices.     

The effect of size variation on univariate assessments of morphological difference in human crania.

The present research was undertaken to determine the contribution of general size to craniometric variation in two previously described Paleo-Amerindian series, and to evaluate the effect of size variation on univariate assessments of morphological difference between the two. The analysis was based upon 19 measurements of 81 crania representing the Iswanid and Fort Ancient Muskogid varieties. The results of principal components analysis indicate that the 19 measurements can be represented as five principal component variates. Inspection of component eigenvectors indicates that variation in body size accounts for 40% of the variation within the metric data. Analysis of covariance lends support to the hypothesis that this size variation contributes substantially to statistical tests of difference between the two groups based on Student's t.     

Linear Predictivity: An Alternative for MANOVA and Multivariate Multiple Regression

The maximal linear predictable combination of a set of dependent variables is defined as that linear combination maximizing the multiple correlation coefficient with the predictor set. It allows the relative importance of a number of factors to be evaluated for the joint response, rather than for the response of each dependent variable in turn. The procedure is illustrated by an example. AMS subject classification: major 62J10, 62H20; minor 62H25.     

Shape components of the maxillary molars in Australian aboriginals

Principal components analysis was used to quantify the variability in crown outlines of maxillary molars in Australian Aboriginals. The outlines were measured by 36 radii from the central pit to the crown periphery. The first component, responsible for over half of the total variance, was concerned with general crown size. Four remaining components were retained to indicate sources of variability resulting from contrasting degrees of development or reduction of different crown components. Shape changes from the first to third molars were identified with components representing overall size reduction, diminution of the hypocone, and metacone elements and mesiodistal compression. An anteroposterior gradient along the molar series in average scores and variances for all components resulted from the progressive reduction of distal crown elements, increasing mesiodistal compression, and greater morphological variation.     

Comparison of trait associations in adapted × exotic matings of sorghum developed by two introgression methods

The association among six traits in the F₂ lines derived from adapted × exotic backcrosses of sorghum developed via two introgression methods was studied using principal component analysis. The first principal component defined a hybrid index in matings of the wild accession (12–26) but not in matings of the cultivated sorghum genotypes (Segeolane and SC408), no matter which adapted parent was used. This component accounted for 27–42% of the total variation in each mating. The recombination spindle was wide in all matings of CK60 and KP9B, which indicated that the relationships among traits were not strong enough to restrict recombination among the parental characters. The index scores of both CK60 and KP9B matings showed clear differentiation of the backcross generations only when the exotic parent was the undomesticated wild accession (12–26). None of the distributions of the first principal component scores in any backcross population was bimodal. The frequency of recombinant genotypes derived from a mating was determined by the level of domestication and adaptation of the exotic parent and the genetic background of the adapted parent. Backcrossing to a population (KP9B) was found to be superior to backcrossing to an inbred line (CK60) to produce lines with an improved adapted phenotype.Contribution no. 93-574-J from the Kansas Agricultural Experiment Station.     

On the interpretation of principal components analysis in ecological contexts

Summary Principal components analysis is well suited for many data analysis problems in ecology, particularly for data reduction and hypothesis generation; but the structure of PCA is poorly suited for indirect gradient analysis. Whatever the intended application of PCA, the user must exercise special care in selecting data transformations to prevent the analysis from being overwhelmed by the purely numerical effects in the variance structure of the data.I would like to thank R. H. Whittaker, H. G. Gauch, R. E. Moeller, and S. R. Searle for their guidance and assistance.     

影响林火灾变生态阈值数学模拟的潜在因子的数学模型

用多元统计分析方法对大兴安岭林区的林火灾变的有关观测数据进行综合分析,提出了影响林火灾变性生态阈值数学模拟的潜在因子的数学模型,并对该模型作出了一些有益的讨论。     

Bivariate versus multivariate allometry: A note on a paper by Jungers and German

Jungers and German (1981) found differences when they compared 1) coefficients of allometry from bivariate plots of log measurements versus log body weight with 2) those coefficients from the first principal component of the log measurements excluding body weight. It is argued here that an arbitrary choice of unit for “internal size” is all that separates these coefficients. When the unit is chosen to make internal size isometric with body weight the coefficients agree rather well.