A canonical correlation analysis of the association between carcass and ham traits in pigs used to produce dry-cured ham

The association between carcass and ham traits in a pig population used to produce dry-cured ham was studied using canonical correlation analysis. The carcass traits examined were hot carcass weight (HCW), backfat thickness (BT) and loin depth (LD), and the ham traits studied were gross ham weight (GHW), trimmed ham weight (THW), ham inner layer fat thickness (HIFT), ham outer layer fat thickness (HOFT), pH (pH) and the Göfo value. Carcass and ham traits are not independent. The canonical correlations (r) between the carcass and ham traits at 130 kg were 0.77, 0.24 and 0.20 for the first, second and third canonical pair, respectively, and were all significant (p < 0.01) by the Wilks test. The corresponding canonical correlations between the three canonical variate pairs for the carcass and ham traits at 160 kg were 0.88, 0.42 and 0.14, respectively (p < 0.05 for all, except the third). The correlations between the traits and their canonical variate showed an association among HCW, GHW and THW, and between BT and HOFT. These results indicate that carcass traits should be used to cull pigs that are not suitable for dry-cured ham production.     

Climatic variability and body size variation in the muskrats (Ondatra zibethicus) of North America

Summary Patterns of geographic variation in nine morphological characters of adult muskrats (Ondatra zibethicus) are investigated by multiple regression and canonical correlation analysis. Three variables describing the annual precipitation regimen account for 16 to 33% of the variance in each of the skeletal measurements. Highly variable precipitation patterns result in low rates of germination and survivorship for preferred aquatic food plants which in turn reduces average total food availability for muskrats. In large individuals nutritive demands may exceed supply, thus selection favors smaller body size in areas of low food availability.After removing the variation attributable to three precipitation variables, the residual variation in the morphological variables is exposed to canonical correlation analysis with a set of 10 environmental and geographic variables. A canonical variate loaded for climatic seasonality accounts for 60% of the variance in a canonical variate of the morphological residuals which load as a general body size variate. It is argued that seasonality is a major factor selecting for large body size in muskrats and other organisms. During seasonal periods of resource abundance natural selection favors individuals with rapid growth to a large size, while concurrently enhancing survivorship through oncoming periods of resource shortage.     

Morphological correlates of sprint swimming speed in five species of spadefoot toad tadpoles: Comparison of morphometric methods

The relationship between vertebrate morphology and swimming performance has long interested biologists. Recent work on predator‐induced morphological plasticity of anuran tadpoles has increased this interest. Here, I use data on five species of spadefoot toad tadpoles (Scaphiopodidae) to compare linear and geometric morphometrics. Linear measures explain only 7–26% of the variation in swimming speed, depending on species, whereas geometric morphometrics could explain 24–46% of the same variation. I also compare two methods for examining how similar the morphology–swimming speed relationship is among species. A canonical variate derived from a MANCOVA approach successfully detected species differences in these relationships, whether using linear or geometric methods, but a canonical correlation approach failed in both cases. Overall, tadpoles with smaller bodies, larger tails, and larger tail muscles are faster swimmers but the details of how these shape changes are achieved differed among species. For example, in some species a smaller body was achieved primarily by reducing abdomen size, whereas in others both the head and abdomen are smaller. Faster swimmers also had deeper tails, especially in the posterior half of the tail. This pattern would have been missed in standard linear morphometrics which usually only measures maximum tail depth. J. Morphol. 271:1044‐1052, 2010. © 2010 Wiley‐Liss, Inc.     

Geographic variation for wing shape in Drosophila serrata

Geographic variation in wing shape in female Drosophila serrata was examined by characterizing isofemale strains from 19 localities collected along a transect on the eastern coast of Australia. Shape variation was analyzed by Procrustes superimposition of landmark data followed by canonical variate analysis. The first extracted canonical variate showed a nonlinear association with latitude and accounted for 43% of the variance. There was a sharp increase in this variate at low latitudes as well as a gradual increase at high latitudes. These shape changes were associated with two landmarks at the edge of the wing. There was also a linear change in wing aspect. The isofemale heritability for two measures of shape was around 30%. Allometric relationships were weak both between localities and among isofemale strains within localities. The possibility that wing shape parameters are under selection independent of wing size is discussed.     

Within-island microgeographic variation in the colour pattern of the skink,Chalcides sexlineatus: Pattern and cause

The colour pattern of the Gran Canarian skink is described with eight independent colour pattern characters. Significant geographic variation occurs in each character. There are generally high levels of congruence between the patterns of geographic variation in each character although some differences exist. In canonical variate analyses, the first canonical variate expresses most of the among-locality variation in colour pattern, indicating a largely unidimensional pattern. Patterns of geographic variation in the colour pattern are portrayed by contouring. This reveals north-east/south-west clines for seven of the individual characters and the generalized pattern (CV1). Four causal hypotheses were erected which predicted four different unidimensional patterns of geographic variation. Mantel tests and partial correlation analyses were used to compare the observed patterns of microgeographic variation with the four hypothesized patterns. This method suggests differential selection occurring between ecotones as the cause of the microgeographic variation. Microgeographic variation in some aspects of the colour pattern can be explained by selection for different anti-predator strategies in the hot, arid southern areas vs the cooler, lusher northern areas.     

A biotic index using benthic macroinvertebrates for Italian lakes

The relationship between benthic macroinvertebrates and environmental variables from 42 Italian lakes were analysed with the aim of developing a biotic index.In the investigated lakes, 570 species were found of which 373 belonged to the family of Chironomidae and 85 to the class of oligochaeta. Rare species, those present in less than 10 samples, were excluded from the analysis, leaving 57 species for data analysis.Multivariate analysis: canonical correlation analysis (CANON) and multivariate analysis of variance and covariance (MANCOVA) were carried out on a large database of 1060 sampling points, for which both environmental data (16 chemical and morphometric variables) and 57 species counts from soft bottom samples were available. In addition, a second dataset of 94 sites from small lakes sampled in 2005 in Northern Italy (Lombardy), was analysed for comparison.The data analysis (CANON) from the large database gave the following results:

• (1)the first canonical variate was related to conductivity, pH and alkalinity and accounted for 17% of the total variation;
• (2)the second canonical variate was related to total phosphorus, N-NH₄ and dissolved oxygen, and accounted for 15% of the total variation;
• (3)lake maximum depth, volume and water temperature were related to the third canonical variate, which accounted for 14% of the source of variation.

The analysis of the database from small lakes revealed that in the plane of the first two canonical variates dissolved oxygen was inversely correlated with the depth of sampling and that the second canonical variate showed an inverse relationship between transparency and nutrients.MANCOVA found evidence for differences between lake types and sampling years, confirmed the CANON results and allowed the quantification of the contribution of different target variables on species composition.A trophic status index was calculated ranking percentage oxygen saturation (O₂ %sat), transparency (transp) and total phosphorus (TP). The means of O₂ %sat, transp and TP weighted by the species abundances were calculated to have optimum values for each species; a benthic quality index was then obtained by multiplying the weighted means of O₂ %sat, transp and TP by species abundances and dividing the product by the total number of specimens present at each station. A significant correlation was observed between trophic status and the benthic quality index. A good agreement was also observed between the indexes calculated using the large database and the second dataset on small lakes.     

节肢动物群落稳定性分析灰典型相关模型及其应用

稳定性是生态系统最重要的特征之一。根据累加生成可增强两单调增序列线性相关性原理,应用典型相关分析方法,以比值mn/mp(mp为害虫个体数,mn为天敌个体数)为测度群落稳定性的指数,构建群落稳定性分析灰典型相关模型。具体做法是:(1)将各种群的数量序列按害虫各次总数量的递增顺序进行重排,用各种群数量序列的极差去除该序列,将其无量纲化,然后对各序列进行累加生成;(2)以害虫各种群为一组变量,天敌各种群为另一组变量,应用典型相关分析的方法,求出各对典型变量。对达到线性拟合要求的典型变量对,以害虫为自变量,天敌为因变量建立回归方程,并对这些方程中的变量进行累减还原;(3)对这些方程进行线性组合,合并成一个方程,组合系数是使这些害虫典型变量的线性组合与害虫总数量序列的线性相关值达到最大;(4)引进转换系数的概念,建立天敌、害虫总量相互转换模型,该模型称之为灰典型相关模型,通过模型可分析各种群在群落稳定性中的作用。将模型应用于福州金山茶园节肢动物群落的稳定性分析,所得结果与实际基本相符,表明建立的灰典型相关模型是可行的。     

Evaluation of the Culling Variate Used by Breeders in Actual Selection

The theoretical basis and computational procedures for estimating the culling variate utilized by breeders in actual selection are presented. The essential part of this procedure is to derive the unknown culling variate in terms of a linear combination of traits based on realized indirect selection differentials of those traits and phenotypic variances and covariances among traits in the population. Special emphasis is placed on the distribution of the variables involved. The accuracy of the culling variate is estimated by use of the biserial correlation with some modifications. Numerical illustrations are given for different types of selection.     

等位基因多态性群体遗传结构的多元非线性分析方法

长期以来,对于多维基因多态性数据的多元统计分析,如计算遗传距离时昕用的聚类分析、分析群体遗传结构时所用的主成分分析、因子分析和典型相关分析等,一直应用为无约束条件数据而设计的经典多元线性分析方法,并没有注意基因多态性数据的“闭合效应”所带来的问题。从分析基因多态性数据的分布和结构特征入手,文中指出了基因多态性分布具有“闭合数据”的特点,分析了由于“闭合效应”的影响,经典多元线性方法用于群体遗传结构分析昕面临的困难。根据成分数据统计分析的理论和方法,提出了基因多态性群体遗传结构的多元非线性分析基本方法。并以主成分分析为例,通过实例比较和分析了经典线性主成分分析和“对数比”非线性主成分分析的结果,证明“对数比”非线性主成分分析方法是研究基因多态性群体遗传结构的良好方法,具有特异、灵敏等优点,其结果符合群体遗传学规律。     

Assessing the affinities of fossils using canonical variates and generalized distances

Canonical variate analysis and generalized distances are commonly used multivariate statistical techniques for assessing the comparative morphology of living and fossil primates. Some common pitfalls of these methods when used to analyze fossil specimens are: (1) ignoring the possibility that a fossil belongs to a group other than one of the predefined reference samples (i.e., restricted versus unrestricted approaches to classification), (2) misinterpreting probabilities of group membership (i.e., posterior versus typicality probabilities), and (3) failing to understand how sample sizes influence multivariate ordinations in trying to effectively illustrate the morphometric affinities of a fossil (i.e., weighted versus unweighted analyses with fossils entered indirectly or directly into the analysis). To better understand canonincal variate analysis and generalized distances, the workings of these methods are portrayed graphically as a series of rotations and rescaling of data plotted in a multivariate data space. The influence of sample sizes and the importance of higher-numberer canonical variates are emphasized. Simple examples taken from the literature illustrate how the different approaches to including a fosil in canonical variate analysis may affect the multivariate results upon which physical anthropologists base their interpretations of the fossil's morphology.     

Anatomical wood variation of Buddleja cordata (Buddlejaceae) along its natural range in Mexico

Buddleja cordata is an evergreen species of wide distribution in Mexico that is represented by shrubs and trees. Wood variability of B. cordata was evaluated in relation to plant size as well as latitude, altitude, soils, and climatic data. Canonical correlation analysis (CCA) showed that two canonical correlations are significant (Wilks' λ, p<0.0001) and explained 76% of total variance. Redundancy analysis revealed that the first pair of canonical variates are significant, thus the canonical variate, named distribution, represents a gradient of maximum temperature of the warmest period, annual temperature range, and latitude in its area of distribution; whereas the canonical variate named wood represents vessel density, fiber length, and plant size, best associated to the environmental gradient. Vessel density expressed by its distribution in latewood and porosity type showed that ring-porosity is common in individuals from high latitudes. Temperatures below zero or lack of rainfall during several months might induce porosity variability in B. cordata as suggested by CCA, but was not related to phenology since the species is evergreen along its latitudinal range. Plant size was also influenced by extreme temperature and rainfall. Shorter plants are distributed in the northern population or driest sites located in north-central Mexico, and in addition, fiber length followed an allometric relation with individuals' height. Wood characters in B. cordata as for simple perforation plate, helical thickenings, type of intervascular and vessel-ray pits, scanty paratracheal parenchyma, and heterogeneous type IIB rays were not correlated with plant size, climate, and soil parameters or species distribution. These features are common with other species of Buddleja.An erratum to this article can be found at     

The use of canonical analysis for selection within a population of spring barley

A selection method is described involving the application of canonical analysis to data for a number of measured traits in a composite population of spring barley grown in two seasons. Lines were selected which fell within the Euclidean space defined by the range, for a number of standard cultivars, on each significant canonical variate. Alternatively, limits were fixed for an acceptable range for each trait and transformed to canonical variates. Lines were selected which fell nearest to the centroid of this acceptable space. The method might be used as an alternative to the selection index method where difficulty is often encountered in assigning appropriate economic weightings to the traits measured.     

A Geometric Morphometric Approach to the Analysis of Lip Shape during Speech: Development of a Clinical Outcome Measure

Objective assessments of lip movement can be beneficial in many disciplines including visual speech recognition, for surgical outcome assessment in patients with cleft lip and for the rehabilitation of patients with facial nerve impairments. The aim of this study was to develop an outcome measure for lip shape during speech using statistical shape analysis techniques. Lip movements during speech were captured from a sample of adult subjects considered as average using a three-dimensional motion capture system. Geometric Morphometrics was employed to extract three-dimensional coordinate data for lip shape during four spoken words decomposed into seven visemes (which included the resting lip shape). Canonical variate analysis was carried out in an attempt to statistically discriminate the seven visemes. The results showed that the second canonical variate discriminated the resting lip shape from articulation of the utterances and accounted for 17.2% of the total variance of the model. The first canonical variate was significant in discriminating between the utterances and accounted for 72.8% of the total variance of the model. The outcome measure was created using the 95% confidence intervals of the canonical variate scores for each subject plotted as ellipses for each viseme. The method and outcome model is proposed as reference to compare lip movement during speech in similar population groups.     

A unified procedure for meta-analytic evaluation of surrogate end points in randomized clinical trials

The meta-analytic approach to evaluating surrogate end points assesses the predictiveness of treatment effect on the surrogate toward treatment effect on the clinical end point based on multiple clinical trials. Definition and estimation of the correlation of treatment effects were developed in linear mixed models and later extended to binary or failure time outcomes on a case-by-case basis. In a general regression setting that covers nonnormal outcomes, we discuss in this paper several metrics that are useful in the meta-analytic evaluation of surrogacy. We propose a unified 3-step procedure to assess these metrics in settings with binary end points, time-to-event outcomes, or repeated measures. First, the joint distribution of estimated treatment effects is ascertained by an estimating equation approach; second, the restricted maximum likelihood method is used to estimate the means and the variance components of the random treatment effects; finally, confidence intervals are constructed by a parametric bootstrap procedure. The proposed method is evaluated by simulations and applications to 2 clinical trials.     

Multivariate analysis of avian vocalizations

This paper examines several multivariate techniques that may be used in analyzing vocalizations. A general comparison of multiple linear regression, discriminant analysis, canonical correlation, cluster analysis, and principal components analysis is included with a discussion of when these tests may be appropriate for vocalization studies. Examples using vocalizations from Laysan and black-footed albatrosses are given to illustrate each technique.     

A new approach to the analysis of complex dose-response relationships: a multivariate study of octopamine action on the leech Leydig neurone

Octopamine (OA) hyperpolarizes leech Leydig neurones but response amplitudes and thresholds vary. Associations between response, OA dose and other variables [initial resting potential, action potential (AP) frequency and amplitude, temperature, microelectrode resistance, position of ganglion along nerve cord, animal, treatment order] were examined using canonical correlation. A complex response was expressed by summing changes in membrane potential and AP frequency over 2 min of OA treatment. Only dose and ganglion position influenced this response. One significant canonical variate related dose to immediate changes in membrane potential and summed changes in AP frequency throughout the OA effect. Response to OA was greater in cells in posterior ganglia.