A multivariate approach to host plant associated morphological variation in the polyphagous leafhopper, Alnetoidia alneti (Dahlbom)

Canonical variate analysis (CVA) on morphological distance measurements shows that differences exist among adult samples of A. alneti taken from a number of host plant species in South Wales. This variation is also correlated with variation in the degree of yellow pigmentation. Adults taken from alder and hazel form extremes in a continuum of variation, those from alder being larger and more pigmented. The variation between these two populations is greater than host-independent variation among samples of each population taken from a number of individual trees at different localities in Britain in different years. Ordination shows that the variation between the alder and hazel populations is along different axes to that among samples in these populations. Different axes of variation are also found among adults from different pairs of host plant species. Multiple-group principal component analysis (MGPCA) suggests that much of the variation between adults from alder and hazel may be interpreted as allometry-free 'shape' that is uncorrelated with variation in overall size within each population. Transfer experiments showed that the differences in both size and shape may have little genetic basis and are probably host plant induced> The taxonomic and ecological implications of these results are discussed.     

An application of common principal component analysis to cranial morphometry of Microtus californicus and M. ochrogaster (Mammalia, Rodentia): further remarks

We welcome Dr Thorpe's interesting discussion (Thorpe, 1988), and we would like to take this opportunity to clarify some points.
Both MGPCA (multiple group principal component analysis) and CPCA (common principal component analysis) serve essentially the same purpose, namely estimation of principal components simultaneously in several groups, based on the assumption of equality of principal component directions across groups, while eigenvalues may differ between groups. However, CPCA has the distinct advantage that this assumption can actually be tested, using the (CPC) statistic. In analyses involving more than two variables, it is usually difficult to decide, without a formal test, whether or not the assumption of common directions of principal components is reasonable.
There is also a conceptual difficulty with MGPCA. In statistical terms, both methods assume that:
(a) a certain set of parameters (namely those determining the eigenvectors) are common to all groups
(b) there are sets of parameters (namely p eigenvalues per group) which are specific to each group.
CPCA sets up a model that reflects this structure and estimates the parameters accordingly. MGPCA, on the other hand, ignores part (b), at least temporarily, by pooling the variance-covariance matrices and extracting eigenvectors from the single pooled matrix. This may lead to reasonable results, but there is no guarantee that it will indeed do so. The reader may find a more familiar analog in the fitting of regression lines when data are in groups. If it is assumed that all regression lines are parallel, one should set up an appropriate model based on a single slope parameter common to all groups, and groupwise intercepts. One should then estimate the parameters of this model, and not simply apply a technique which is appropriate in the one-group case only.     

An application of common principal component analysis to cranial morphometry of Microtus californicus and M. ochrogaster(Mammalia, Rodentia)

Principal component analysis (PCA) is a one-group method. Its purpose is to transform correlated variables into uncorrelated ones and to find linear combinations accounting for a relatively large amount of the total variability, thus reducing the number of original variables to a few components only.
In the simultaneous analysis of different groups, similarities between the principal component structures can often be modelled by the methods of common principal components (CPCs) or partial CPCs. These methods assume that either all components or only some of them are common to all groups, the discrepancies being due mainly to sampling error.
Previous authors have dealt with the k-group situation either by pooling the data of all groups, or by pooling the within-group variance-covariance matrices before performing a PCA. The latter technique is known as multiple group principal component analysis or MGPCA (Thorpe, 1983a). We argue that CPC- or partial CPC-analysis is often more appropriate than these previous methods.
A morphometrical example using males and females of Microtus californicus and M. ochrogaster is presented, comparing PCA, CPC and partial CPC analyses. It is shown that the new methods yield estimated components having smaller standard errors than when groupwise analyses are performed. Formulas are given for estimating standard errors of the eigenvalues and eigenvectors, as well as for computing the likelihood ratio statistic used to test the appropriateness of the CPC- or partial CPC-model.     

Effects of population structure on within-group variation in the Jirels of Nepal

The impact of population structure on phenotypic differentiation is most frequently considered in terms of between-subdivision variation. However, the demographic and social structures of a population also induce changes in within-group variation. We analyze the intragenerational dynamics of within-group variation for the Jirels, a tribal population of eastern Nepal. In the analyses we utilized age- and sex-corrected cranial measures (head length, head breadth, bizygomatic diameter, minimum frontal diameter, and head circumference) available for 526 adults (ages 15-54 years). We used a multivariate measure of variance, the standardized generalized variance, to assess levels of within-village variability, quantifying the sampling variance for this statistic by using a jackknife methodology. To generate null expectations of within-group variation, we used permutation procedures, which permit robust testing of significance without distributional assumptions. We also compared the within-birthplace variation in adults to the observed within-residence variation to examine migration effects. Contrary to expectation, some villages with high rates of in-migration have less variability than those with few migrants. When differences between the sexes at birth are controlled for, females in some villages exhibit greater variance than males, reflecting known differences in sex-specific dispersal.     

新疆哈密拉甫却克墓地人的颅面部测量学特征

新疆地处欧亚大陆东西方交汇处,公元前200年以后的人群迁徙、融合历程能够反映丝绸之路沿线地区不同族群的形成历史和多元文化的互动模式。拉甫却克墓地是东疆哈密地区首次发掘的历史时期墓葬群。本文基于该墓地10例成年人颅面部测量数据,采用多元统计及生物距离的方法来评估拉甫却克墓地的人群结构,并对哈密绿洲地带青铜时代晚期到历史时期的人群变迁进行初步探索。结果显示：1）拉甫却克人群呈现出明显的异质性,既有与欧亚大陆东部人群颅面部特征相近的个体,也有表现出东西方混合特征的个体;2）青铜时代晚期至早期铁器时代（公元前2000年至公元前1000年）,哈密人群在体质特征上存在连续性;而早期铁器时代到历史时期（公元前1000年以后）,随着欧亚大陆东部人群遗传贡献的增加,哈密人群体质特征发生明显变化。结合考古证据和历史记录,新的人骨标本让我们对哈密历史时期的人群迁徙和融合有了初步认识,也使后续可以针对这一问题展开更详细的多学科研究。     

Genetic drift and gene flow in a prehistoric population of the Azapa valley and coast,Chile

The present paper studies the evolutionary process operating on prehistoric groups from the Azapa valley and coast (northern Chile). The sample consists of 237 crania from the Archaic Late, Early Intermediate, Middle, Late Intermediate, and Late periods. Six metric variables were used, which were transformed to eliminate the special environmental component and to increase the proportion of genetic variance. Population structure was assessed using a method based on quantitative genetic theory, which predicts a lineal relationship between average within-group phenotypic variance and group distance to the population centroid. Results indicate that 17.5% of the total variance accounts for special environmental variance. An excess in extraregional genetic flow is observed in the population corresponding to the Early Intermediate period in the valley. A reduced differentiation is observed between Archaic and Early Intermediate coastal groups, as well as between the latter and the inhabitants of the valley in the same period. Genetic differences between both areas increased substantially since the Middle period. Evidence indicates that long-range gene flow was lower on the coast than in the valley, the lowest estimated Fst being 0.0199 for the total population (coast and valley), 0.0111 for the coastal population, and 0.0057 for the valley. Results are discussed in terms of regional archeological and ethnohistorical evidence, and a microevolutionary model is presented to account for the biological history of the population.     

Components of variance underlying fitness in a natural population of the great tit Parus major

Traits that are closely associated with fitness tend to have lower heritabilities (h2) than those that are not. This has been interpreted as evidence that natural selection tends to deplete genetic variation more rapidly for traits more closely associated with fitness (a corollary of Fisher's fundamental theorem), but Price and Schluter (1991) suggested the pattern might be due to higher residual variance in traits more closely related to fitness. The relationship between 10 different traits for females, seven traits for males, and overall fitness (lifetime recruitment) was quantified for great tits (Parus major) studied in their natural environment of Wytham Wood, England, using data collected over 39 years. Heritabilities and the coefficients of additive genetic and residual variance (CVA and CVR, respectively) were estimated using an "animal model." For both males and females, a trait's correlation (r) with fitness was negatively related to its h2 but positively related to its CVR. The CVA was not related to the trait's correlation with fitness in either sex. This is the third study using directly measured fitness in a wild population to show the important role of residual variation in determining the pattern of lower heritabilities for traits more closely related to fitness.     

Multivariate analysis of the phenotypic relationships of the species of Paragalaxias and Galaxias (Pisces: Galaxiidae) in Tasmania

The 10 species of Galaxias in Tasmania, G. olidus from mainland Australia and the four species of Paragalaxias were studied using principal co-ordinates analysis (PCOA) and cluster analysis of a standardized Euclidean distance matrix based upon variate means, and by canonical variate analysis (CVA) conducted as a stepwise multiple discriminant analysis. Thirty-five variables comprising 30 morphometric and five meristic characters were analysed. The meristic characters were not included in the CVA. Excellent separation of the two genera was achieved in all analyses. The multivariate analyses were repeated on each genus separately to see if relationships suggested by the overall analysis remain stable. When the resultant groupings of species are compared for the different analyses, no consistent, distinct groupings of species within each genus are apparent. Despite the absence of distinct groupings, some trends in the affinities of some species are evident. In particular, species affinities as indicated by the CVA are more consistent with established opinions of species relationships. From the results of the study it is suggested that caution be exercised in the application of multivariate statistical analyses of morphological data to ichthyological systematics and phylogeny.     

Linear Discrimination,Ordination, and the Visualization of Selection Gradients in Modern Morphometrics

Linear discriminant analysis (LDA) is a multivariate classification technique frequently applied to morphometric data in various biomedical disciplines. Canonical variate analysis (CVA), the generalization of LDA for multiple groups, is often used in the exploratory style of an ordination technique (a low-dimensional representation of the data). In the rare case when all groups have the same covariance matrix, maximum likelihood classification can be based on these linear functions. Both LDA and CVA require full-rank covariance matrices, which is usually not the case in modern morphometrics. When the number of variables is close to the number of individuals, groups appear separated in a CVA plot even if they are samples from the same population. Hence, reliable classification and assessment of group separation require many more organisms than variables. A simple alternative to CVA is the projection of the data onto the principal components of the group averages (between-group PCA). In contrast to CVA, these axes are orthogonal and can be computed even when the data are not of full rank, such as for Procrustes shape coordinates arising in samples of any size, and when covariance matrices are heterogeneous. In evolutionary quantitative genetics, the selection gradient is identical to the coefficient vector of a linear discriminant function between the populations before vs. after selection. When the measured variables are Procrustes shape coordinates, discriminant functions and selection gradients are vectors in shape space and can be visualized as shape deformations. Except for applications in quantitative genetics and in classification, however, discriminant functions typically offer no interpretation as biological factors.     

哈密天山北路墓地出土颅骨的测量性状

本文是对出土于新疆哈密地区天山北路青铜时代墓地颅骨测量性状的研究。文中公布了24例天山北路墓地古代人群77项颅骨测量性状基本数据, 在此基础上, 对男、女两性的测量性状特点进行了统计分析, 并结合考古学文化研究和分子生物学研究的相关结论对实验结果进行了讨论和推论。主要研究结论如下: 一是该人群虽已经形成了具有自身特点的、共性的体质特征, 但人群内部也存在些许差异, 尤其是在男性个体数据之中。二是该人群是由分别具有东、西方体质特征的祖先人群混杂融合而成, 是处于当时大人种分布过渡地带的过渡人群。     

Modeling wetland plant metrics to improve the performance of vegetation-based indices of biological integrity

The objective of this study was to determine if the accuracy and precision of wetland plant indices of biological integrity (IBIs) could be improved through the use of modeling techniques. To do this, we developed a modeled vegetation IBI (MVIBI) based on metrics previously used to develop vegetation indices of biological integrity (VIBIs) for Ohio wetlands (e.g. % invasive grass, % sensitive species, shrub richness). We selected 82 emergent, forested, and shrub-dominated reference sites distributed across the State of Ohio and built Random Forest models to predict plant metric scores at reference wetlands from naturally occurring environmental features related to climate, hydrology, geology, soils, and landscape position. The models explained between 14 and 52% of the variance in the scores of 21 metrics indicating that variation in wetland plant assemblages was significantly associated with naturally occurring environmental gradients. We used principal component analysis to identify ten groups of statistically independent metrics and selected one metric from each group that discriminated most strongly between reference and most degraded sites based on t-scores. Two axes did not contain discriminating metrics so we used eight metrics in the MVIBI. Analysis of variance of reference site MVIBI scores indicated that we could use one distribution of reference site scores to assess multiple wetland types, thus eliminating the need to separately designate wetland types. We used the MVIBI to assess 170 test sites and compared the accuracy, precision, responsiveness, and sensitivity of the MVIBI to those of the original VIBIs. The MVIBI was up to twice as accurate and precise as the original VIBIs, indicating that modeling can be used to improve the performance of vegetation-based IBIs. The use of model-based IBIs for wetland plants should reduce assessment errors associated with natural variation in plant metrics and should increase confidence in wetland assessments.     

Bootstrapped ordination: a method for estimating sampling effects in indirect gradient analysis

Indirect gradient analysis, or ordination, is primarily a method of exploratory data analysis. However, to support biological interpretations of resulting axes as vegetation gradients, or later confirmatory analyses and statistical tests, these axes need to be stable or at least robust into minor sampling effects. We develop a computer-intensive bootstrap (resampling) approach to estimate sampling effects on solutions from nonlinear ordination.We apply this approach to simulated data and to three forest data sets from North Carolina, USA and examine the resulting patterns of local and global instability in detrended correspondence analysis (DCA) solutions. We propose a bootstrap coefficient, scaled rank variance (SRV), to estimate remaining instability in species ranks after rotating axes to a common global orientation. In analysis of simulated data, bootstrap SRV was generally consistent with an equivalent estimate from repeated sampling. In an example using field data SRV, bootstrapped DCA showed good recovery of the order of common species along the first two axes, but poor recovery of later axes. We also suggest some criteria to use with the SRV to decide how many axes to retain and attempt to interpret.Abbreviations DCA= detrended correspondence analysis - SRV= scaled rank variance     

A MODEL OF KIN-STRUCTURED MIGRATION

When individuals disperse from one local group to another, they often do so in the company of relatives. This is known as “kin-structured migration,” and its effect on genetic population structure is investigated here. It is shown that when migration is kin-structured, the ratio of between- to within-group variance is increased by a quantity that can be estimated either from behavioral or genetic data. Theoretical results indicate that kin-structured migration should be most important in populations with high mobility, and analysis of data for humans and lions suggests the kin-structured migration may have a substantial effect on genetic population structure in both species. Its effect seems to be small in a population of pine voles.     

Relationships between macrophytic vegetation and physical features of river habitats: the need for a morphological approach

The aim of this paper is to study the relationships between the physical features of rivers and the distribution of macrophyte vegetation. Field work was undertaken at 207 stations along the Scorff River and its tributaries, a salmon river system in southern Brittany (western France). The physical features were considered using a principal component analysis (PCA). Stepwise multiple regression models made it possible to assess their relationships with the botanical data. The first five axes of the physical PCA (used as explicative variables) were initially linked to the most frequently surveyed species, then to their eco-morphological types, and, finally to Arber’s (1920. Water Plants. A Study of Aquatic Angiosperms. Cambridge Univ. Press, Cambridge, 414 pp) morphological classification. It was concluded that plant morphology was closely related to these environmental factors. This could contribute to the development of predictive models for plant distribution and could increase the knowledge of reference vegetation related to bioindication systems.     

A multivariate morphometric investigation of Atherina boyeri Risso, 1810 and A. presbyter Cuvier, 1829 (Teleostei: Atherinidae): morphometric evidence in support of the two species

Two recently developed morphometric methodologies, multiple group principal components analysis (MGPCA) and the box truss method of body form transformation are used to re-address whether Atherina boyeri Risso, 1810 and A. presbyter Cuvier, 1829 are morphometrically distinct. The results revealed that morphometric differences are present between A. boyeri and A. presbyter , consistent with expectations of the existence of two species.
Females of the two species were clearly discriminated into two separate groups because the within-group covariances of several characters within populations of each species were different between species i.e., the covariances were heteroscedastic. The occurrence of heteroscedasticity within the data, although statistically invalidating the results of canonical variates anslysis, indicated there to be a large amount of morphological variation between females of the two species. Males were differentiated as a result of differences in body 'shape', particularly the relationship between head 'shape' and body 'shape'.
Several probable reasons are given for the failure of a previous study to differentiate the two species. The data rejects the synonymy of the two species in support of the continued use of the taxa A. boyeri Risso, 1810 and A. presbyter Cuvier, 1829.     

The application of MANOVA to analyse <Emphasis Type="Italic">Arabidopsis thaliana</Emphasis> metabolomic data from factorially designed experiments

Metabolomic technologies produce complex multivariate datasets and researchers are faced with the daunting task of extracting information from these data. Principal component analysis (PCA) has been widely applied in the field of metabolomics to reduce data dimensionality and for visualising trends within the complex data. Although PCA is very useful, it cannot handle multi-factorial experimental designs and, often, clear trends of biological interest are not observed when plotting various PC combinations. Even if patterns are observed, PCA provides no measure of their significance. Multivariate analysis of variance (MANOVA) applied to these PCs enables the statistical evaluation of main treatments and, more importantly, their interactions within the experimental design. The power and scope of MANOVA is demonstrated through two different factorially designed metabolomic investigations using Arabidopsis ethylene signalling mutants and their wild-type. One investigation has multiple experimental factors including challenge with the economically important pathogen Botrytis cinerea and also replicate experiments, while the second has different sample preparation methods and one level of replication ‘nested’ within the design. In both investigations there are specific factors of biological interest and there are also factors incorporated within the experimental design, which affect the data. The versatility of MANOVA is displayed by using data from two different metabolomic techniques; profiling using direct injection mass spectroscopy (DIMS) and fingerprinting using fourier transform infra-red (FT-IR) spectroscopy. MANOVA found significant main effects and interactions in both experiments, allowing a more complete and comprehensive interpretation of the variation within each investigation, than with PCA alone. Canonical variate analysis (CVA) was applied to investigate these effects and their biological significance. In conclusion, the application of MANOVA followed by CVA provided extra information than PCA alone and proved to be a valuable statistical addition in the overwhelming task of analysing metabolomic data.     

Craniometric variation,genetic theory,and modern human origins

Recent controversies surrounding models of modern human origins have focused on among-group variation, particularly the reconstruction of phylogenetic trees from mitochondrial DNA (mtDNA) and, the dating of population divergence. Problems in tree estimation have been seen as weakening the case for a replacement model and favoring a multiregional evolution model. There has been less discussion of patterns of within-group variation, although the mtDNA evidence has consistently shown the greatest diversity within African populations. Problems of interpretation abound given the numerous factors that can influence within-group variation, including the possibility of earlier divergence, differences in population size, patterns of population expansion, and variation in migration rates. We present a model of within-group phenotypic variation and apply it to a large set of craniometric data representing major Old World geographic regions (57 measurements for 1,159 cases in four regions: Europe, Sub-Saharan Africa, Australasia, and the Far East). The model predicts a linear relationship between variation within populations (the average within-group variance) and variation between populations (the genetic distance of populations to pooled phenotypic means). On a global level this relationship should hold if the long-term effective population sizes of each region are correctly specified. Other potential effects on withingroup variation are accounted for by the model. Comparison of observed and expected variances under the assumption of equal effective sizes for four regions indicates significantly greater within-group variation in Africa and significantly less within-group variation in Europe. These results suggest that the long-term effective population size was greatest in Africa. Closer examination of the model suggests that the long-term African effective size was roughly three times that of any other geographic region. Using these estimates of relative population size, we present a method for analyzing ancient population structure, which provides estimates of ancient migration. This method allows us to reconstruct migration history between geographic regions after adjustment for the effect of genetic drift on interpopulational distances. Our results show a clear isolation of Africa from other regions. We then present a method that allows direct estimation of the ancient migration matrix, thus providing us with information on the actual extent of interregional migration. These methods also provide estimates of time frames necessary to reach genetic equilibrium. The ultimate goal is extracting as much information from present-day patterns of human variation relevannt to issues of human origins. Our results are in agreement with mismatch distribution analysis of mtDNA, and they support a “weak Garden o Eden” model. In this model, modern-day variation can be explained by divergence from an initial source (perhaps Africa) into a number o small isolated populations, followed by later population expansion throughout our species. The major populationn expansions of Homo sapiens during and after the late Pleistocene have had the effect of “freezing” ancient patterns of population structure. While this is not the only possible scenario, we do note the close agreement with ecent analyses of mtDNA mismatch distibutions. © 1994 Wiley-Liss, Inc.     

The macroevolution of climatic niches and its role in ant diversification

1. Investigating how climatic niches change over evolutionary timescales is a necessary step to understanding the current distribution of lineages, yet few studies have addressed this issue using comprehensive datasets. In this study, the evolution of ant climatic niches is investigated at a global scale based on bioclimatic data associated with 163 481 ant occurrence records. The resulting dataset was subjected to principal component analysis, and the scores obtained were used to characterise the main axes of ant climatic niche evolution. 2. Principal component axis 1 (PC1) reflected variation in average temperature and seasonality – consistent with typical tropical/temperate gradients – whereas PC2 was associated with varying levels of aridity. Evolution along these two niche axes was markedly different: differences in the amount of explained variance between PC1 (65%) and PC2 (19%) suggest that climatic niche evolution was nearly three times more pronounced along a tropical–temperate climate axis. 3. There was statistically significant phylogenetic signal on PC1, with genera occupying more tropical conditions diversifying at a faster rate, yet neither of these results is significant on PC2. In addition, most of the ancient ant lineages are associated with conditions of low seasonality and high temperatures. 4. These results provide partial support for the tropical conservatism hypothesis as an explanation for geographical patterns of ant species richness.     

Partitioning additive genetic variance into genomic and remaining polygenic components for complex traits in dairy cattle

ABSTRACT: BACKGROUND: Low cost genotyping of individuals using high density genomic markers were recently introduced as genomic selection in genetic improvement programs in dairy cattle. Most implementations of genomic selection only use marker information, in the models used for prediction of genetic merit. However, in other species it has been shown that only a fraction of the total genetic variance can be explained by markers. Using 5217 bulls in the Nordic Holstein population that were genotyped and had genetic evaluations based on progeny, we partitioned the total additive genetic variance into a genomic component explained by markers and a remaining component explained by familial relationships. The traits analyzed were production and fitness related traits in dairy cattle. Furthermore, we estimated the genomic variance that can be attributed to individual chromosomes and we illustrate methods that can predict the amount of additive genetic variance that can be explained by sets of markers with different density. RESULTS: The amount of additive genetic variance that can be explained by markers was estimated by an analysis of the matrix of genomic relationships. For the traits in the analysis, most of the additive genetic variance can be explained by 44 K informative SNP markers. The same amount of variance can be attributed to individual chromosomes but surprisingly the relation between chromosomal variance and chromosome length was weak. In models including both genomic (marker) and familial (pedigree) effects most (on average 77.2%) of total additive genetic variance was explained by genomic effects while the remaining was explained by familial relationships. CONCLUSIONS: Most of the additive genetic variance for the traits in the Nordic Holstein population can be explained using 44 K informative SNP markers. By analyzing the genomic relationship matrix it is possible to predict the amount of additive genetic variance that can be explained by a reduced (or increased) set of markers. For the population analyzed the improvement of genomic prediction by increasing marker density beyond 44 K is limited.     

Behavioral attributes influence annual mating success more than morphological traits in male collared lizards

Traits that potentially influence mating success (MS) may be"static" with low lability once they develop or "dynamic" withhighly modifiable expression. We used principal components (PCs)analyses of dynamic behavioral and morphological traits thatare static over the short term to determine their relative contributionsto the ability of territorial male collared lizards to acquireaccess to females and obtain high MS. We estimated annual MSof males as the relative frequency with which they engaged incourtship with reproductively active resident females. ThreePCs explained statistically significant phenotypic variationamong males. Morphological traits loaded significantly on 2PCs that explained 26.3% and 13.0% of the variance, respectively,whereas behavioral variables loaded significantly on a differentcomponent that explained 15.7% of the variance in male traits.The frequency with which males initiated aggressive encounterswith same-sex competitors did not load significantly on thesePC axes. Males having behavioral PC scores above the mean hadsignificantly higher MS than those with behavioral scores belowthe mean, whereas male MS was not related to component scoresfor either of the axes describing static morphological variables.Results indicate that in our population behavior patterns associatedwith advertisement, particularly to females, influence maleMS more strongly than morphological traits or the initiationof direct aggression with same-sex competitors.