Correlation between qualitatively distributed predicting variables and chemical terms in acridine derivatives using principal component analysis

When biological variables are not continuously distributed, the multiple and multivariate regression analysis cannot be used to correlate these variables against chemical regressors. As the employment of discriminant analysis requires the homogeneity of dispersion matrices and, that n_hp where n_h= degree of freedom of hypothesis, p =number of chemical terms, the reliability and validity of this method is highly questionable here. An alternative method is based on the principal component analysis where multicategory variables of drug responses can be classified into measures of inactive, slightly active, sufficiently active, and highly active drugs, for instance. The rules for classification are based on biological sources that can be expressed by chemical terms, too. An example adapted from antitumor action of acridine derivatives shows the working technique.     

A method of factor analysis for shape coordinates

Currently the most common reporting style for a geometric morphometric (GMM) analysis of anthropological data begins with the principal components of the shape coordinates to which the original landmark data have been converted. But this focus often frustrates the organismal biologist, mainly because principal component analysis (PCA) is not aimed at scientific interpretability of the loading patterns actually uncovered. The difficulty of making biological sense of a PCA is heightened by aspects of the shape coordinate setting that further diverge from our intuitive expectations of how morphometric measurements ought to combine. More than 50 years ago one of our sister disciplines, psychometrics, managed to build an algorithmic route from principal component analysis to scientific understanding via the toolkit generally known as factor analysis. This article introduces a modification of one standard factor‐analysis approach, Henry Kaiser's varimax rotation of 1958, that accommodates two of the major differences between the GMM context and the psychometric context for these approaches: the coexistence of “general” and “special” factors of form as adumbrated by Sewall Wright, and the typical loglinearity of partial warp variance as a function of bending energy. I briefly explain the history of principal components in biometrics and the contrast with factor analysis, introduce the modified varimax algorithm I am recommending, and work three examples that are reanalyses of previously published cranial data sets. A closing discussion emphasizes the desirability of superseding PCA by algorithms aimed at anthropological understanding rather than classification or ordination.     

Relating new information to a previous vegetation classification: a case of discriminant coordinates analysis

Discriminant coordinates analysis is an adequate technique for analyzing the linear relationships between a number of new variates (i.e. environmental or functional attributes) and a set of vegetational attributes already summarized in the form of a classification. It displays the principal differences among classes in relation to the new variates considered. The procedure and its rationale are equivalent to a special case of principal components analysis.A case study on radiometer satellite data is presented. Two discriminant coordinates displayed the main differences in the seasonal dynamics of the NDVI (an index of standing green biomass) among broad phytogeo-graphic units in the Patagonia region. The first coordinate can be interpreted as an index of height and convexity of the NDVI seasonal curve. It suggests that the principal difference among regions was the total seasonal growth. The second coordinate represents a contrast that discriminated between two already detected patterns of seasonal NDVI curve.Abbreviations DC Discriminant Coordinate - NDVI Normalized Difference Vegetation Index     

A multivariate morphological analysis of the Cardamine concatenata alliance (Brassicaceae)

Principal coordinate analysis using Gower’s similarity coefficient and canonical discriminant analysis were performed using morphological data to assess species distinctness in theCardamine concatenata alliance, comprising the eastern North American dentarias. The results of an overall principal coordinate analysis of the alliance using quantitative and qualitative characters revealed distinct and separate clusters that correspond to five previously recognized species (C. angustata, C. concatenata, C. diphylla, C. dissecta, C. maxima). One additional taxon,C. incisa, was found to group closely with theC. diphylla cluster. In a second principal coordinate analysis including only individuals fromC. diphylla andC. incisa, both are supported as distinct morphological entities. Canonical discriminant analysis of only above-ground quantitative characters was less effective in distinguishing previously recognized taxa, in keeping with the emphasis on qualitative characters in previous taxonomic treatments of the group.Cardamine incisa (Eames) Schumann (pro hybr.) is raised to the rank of species. A key to the species of theCardamine concatenata alliance is provided.     

Variability of the Root Essential Oils of Seseli rigidum Waldst. & Kit. (Apiaceae) from Different Populations in Serbia

The chemical compositions of the essential oils of seven natural populations of Seseli rigidum were analyzed. The essential‐oil yield ranged from 0.16 to 2.09%. Analysis of variance (ANOVA) revealed that there were no statistically significant differences in the mean essential‐oil yields between the populations, and no significant influence of the climate or soil type on the oil yield was observed. In all 67 analyzed samples, the polyacetylene falcarinol was the main compound, followed by octanal, methyl linoleate, α‐muurolene, 3‐butylphthalide, falcarinone, muurola‐4,10(14)‐dien‐1β‐ol, β‐sesquiphellandrene, salvial‐4(14)‐en‐1‐one, δ‐amorphene, spathulenol, and isospathulenol. The principal component analysis (PCA), the canonical discriminant analysis (CDA), and the cluster analysis (CA) revealed differentiation between the populations based on the climate. Three groups of populations were formed; the first group was composed of samples growing in regions with a humid climate, with oils having high falcarinol and low sesquiterpene contents, and the second and third groups comprised samples exposed to semi‐arid climate, with oils characterized by a lower falcarinol and higher α‐muurolene, δ‐amorphene, β‐sesquiphellandrene, and salvial‐4(14)‐en‐1‐one contents. The semi‐arid populations were divided into two groups, which were distinguished based on the oil contents of sesquiterpenes, falcarinone, and 3‐butylphthalide. On the other hand, no clear separation between populations based on the different soil types could be observed.     

Analysis of the hominoid os coxae by Cartesian coordinates.

This study is based upon 48 3-dimensional coordinates taken on 4 fossil hominid and 127 extant hominoid coxal bones. The follis include Sts 14, SK 3155, MLD 7, and MLD 25. The comparative sample consists of 42 Homo sapiens, 27 Pan troglodytes, 29 Gorilla gorilla and 29 Pongo pygmaeus. The coordinates improve the metrical representation of the bone beyond what can be done with linear measurements because the shape complexity of the os coxae is so great. The coordinates are rotated and translated so that all bones are in a standard position. The coordinates are then standardized for each specimen by dividing all coordinates by the pooled standard deviation of X, Y, and Z coordinates. These data are treated to standard statistical analyses including analysis of variance, Penrose size and shape statistics, principal coordinates and components, and canonical variates analysis. The data are then further altered by using some specimen as a standard and rotating each specimen until the total squared distance between its coordinates and those of the standard are minimized. The same statistics are applied to these "best fit" data. The results show a high degree of agreement between the methods. The hominid os coxae are dundamentally different from the other hominoids and the fossil hominids share the basic hominid configuration but with some unique differences.     

Shape indices to identify regional differences in otolith morphology of comber, Serranus cabrilla (L., 1758)

Sagittal otoliths from the Atlantic and Mediterranean regions of Serranus cabrilla L. were compared using shape indices (form‐factor, roundness, circularity, rectangularity, ellipticity and eccentricity). Regional differences were best described by form‐factor, circularity and eccentricity variables. The canonical discriminant functions were built with form‐factor or rectangularity indices. The results indicated slight regional variations. The G‐test was the criterion more useful to identify the otolith origin in the discriminant analysis.     

Reducing the babel in plant volatile communication: using the forest to see the trees

While plants of a single species emit a diversity of volatile organic compounds (VOCs) to attract or repel interacting organisms, these specific messages may be lost in the midst of the hundreds of VOCs produced by sympatric plants of different species, many of which may have no signal content. Receivers must be able to reduce the babel or noise in these VOCs in order to correctly identify the message. For chemical ecologists faced with vast amounts of data on volatile signatures of plants in different ecological contexts, it is imperative to employ accurate methods of classifying messages, so that suitable bioassays may then be designed to understand message content. We demonstrate the utility of ‘Random Forests’ (RF), a machine‐learning algorithm, for the task of classifying volatile signatures and choosing the minimum set of volatiles for accurate discrimination, using data from sympatric Ficus species as a case study. We demonstrate the advantages of RF over conventional classification methods such as principal component analysis (PCA), as well as data‐mining algorithms such as support vector machines (SVM), diagonal linear discriminant analysis (DLDA) and k‐nearest neighbour (KNN) analysis. We show why a tree‐building method such as RF, which is increasingly being used by the bioinformatics, food technology and medical community, is particularly advantageous for the study of plant communication using volatiles, dealing, as it must, with abundant noise.     

Metabolomic approaches reveal that cell wall modifications play a major role in ethylene-mediated resistance against Botrytis cinerea

In Arabidopsis, resistance to the necrotrophic fungus Botrytis cinerea is conferred by ethylene via poorly understood mechanisms. Metabolomic approaches compared the responses of the wild‐type, the ethylene‐insensitive mutant etr1‐1, which showed increased susceptibility, and the constitutively active ethylene mutants ctr1‐1 and eto2 both exhibited decreased susceptibility to B. cinerea. Fourier transform–infrared (FT‐IR) spectroscopy demonstrated reproducible biochemical differences between treatments and genotypes. To identify discriminatory mass‐to‐charge ratios (m/z) associated with resistance, discriminant function analysis was employed on spectra derived from direct injection electrospray ionisation‐mass spectrometry on the derived principal components of these data. Ethylene‐modulated m/z were mapped onto Arabidopsis biochemical pathways and many were associated with hydroxycinnamate and monolignol biosynthesis, both linked to cell wall modification. A high‐resolution linear triple quadrupole‐Orbitrap hybrid system confirmed the identity of key metabolites in these pathways. The contribution of these pathways to defence against B. cinerea was validated through the use of multiple Arabidopsis mutants. The FT‐IR microspectroscopy indicated that spatial accumulation of hydroxycinnamates and monolignols at the cell wall to confine disease was linked ot ethylene. These data demonstrate the power of metabolomic approaches in elucidating novel biological phenomena, especially when coupled to validation steps exploiting relevant mutant genotypes.     

Multivariate morphometric analyses of the predatory ciliate genus Semispathidium (Ciliophora: Litostomatea), with description of S. longiarmatum nov. spec.

We studied morphometrical variation, species boundaries, and importance of morphometric features for a reliable separation of five African Semispathidium taxa. Altogether, 20 features traditionally used in alpha-taxonomy of the predatory genus Semispathidium were measured or scored on 85 protargol-impregnated interphase specimens, and were analyzed using hierarchical clustering as well as principal component and canonical discriminant analyses. This multivariate approach confirmed that a population found in Botswanan floodplain soil represents a distinct taxon. The new species is described here as S. longiarmatum, using live observation, protargol impregnation, and scanning electron microscopy. Semispathidium longiarmatum strongly resembles S. armatum and S. breviarmatum but it is clearly distinguished from these species by the extrusome pattern. The reliability of S. longiarmatum is also strengthened, according to the canonical discriminant analysis, by several quantitative features, viz., the number of ciliary rows, the length:width ratio of the macronucleus, and the number of dikinetids in brush row 1. Moreover, the present study documents the distinctness of all African Semispathidium species which can be separated by a combination of both qualitative and quantitative (morphometric) features. Consequently, Semispathidium species do not form a continuous complex but fairly discrete clusters in the phenotypic space.     

Guidelines for standardizing the application of discriminant analysis of principal components to genotype data

Despite the popularity of discriminant analysis of principal components (DAPC) for studying population structure, there has been little discussion of best practice for this method. In this work, I provide guidelines for standardizing the application of DAPC to genotype data sets. An often overlooked fact is that DAPC generates a model describing genetic differences among a set of populations defined by a researcher. Appropriate parameterization of this model is critical for obtaining biologically meaningful results. I show that the number of leading PC axes used as predictors of among-population differences, p_axes, should not exceed the k−1 biologically informative PC axes that are expected for k effective populations in a genotype data set. This k−1 criterion for p_axes specification is more appropriate compared to the widely used proportional variance criterion, which often results in a choice of p_axes ≫ k−1. DAPC parameterized with no more than the leading k−1 PC axes: (i) is more parsimonious; (ii) captures maximal among-population variation on biologically relevant predictors; (iii) is less sensitive to unintended interpretations of population structure; and (iv) is more generally applicable to independent sample sets. Assessing model fit should be routine practice and aids interpretation of population structure. It is imperative that researchers articulate their study goals, that is, testing a priori expectations vs. studying de novo inferred populations, because this has implications on how their DAPC results should be interpreted. The discussion and practical recommendations in this work provide the molecular ecology community with a roadmap for using DAPC in population genetic investigations.     

Metabolic fingerprinting to discriminate diseases of stored carrots

Volatile metabolites from headspace gas of carrot cv. Vita‐treat inoculated with water or four different pathogens Botrytis cinerea, Erwinia carotovora subsp. carotovora, Aspergillus niger and Fusarium avenaceum were profiled using gas chromatography and mass spectrometry to develop a technology to discriminate diseases. The inoculation of carrot roots with water or different pathogens released a total of 137 different volatile metabolites. Among them, 39 compounds were relatively consistent and 11 were specific to one or more diseases/inoculations. E. carotovora subsp. carotovora produced seven disease‐specific metabolites: 1‐butanol, 3‐methyl; 1‐pentanol; 1‐propanol, 2‐methyl; 2,3‐butanedione; boronic acid, ethyl; butane, 1‐methoxy‐3‐methyl; and ethane, ethoxy. Some metabolites were disease/inoculation discriminatory and were not detected in all treatments: 1,2‐dimethoxy‐ethene was common in carrots inoculated with E. carotovora subsp. carotovora and B. cinerea, while 2‐butanone, 3‐chloro‐4‐hydroxy‐1,4‐diphenyl was common in carrots inoculated with E. carotovora subsp. carotovora, F. avenaceum and water‐inoculated control. The significant mass ions, based on univariate analysis, from a total of 150 (46–195 m/z) and compounds from a total of 32 were further subjected to stepwise discriminant analysis and discriminant analysis. The models for 3 days after inoculation (DAI) were better than those for 6 DAI and 3 + 6 DAI, where up to 90% of the observations were correctly classified into respective inoculations. The disease‐discriminatory compounds from different diseases/inoculations and discriminant analysis models developed here have the potential for the early detection and discrimination of postharvest diseases of carrot cv. Vita‐treat, after validation under commercial conditions.     

Validation of archived chemical shifts through atomic coordinates

The public archives containing protein information in the form of NMR chemical shift data at the BioMagResBank (BMRB) and of 3D structure coordinates at the Protein Data Bank are continuously expanding. The quality of the data contained in these archives, however, varies. The main issue for chemical shift values is that they are determined relative to a reference frequency. When this reference frequency is set incorrectly, all related chemical shift values are systematically offset. Such wrongly referenced chemical shift values, as well as other problems such as chemical shift values that are assigned to the wrong atom, are not easily distinguished from correct values and effectively reduce the usefulness of the archive. We describe a new method to correct and validate protein chemical shift values in relation to their 3D structure coordinates. This method classifies atoms using two parameters: the per‐atom solvent accessible surface area (as calculated from the coordinates) and the secondary structure of the parent amino acid. Through the use of Gaussian statistics based on a large database of 3220 BMRB entries, we obtain per‐entry chemical shift corrections as well as Z scores for the individual chemical shift values. In addition, information on the error of the correction value itself is available, and the method can retain only dependable correction values. We provide an online resource with chemical shift, atom exposure, and secondary structure information for all relevant BMRB entries ( http://www.ebi.ac.uk/pdbe/nmr/vasco ) and hope this data will aid the development of new chemical shift‐based methods in NMR. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Maternity validation using sire‐only BovineSNP50 BeadChip data

Based on pairwise identity‐by‐state (IBS) distances and whole‐genome SNP data, kinship was investigated in the Israeli Holstein population. A total of 789 bulls, including most of the artificial insemination sires in service since 1987, were genotyped by the BovineSNP50 BeadChip. This sample included up to five generations. For each bull‐by‐bull combination, three states are possible for each marker: no match, a single match and both alleles match. Summing over all markers, the 932 598 IBS scores (three match frequencies*310 866 bull‐by‐bull combinations) were visualized using three‐dimensional coordinates that corresponded to the frequencies of the three possible states. Results were reduced to two dimensions using the transformations x’ = 0.7071(1 + freq1?freq2) and y’ = 1.2247freq0. Bull‐by‐bull pairs were grouped according to their level of kinship, and canonical scores were calculated using discriminant analysis and the x’ and y’ features. Of the 474 pairs of recorded maternal grandsire–grandson with both individuals genotyped, the probability for 28 pairs to belong to this level of kinship was low (P < 0.05), suggesting an error rate of around 3% per generation in pedigree determination.     

Stock structure analysis of Labeo rohita (Hamilton, 1822) across the Ganga basin (India) using a truss network system

In this study the intraspecific variation of wild Labeo rohita was investigated on the basis of morphometric characters using the truss network system constructed from the fish body. Altogether 435 fish samples were collected from six drainages of the Ganga basin in India. Data were subjected to principal component analysis, discriminant function analysis and univariate analysis of variance. The first principal component (PC1) explained 47.88% of the total variation, while PC2 and PC3 explained 17.22 and 8.33%, respectively. The step‐wise discriminant function analysis retained three variables that significantly discriminated the populations. Using these variables, 62.3% of the original groups were classified into their correct samples and 53.1% of the cross‐validated groups omitting one procedure were classified into their correct samples. Misclassification was higher for samples from the River Gomti (28.6%). Of the total of 31 transformed truss measurements, 30 exhibited significant differences among populations. These findings indicate the presence of six different stocks of L. rohita in the Ganga basin.     

Morphometric analysis of Cartesian coordinates of the human skull

A method for locating the three dimensional coordinates of cranial landmarks with respect to the Frankfort, midsagittal, and coronal planes is presented. Sliding calipers were used to obtain the distances from left and right porion and apex to each landmark, except for a few points where spreading calipers are required. In the present example, 35 landmarks (for a total of 105 measurements) were located for each of 35 Peruvian precolumbian skulls. These distances were entered into a program (SKULL) which calculates the Cartesian coordinates of each landmark. The XYZ coordinates of each landmark contain all the information necessary for calculation of the distances between any two landmarks, and these distances may also be obtained as output from program SKULL, if desired (595 distances if all 35 landmarks are used). Reliability of the location of coordinates was determined by comparing computed distances among selected landmarks from program SKULL with traditional anthropometric measurements. Satisfactory agreements were found. Direct multivariate analysis of the coordinates of the landmarks produced insights not available in traditional multivariate analysis of conventional anthropometric measurements.     

Multivariate morphometric analysis of the Potamogeton compressus group (Potamogetonaceae)

The Potamogeton compressus group is a complex of three to five closely related species with a circumpolar distribution in the Northern Hemisphere. Multivariate morphometric analyses (principal component analysis, cluster analysis, canonical and classificatory discriminant analyses) were used to elucidate the patterns of variation within this group and to test the morphological differentiation of the species recognized in the current literature. From the entire distribution range, 156 specimens of the group were included in the numerical methods. Results from morphological comparison are discussed in relation to molecular data, reproductive behaviour and geographical distribution. Morphometric analyses provided evidence that this complex can be clearly divided into three groups, one of which was subdivided mainly on the basis of allopatric occurrence and genetic differentiation. These groups correspond to four species accepted here: P. acutifolius (temperate regions of Europe), P. compressus (boreal and temperate regions of Europe and Asia), P. manchuriensis (northeastern China and Russian Far East) and P. zosteriformis (boreal and temperate regions of North America). Two species, P. acutifolius and P. compressus, are partly sympatric, but clearly differentiated morphologically and genetically, and effectively isolated reproductively. Endemic P. manchuriensis is characterized by a unique combination of characters and an occurrence in a limited geographical area. Allopatric P. zosteriformis is weakly differentiated morphologically from P. compressus, but differs markedly in molecular markers correlated with geographical differentiation. It may represent a cryptic species. In contrast, a recently suggested concept of southern Siberian P. henningii was not supported by our analyses. Plants so named are considered here as slender phenotypes of the widespread and variable P. compressus. © 2012 The Linnean Society of London, Botanical Journal of the Linnean Society, 2012, 170 , 112–130.