The position of the Nazlet Khater specimen among prehistoric and modern African and Levantine populations

The morphometric affinities of the 33,000 year old skeleton from Nazlet Khater, Upper Egypt are examined using multivariate statistical procedures. In the first part, principal components analysis is performed on a dataset of mandible dimensions of 220 fossils, sub-fossils and modern specimens, ranging in time from the Late Pleistocene to recent and restricted in space to the African continent and Southern Levant. In the second part, mean measurements for various prehistoric and modern African and Levantine populations are incorporated in the statistical analysis. Subsequently, differences between male and female means are examined for some of the modern and prehistoric populations. The results indicate a strong association between some of the sub-Saharan Middle Stone Age (MSA) specimens, and the Nazlet Khater mandible. Furthermore, the results suggest that variability between African populations during the Neolithic and Protohistoric periods was more pronounced than the range of variability observed among recent African and Levantine populations. Results also demonstrate a general reduction in the degree of sexual dimorphism during the Holocene. However, this pattern of reduction pattern varies by geographic location and is not uniform across the African continent.     

Trapline foraging by bumble bees: II. Definition and detection from sequence data

Trapline foraging—repeated sequential visits to a seriesof feeding locations—presents interesting problems seldomtreated in foraging models. Work on traplining is hampered bythe lack of statistical, operational approaches for detectingits existence and measuring its strength. We propose severalstatistical procedures, illustrating them with records of interplantflight sequences by bumble bees visiting penstemon flowers.An asymmetry test detects deviations from binomial expectationin the directionality of visits between pairs of plants. Severaltests compare data from one bee to another frequencies of visitsto plants and frequencies of departures to particular destinationsare compared using contingency tables; similarities of repeatedsequences within bees are compared to those between bees bymeans of sequence alignment and Mantel tests. We also comparedobserved movement patterns to those generated by null modelsdesigned to represent realistic foraging by non-traplining bees,examining: temporal patterns of the bee's spatial displacementfrom its starting point using spectral analysis; the varianceof return times to particular plants; and the sequence alignmentof repeated cycles within sequences. We discuss the differentindications and the relative strengths of these approaches     

Genetic differentiation of Yemeni people according to rhesus and Gm polymorphisms

For introducing Yemeni population in synthesis of genetic relationships of human populations, analysis of rhesus and Gm polymorphisms have been carried out for a population sample of 210 Yemenites. Rhesus haplotype frequencies were compared to those estimated in an original sample of 171 Tunisians and to available data for other populations. Gm haplotype frequencies were introduced in a wide synthesis of genetic relationships for 67 populations from Africa, Europe, the Near East and India. The genetic profile of Yemeni people would be close to that of a highly diversified ancestral population. The first inhabitants of North Africa, the Berbers and Yemenites have very likely a common origin and were not subject to important genetic drift after their geographic differentiation. While, the divergence between Yemenites and their neighbours of sub-Saharan Africa would have occurred with a founder effect and a long isolation. An important parallelism is observed for the Gm system between genetic and linguistic differentiations.     

Reflections on univariate and multivariate analysis of metabolomics data

Metabolomics experiments usually result in a large quantity of data. Univariate and multivariate analysis techniques are routinely used to extract relevant information from the data with the aim of providing biological knowledge on the problem studied. Despite the fact that statistical tools like the t test, analysis of variance, principal component analysis, and partial least squares discriminant analysis constitute the backbone of the statistical part of the vast majority of metabolomics papers, it seems that many basic but rather fundamental questions are still often asked, like: Why do the results of univariate and multivariate analyses differ? Why apply univariate methods if you have already applied a multivariate method? Why if I do not see something univariately I see something multivariately? In the present paper we address some aspects of univariate and multivariate analysis, with the scope of clarifying in simple terms the main differences between the two approaches. Applications of the t test, analysis of variance, principal component analysis and partial least squares discriminant analysis will be shown on both real and simulated metabolomics data examples to provide an overview on fundamental aspects of univariate and multivariate methods.     

Revealing cryptic spatial patterns in genetic variability by a new multivariate method

Increasing attention is being devoted to taking landscape information into account in genetic studies. Among landscape variables, space is often considered as one of the most important. To reveal spatial patterns, a statistical method should be spatially explicit, that is, it should directly take spatial information into account as a component of the adjusted model or of the optimized criterion. In this paper we propose a new spatially explicit multivariate method, spatial principal component analysis (sPCA), to investigate the spatial pattern of genetic variability using allelic frequency data of individuals or populations. This analysis does not require data to meet Hardy-Weinberg expectations or linkage equilibrium to exist between loci. The sPCA yields scores summarizing both the genetic variability and the spatial structure among individuals (or populations). Global structures (patches, clines and intermediates) are disentangled from local ones (strong genetic differences between neighbors) and from random noise. Two statistical tests are proposed to detect the existence of both types of patterns. As an illustration, the results of principal component analysis (PCA) and sPCA are compared using simulated datasets and real georeferenced microsatellite data of Scandinavian brown bear individuals (Ursus arctos). sPCA performed better than PCA to reveal spatial genetic patterns. The proposed methodology is implemented in the adegenet package of the free software R.     

The Dagestan gene pool: Polymorphism of immunogenetic and biochemical markers in Kumyks

This study is a part of long-term investigations devoted to the analysis of the gene pool of Dagestan ethnic groups. The phenotype (in %), gene, and haplotype frequencies in Kumyk ethnic group are reported. A total of 39 alleles and six haplotypes of 14 loci (AB0, Rhesus, P, Levis, Kell, HP, GC, C’3, TF, 6PGD, GLO1, ESD, ACP, and PGM1) of immunobiochemical genetic marker systems were examined. Rare haplotypes of the Rhesus system were identified, including CDE in the Karabudakhkent population with the frequency of 0.030, and Cde and cdE in the Dorgeli population with the frequencies of 0.034 and 0.38, respectively. Similarly to the other ethnic populations of Dagestan examined, Kukyk populations carried rare, albeit typically “Caucasoid” gene ACP1 ^c of the AcP1 locus. The frequency of this allele in the two populations was similar, constituting 0.031 for Karabudakhkent and 0.032 for Dorgeli. In Kumyks, allele frequencies of the AB0, Rhesus, P, Lewis, Kell, HP, GC, C′3, TF, 6PGD, GLO1, ESD, ACP, but not PGM1, systems were similar to the mean allele frequencies at these loci observed in the other ethnic groups from the Dagestan, Caucasus, and the whole European historical ethnographic province. At the same time, the allele frequency values obtained were different from those for the populations of Kazakhstan, Central Asia, Siberia, and the Ruswsian Far East. Thus, the results obtained for classical genetic markers indicate that Kumyks are genetically closer to the indigenous populations of Dagestan than to Turkic-speaking populations. Analysis of the fit of the observed phenotype frequencies to the Hardy-Weinberg expectations showed that compared to other indigenous populations of Dagestan examined, in Kumyks the genetic state of the population upon random allele association was close to equilibrium. Probably, this state was determined by practical absence of the consanguineous marriages upon preservation of intra-aul endogamy.     

Resource partitioning in rhinolophoid bats revisited

We assessed the ecomorphological structure of a guild of rhinolophoid bats in a Malaysian rainforest first described by Heller and von Helversen (1989). These authors found that the distribution of echolocation call frequencies used by 12 syntopic species was more even than expected from allometric relationships or in randomly generated communities, and that the observed minimal ratio was greater than expected by chance alone. In this study we were able to expand their guild to 15 species, but in doing so it became apparent that call frequencies might be less evenly distributed across the total frequency range than previously proposed. We replicated Heller and von Helversen’s (1989) analyses with the full 15-species complement but were unable to support their suggestion that rhinolophoid bats exhibit resource partitioning through differences in frequency bands. We adopted a multivariate approach and incorporated measures of body size and wing morphology into the analysis. We used phylogenetic autocorrelation to ensure that the species were statistically independentand principal component analysis to describe the morphological space occupied by the 15 species in the community and four additional species representing the extremes of phenotypic variation. We derived interspecific Euclidean distances and tested the mean values and SDs of these distances against those of 100 guilds of ”synthetic” species created randomly within the principal component space. The guild of Rhinolophoidea was not distributed randomly in multivariate space. Instead we found evidence of morphological overdispersion of the most similar species, which suggests niche differentiation in response to competition. Less similar species were nearer in morphological space than expected, and we suggest this is a consequence of ecological constraints on parameter combinations. Despite this underdispersion, many of the more distant neighbours were evenly rather than randomly spaced or clumped in morphospace, suggesting that, given the environmental constraints on morphology, species in this guild do experience limits to their similarity. Finally, we tested the influence of the relative abundance of species on morphological displacement, and found no evidence that abundant, spatially correlated species reduce interspecific overlap in morphological space. Received: 10 April 1999 / Accepted: 28 February 2000     

The dagestan gene pool: Analysis of the frequencies of classical genetic markers in Avars

This study is part of long-term research in the gene pool of Dagestan ethnic groups. The phenotype (in percent), gene, and haplotype frequencies in three Avar populations are reported. A total of 37 alleles of 13 loci of immune and biochemical genetic marker systems (ABO, Rhesus, P, Lewis, HP, GC, C′3, TF, 6PGD, GLO1, ESD, ACP, and PGM1) have been studied. Rare haplotypes of the Rhesus system (CDE, Cde and cdE) have been found in the populations studied. In two out of three local populations (Khunzakh and Kharakhi), a typically “Caucasoid” rare gene ACP1 ^c of the AcP1 locus has proved to be relatively frequent (0.030 and 0.023, respectively). The frequencies of the allele variantsP ² , le, and Hp ¹ of loci of the P, Lewis, and HP systems, respectively, have been found to be lower than in other Caucasian ethnic groups and the total northern Eurasian population. The mean allele frequencies for the GC, C′3, TF, 6PGD, GLO1, and ESD systems in the populations studied are comparable wit those for both Caucasian ethnic groups and the total population of the European historical ethnographic province. Statistical analysis of the results has shown 11 cases of significant deviations of the observed phenotype frequencies from the Hardy-Weinberg equilibrium.     

mvmapper: Interactive spatial mapping of genetic structures

Characterizing genetic structure across geographic space is a fundamental challenge in population genetics. Multivariate statistical analyses are powerful tools for summarizing genetic variability, but geographic information and accompanying metadata are not always easily integrated into these methods in a user‐friendly fashion. Here, we present a deployable Python‐based web‐tool, mvmapper , for visualizing and exploring results of multivariate analyses in geographic space. This tool can be used to map results of virtually any multivariate analysis of georeferenced data, and routines for exporting results from a number of standard methods have been integrated in the R package adegenet , including principal components analysis (PCA), spatial PCA, discriminant analysis of principal components, principal coordinates analysis, nonmetric dimensional scaling and correspondence analysis. mvmapper 's greatest strength is facilitating dynamic and interactive exploration of the statistical and geographic frameworks side by side, a task that is difficult and time‐consuming with currently available tools. Source code and deployment instructions, as well as a link to a hosted instance of mvmapper , can be found at https://popphylotools.github.io/mvMapper/ .     

Advances in Geometric Morphometrics

Geometric morphometrics is the statistical analysis of form based on Cartesian landmark coordinates. After separating shape from overall size, position, and orientation of the landmark configurations, the resulting Procrustes shape coordinates can be used for statistical analysis. Kendall shape space, the mathematical space induced by the shape coordinates, is a metric space that can be approximated locally by a Euclidean tangent space. Thus, notions of distance (similarity) between shapes or of the length and direction of developmental and evolutionary trajectories can be meaningfully assessed in this space. Results of statistical techniques that preserve these convenient properties—such as principal component analysis, multivariate regression, or partial least squares analysis—can be visualized as actual shapes or shape deformations. The Procrustes distance between a shape and its relabeled reflection is a measure of bilateral asymmetry. Shape space can be extended to form space by augmenting the shape coordinates with the natural logarithm of Centroid Size, a measure of size in geometric morphometrics that is uncorrelated with shape for small isotropic landmark variation. The thin-plate spline interpolation function is the standard tool to compute deformation grids and 3D visualizations. It is also central to the estimation of missing landmarks and to the semilandmark algorithm, which permits to include outlines and surfaces in geometric morphometric analysis. The powerful visualization tools of geometric morphometrics and the typically large amount of shape variables give rise to a specific exploratory style of analysis, allowing the identification and quantification of previously unknown shape features.     

Gene pool of Daghestan ethnic groups: Polymorphism of classical gene markers in the Darghin ethnic group

The work is part of a study of the gene pool for Daghestan ethnic groups. In total, 38 alleles and eight genotypes were studied at 14 loci (AB0, Rhesus, P, Lewis, Kell, PH, GC, C′3, TF, 6-PGD, GLO1, ESD, ACP, and PBM1) of immunogenetic and biochemical polymorphic gene systems. A high frequency of allele d of the Rhesus system was observed in all populations examined (0.399–0.474). Among the rare haplotypes of the Rhesus system, we observed CDE in the Degva population, Cde in the Sergokala and Degva populations, and cdE in the Sergokala and Vanashimakhi populations. The typical Caucasian ACP1 ^c allele of the ACP1 locus, which is rather uncommon, was observed at a relatively high frequency in three (Segokala, Vanashimakhi, and Gubden) of the four local populations under study. In the Lewis system, a high frequency of the Le(a+b+) phenotype, which is characteristic of early childhood, was detected in the adult populations of Sergokala and Degva. The rare PGM ₁ ^V allele of the phosphoglucomutase 1 system (PGM1) was additionally observed in the Sergokala population. Statistical analysis identified 19 cases where the observed phenotype frequencies significantly differed from the frequencies expected from the Hardy-Weinberg equilibrium.     

A simple multivariate analysis to assess diversity in a complex long-term managed forest area in central Italy

Today wood and nonwood forest resources management meets and often clashes with environment and biological diversity protection. A main problem is to understand relationships between the different roles of forest biodiversity, site, and management parameters. A multivariate statistical analysis has been carried out in order to interpret relationships between some forest biodiversity components and forest inventory data. Several indices of floristic diversity, species abundance, and structural heterogeneity at stand level have been calculated. The different components of forest biodiversity were separated by principal components analysis. Relations between forest biodiversity indices and site and management attributes have been investigated by two multivariate statistical techniques: bivariate correlation analysis and multiple linear regression. Results showed a high correlation between all the investigated components of forest biodiversity and some topographic and/or forest management attributes. Results also gave ancillary information to define sustainable forest management criteria.     

Permutation-validated principal components analysis of microarray data

Background  

In microarray data analysis, the comparison of gene-expression profiles with respect to different conditions and the selection of biologically interesting genes are crucial tasks. Multivariate statistical methods have been applied to analyze these large datasets. Less work has been published concerning the assessment of the reliability of gene-selection procedures. Here we describe a method to assess reliability in multivariate microarray data analysis using permutation-validated principal components analysis (PCA). The approach is designed for microarray data with a group structure.     

Co-inertia analysis: an alternative method for studying species–environment relationships

• 1 Methods used for the study of species–environment relationships can be grouped into: (i) simple indirect and direct gradient analysis and multivariate direct gradient analysis (e.g. canonical correspondence analysis), all of which search for non-symmetric patterns between environmental data sets and species data sets; and (ii) analysis of juxtaposed tables, canonical correlation analysis, and intertable ordination, which examine species–environment relationships by considering each data set equally. Different analytical techniques are appropriate for fulfilling different objectives.
• 2 We propose a method, co-inertia analysis, that can synthesize various approaches encountered in the ecological literature. Co-inertia analysis is based on the mathematically coherent Euclidean model and can be universally reproduced (i.e. independently of software) because of its numerical stability. The method performs simultaneous analysis of two tables. The optimizing criterion in co-inertia analysis is that the resulting sample scores (environmental scores and faunistic scores) are the most covariant. Such analysis is particularly suitable for the simultaneous detection of faunistic and environmental features in studies of ecosystem structure.
• 3 The method was demonstrated using faunistic and environmental data from Friday (Freshwater Biology 18, 87-104, 1987). In this example, non-symmetric analyses is inappropriate because of the large number of variables (species and environmental variables) compared with the small number of samples.
• 4 Co-inertia analysis is an extension of the analysis of cross tables previously attempted by others. It serves as a general method to relate any kinds of data set, using any kinds of standard analysis (e.g. principal components analysis, correspondence analysis, multiple correspondence analysis) or between-class and within-class analyses.

     

Spatial ordination of vegetation data using a generalization of Wartenberg's multivariate spatial correlation

Question: Are there spatial structures in the composition of plant communities? Methods: Identification and measurement of spatial structures is a topic of great interest in plant ecology. Univariate measurements of spatial autocorrelation such as Moran's I and Geary's c are widely used, but extensions to the multivariate case (i.e. multi‐species) are rare. Here, we propose a multivariate spatial analysis based on Moran's I (MULTISPATI) by introducing a row‐sum standardized spatial weight matrix in the statistical triplet notation. This analysis, which is a generalization of Wartenberg's approach to multivariate spatial correlation, would imply a compromise between the relations among many variables (multivariate analysis) and their spatial structure (autocorrelation). MULTISPATI approach is very flexible and can handle various kinds of data (quantitative and/or qualitative data, contingency tables). A study is presented to illustrate the method using a spatial version of Correspondence Analysis. Location: Territoire d'Etude et d'Expérimentation de Trois‐Fontaines (eastern France). Results: Ordination of vegetation plots by this spatial analysis is quite robust with reference to rare species and highlights spatial patterns related to soil properties.     

Synthetic taxonomy of Rosa races using ACT-STATIS

Fifteen Rosa cultivated races were described by means of phenotypic frequencies (11 tables). Two groups of correlated contingency tables were identified by ACT-STATIS (Analyse Conjointe de Tableaux-Structuration de Tableaux à Trois Indices de la Statistique) interstructure analysis. Three data sets appeared to be independent from the others. Typologies of races were obtained after ACT-STATIS compromise analyses for the two groups of correlated tables, and after Principal Component Analyses for the independent data sets. Each typology was original and variously influenced by genealogical structure, mutation or artificial selection pressures. A weighted synthesis was attempted in order to build a taxonomy of races taking into account these diversity factors. The good agreement between the resulting classification and the assumptions about the history of Rosa domestication advocated for a wider utilization of ACT-STATIS and RV coefficient when the relationships between individuals or populations have to be studied on the basis of their similarities.     

Prevalence of ΔF508 cystic fibrosis carriers in The Netherlands: logistic regression on sex,age, region of residence and number of offspring

An average cystic fibrosis (CF) carrier frequency of 1 in 25 in Europe is cited in numerous reports, although a great variability in estimated prevalences has been found in different European populations. The estimates of these frequencies were based on numbers of CF patients before identification of the gene in 1989. Here we report the results of a study to determine the carrier frequency of the ΔF508 mutation in The Netherlands by analyzing mouthwashes and matched blood samples from 11 654 blood donors all over the country. We analyzed possible relationships between a number of theoretically explanatory variables and the ΔF508 carrier frequency by means of univariate and multivariate logistic regression. These variables were: distance of the blood banks from the northeastern part of the country (distance); whether the blood donors knew that we were looking for a CF mutation; sex and age of the donor; and number of children of the donor (family size). We detected a ΔF508 carrier frequency of 1 in 42 (95% CI 1/37–1/47) in The Netherlands. If we assume that the relative frequency of the ΔF508 mutation among carriers and patients is comparable in The Netherlands, this gives an estimated overall CF carrier frequency of 1 in 32 (95% CI 1/28–1/36), significantly less than 1 in 25. The univariate logistic regression analysis of the effects of the explanatory variables on the carrier frequency revealed no significant relationships, except for an increase in carrier frequency with increasing distance from the northeastern region. In the multivariate analysis with all five independent variables, distance, age and family size were significantly related to the carrier frequency, but sex and CF information were not. There was a significant interaction between age and family size. In our final model, distance, age and family size were positively related to the carrier frequency, while the interaction of age with family size showed a negative relation. These results confirm that there is a gradient in gene frequency with low frequencies in the northeastern part of the country and high frequencies in the southern part. They also suggest a relation of age and family size with carrier frequency. This relation, however, is too complex to be explained by heterozygote advantage. Received: 10 May 1996     

Investigating microbial associations from sequencing survey data with co‐correspondence analysis

Microbial communities, which drive major ecosystem functions, consist of a wide range of interacting species. Understanding how microbial communities are structured and the processes underlying this is crucial to interpreting ecosystem responses to global change but is challenging as microbial interactions cannot usually be directly observed. Multiple efforts are currently focused to combine next‐generation sequencing (NGS) techniques with refined statistical analysis (e.g., network analysis, multivariate analysis) to characterize the structures of microbial communities. However, most of these approaches consider a single table of sequencing data measured for several samples. Technological advances now make it possible to collect NGS data on different taxonomic groups simultaneously for the same samples, allowing us to analyse a pair of tables. Here, an analytical framework based on co‐correspondence analysis (CoCA) is proposed to study the distributions, assemblages and interactions between two microbial communities. We show the ability of this approach to highlight the relationships between two microbial communities, using two data sets exhibiting various types of interactions. CoCA identified strong association patterns between autotrophic and heterotrophic microbial eukaryote assemblages, on the one hand, and between microalgae and viruses, on the other. We demonstrate also how CoCA can be used, complementary to network analysis, to reorder co‐occurrence networks and thus investigate the presence of patterns in ecological networks.