A maximum likelihood approach to non-linear ordination

Summary A non-linear method of ordinating vegetation samples based on the fitting of bell-shaped response curves is lescribed. For each species two Gaussian curves were itted, one to quantitative values, where the species was present, the other to probabilities of absence. A maximum likelihood approach was then used to obtain a best approximation of the positions of the samples along a one-dimensional gradient. By an iterative process successively better approximations were obtained.The method was successful in recovering gradients based on hypothetical data. With two sets of real data the gradient produced was more ecologically satisfying and far less distorted than that revealed by principal component analysis.     

Effects of sample distribution along gradients on eigenvector ordination

In general, disproportionately heavy sampling of the ends of a gradient increases the interpretability of eigenvector ordinations. More specifically, correspondence analysis (CA) and detrended correspondence analysis (DCA) best reproduce the original positions of samples in simulated coenoclines when samples are clustered toward the ends of the axis. Principal components analysis (PCA) reproduces the original sample positions less well than either CA or DCA and shows no improvement as samples are increasingly clustered toward the ends of the axis. PCA and CA show less curvature of one dimensional data into the second axis when sampling favors the ends of the axis.     

Pluralism and diversity: trends in the use and application of ordination methods 1990‐2007

Question: What are the trends and patterns in the application of ordination techniques in vegetation science since 1990? Location: Worldwide literature analysis. Methods: Evaluation of five major journals of vegetation science; search of all ISI‐listed ecological journals. Data were analysed with ANCOVAs, Spearman rank correlations, GLMs, biodiversity indices and simple graphs. Results: The ISI search retrieved fewer papers that used ordinations than the manual evaluation of five selected journals. Both retrieval methods revealed a clear trend in increasing frequency of ordination applications from 1990 to the present. Canonical Correspondence Analysis was far more frequently detected by the ISI search than any other method. Applications such as Correspondence Analysis/Reciprocal Averaging and Detrended Correspondence Analysis have increasingly been used in studies published in “applied” journals, while Canonical Correspondence Analysis, Redundancy Analysis and Non‐Metric Multidimensional Scaling were more frequently used in journals focusing on more “basic” research. Overall, Detrended Correspondence Analysis was the most commonly applied method within the five major journals, although the number of publications slightly decreased over time. Use of Non‐Metric Multidimensional Scaling has increased over the last 10 years. Conclusion: The availability of suitable software packages has facilitated the application of certain techniques such as Non‐Metric Multidimensional Scaling. However, choices of ordination techniques are currently less driven by the constraints imposed by the software; there is also limited evidence that the choice of methods follows social considerations such as the need to use fashionable methods. Methodological diversity has been maintained or has even increased over time and reflects the researcher's need for diverse analytical tools suitable to address a wide range of questions.     

Extended dissimilarity: a method of robust estimation of ecological distances from high beta diversity data

It is widely accepted that reliable ordination of ecological data requires a strong linear or ordinal relationship between the dissimilarity of sites, based on species composition, and the ecological distance between them. Certain dissimilarity measures, having the property that they take a fixed maximum value when sites have no species in common, have been shown to be strongly correlated with ecological distance. For ecological gradients of moderate length (moderate beta diversity), such measures, in conjunction with non-metric multidimensional scaling, will reliably yield successful ordinations. However, as beta diversity increases, more sites have no species in common, and such measures invariably under-estimate ecological distance for such sites. Thus ordinations of data with high species turnover (high beta diversity) may fail.Extended dissimilarities are defined using an iterative adaptation of flexible shortest path adjustment applied to the matrix of dissimilarities with fixed maximum values. By means of theoretical argument and simulations, this is shown to lead to far stronger correlations between the adjusted site dissimilarity and ecological distance for ecological gradients of greater length than previously considered. Hence ordinations of extended dissimilarities, by means of either metric or non-metric scaling techniques, are shown to outperform corresponding ordinations of unadjusted dissimilarities, with the difference increasing with increasing beta diversity.     

Indigenous and foreign Y-chromosomes characterize the Lingayat and Vokkaliga populations of Southwest India

Previous studies have shown that India's vast coastal rim played an important role in the dispersal of modern humans out of Africa but the Karnataka state, which is located on the southwest coast of India, remains poorly characterized genetically. In the present study, two Dravidian populations, namely Lingayat (N = 101) and Vokkaliga (N = 102), who represent the two major communities of the Karnataka state, were examined using high-resolution analyses of Y-chromosome single nucleotide polymorphisms (Y-SNPs) and seventeen short tandem repeat (Y-STR) loci. Our results revealed that the majority of the Lingayat and Vokkaliga paternal gene pools are composed of four Y-chromosomal haplogroups (H, L, F* and R2) that are frequent in the Indian subcontinent. The high level of L1-M76 chromosomes in the Vokkaligas suggests an agricultural expansion in the region, while the predominance of R1a1a1b2-Z93 and J2a-M410 lineages in the Lingayat indicates gene flow from neighboring south Indian populations and West Asia, respectively. Lingayat (0.9981) also exhibits a relatively high haplotype diversity compared to Vokkaliga (0.9901), supporting the historical record that the Lingayat originated from multiple source populations. In addition, we detected ancient lineages such as F*-M213, H*-M69 and C*-M216 that may be indicative of genetic signatures of the earliest settlers who reached India after their migration out of Africa.