Fast model-based ordination with copulas

Visualising data is a vital part of analysis, allowing researchers to find patterns, and assess and communicate the results of statistical modeling. In ecology, visualisation is often challenging when there are many variables (often for different species or other taxonomic groups) and they are not normally distributed (often counts or presence-absence data). Ordination is a common and powerful way to overcome this hurdle by reducing data from many response variables to just two or three, to be easily plotted. Ordination is traditionally done using dissimilarity-based methods, most commonly non-metric multidimensional scaling (nMDS). In the last decade however, model-based methods for unconstrained ordination have gained popularity. These are primarily based on latent variable models, with latent variables estimating the underlying, unobserved ecological gradients. Despite some major benefits, a major drawback of model-based ordination methods is their speed, as they typically taking much longer to return a result than dissimilarity-based methods, especially for large sample sizes. We introduce copula ordination, a new, scalable model-based approach to unconstrained ordination. This method has all the desirable properties of model-based ordination methods, with the added advantage that it is computationally far more efficient. In particular, simulations show copula ordination is an order of magnitude faster than current model-based methods, and can even be faster than nMDS for large sample sizes, while being able to produce similar ordination plots and trends as these methods.

Ecological ordination of the grass vegetation in Altai Krai

The article shows a variety of ordination methods used to analyze different types of vegetation and presents the results of the ordinal analysis of meadow (i.a. idle lands) and steppe phytocenoses that are widespread in Altai Krai. Ecological ordination is performed by means of the Detrended Correspondence Analysis (DCA) method. The ordination of grass communities is based on 616 complete geobotanical descriptions (330 - meadow, 286 - steppe). The article determines the position of community types on the gradients of humidification and soil richness-salinity for steppes and suggests the directions of the progressive successions of idle land communities in Altai Krai.

Evaluating the Predictive Power of Ordination Methods in Ecological Context

When striving for the ordination methods best predicting independently measured site factors, the following questions arise: does the optimal choice depend on the kind of biological community analysed? Are there different ordination methods needed to address different site factors? Simultaneously, I explore alternative similarity approaches of entire ordinations, as well as the role of the transformations applied to the scale used in measuring species performance. The combination of methods and data transformations results in 96 alternative solutions for any one data set. These are compared by a graphical display, that is, an ordination of ordinations. The goodness-of-fit of independently measured site factors is assessed by two alternative methods. The resulting 96 performance values serve as independent variables in trend surfaces overlaid to the ordination of ordinations. The results from two real-world data sets indicate that some ordination methods greatly vary with data transformation. Scores close to a binary scale perform best in almost all ordination methods. Methods that intrinsically constrain the range of species scores, such as principal components analysis based on correlation, correspondence analysis (including its detrended version), nonmetric multidimensional scaling, as well as principal coordinates analysis based on the Bray-Curtis distance, always figure among the most successful methods, irrespective of data used.

Insulation co-ordination and the enlargement law for the GM counter tube

In this paper we analyze application of contemporary methods of insulation co-ordination and the enlargement law in designing a GM counting tube. It has been shown that by applying insulation co-ordination methods the counting tube can be optimally dimensioned. The application of the enlargement law was demonstrated in generalizing the results of test obtained by the GM tube to those obtained by the counting tube with m-times greater dimensions. The investigations were conducted both theoretically and by experiment. Using theoretical analysis, we derived the expressions that may be applied if a performance function of a random variable breakdown voltage is known. The experiments were conducted on a GM counter model under well controlled laboratory conditions.