The most suitable method for estimation of size diversity is investigated. Size diversity is computed on the basis of the Shannon diversity expression adapted for continuous variables, such as size. It takes the form of an integral involving the probability density function (pdf) of the size of the individuals. Different approaches for the estimation of pdf are compared: parametric methods, assuming that data come from a determinate family of pdfs, and nonparametric methods, where pdf is estimated using some kind of local evaluation. Exponential, generalized Pareto, normal, and log-normal distributions have been used to generate simulated samples using estimated parameters from real samples. Nonparametric methods include discrete computation of data histograms based on size intervals and continuous kernel estimation of pdf. Kernel approach gives accurate estimation of size diversity, whilst parametric methods are only useful when the reference distribution have similar shape to the real one. Special attention is given for data standardization. The division of data by the sample geometric mean is proposed as the most suitable standardization method, which shows additional advantages: the same size diversity value is obtained when using original size or log-transformed data, and size measurements with different dimensionality (longitudes, areas, volumes or biomasses) may be immediately compared with the simple addition of ln k where k is the dimensionality (1, 2, or 3, respectively). Thus, the kernel estimation, after data standardization by division of sample geometric mean, arises as the most reliable and generalizable method of size diversity evaluation.

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BackgroundFecal microbiota transplantation (FMT) has been recently approved by FDA for the treatment of refractory recurrent clostridial colitis (rCDI). Success of FTM in treatment of rCDI led to a number of studies investigating the effectiveness of its application in the other gastrointestinal diseases. However, in the majority of studies the effects of FMT were evaluated on the patients with initially altered microbiota. The aim of our study was to estimate effects of FMT on the gut microbiota composition in healthy volunteers and to monitor its long-term outcomes.ResultsWe have performed a combined analysis of three healthy volunteers before and after capsule FMT by evaluating their general condition, adverse clinical effects, changes of basic laboratory parameters, and several immune markers. Intestinal microbiota samples were evaluated by 16S rRNA gene and shotgun sequencing. The data analysis demonstrated profound shift towards the donor microbiota taxonomic composition in all volunteers. Following FMT, all the volunteers exhibited gut colonization with donor gut bacteria and persistence of this effect for almost ∼1 year of observation. Transient changes of immune parameters were consistent with suppression of T-cell cytotoxicity. FMT was well tolerated with mild gastrointestinal adverse events, however, one volunteer developed a systemic inflammatory response syndrome.ConclusionsThe FMT leads to significant long-term changes of the gut microbiota in healthy volunteers with the shift towards donor microbiota composition and represents a relatively safe procedure to the recipients without long-term adverse events.

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In the life sciences, many measurement methods yield only the relative abundances of different components in a sample. With such relative-or compositional-data, differential expression needs careful interpretation, and correlation-a statistical workhorse for analyzing pairwise relationships-is an inappropriate measure of association. Using yeast gene expression data we show how correlation can be misleading and present proportionality as a valid alternative for relative data. We show how the strength of proportionality between two variables can be meaningfully and interpretably described by a new statistic ϕ which can be used instead of correlation as the basis of familiar analyses and visualisation methods, including co-expression networks and clustered heatmaps. While the main aim of this study is to present proportionality as a means to analyse relative data, it also raises intriguing questions about the molecular mechanisms underlying the proportional regulation of a range of yeast genes. Author SummaryRelative abundance data is common in the life sciences, but appreciation that it needs special analysis and interpretation is scarce. Correlation is popular as a statistical measure of pairwise association but should not be used on data that carry only relative information. Using timecourse yeast gene expression data, we show how correlation of relative abundances can lead to conclusions opposite to those drawn from absolute abundances, and that its value changes when different components are included in the analysis. Once all absolute information has been removed, only a subset of those associations will reliably endure in the remaining relative data, specifically, associations where pairs of values behave proportionally across observations. We propose a new statistic ϕ to describe the strength of proportionality between two variables and demonstrate how it can be straightforwardly used instead of correlation as the basis of familiar analyses and visualization methods. PLOS Computational Biology |