A new distribution on the simplex containing the Dirichlet family

The Dirichlet family owes its privileged status within simplex distributions to easynessof interpretation and good mathematical properties. In particular, we recall fundamentalproperties for the analysis of compositional data such as closure under amalgamationand subcomposition. From a probabilistic point of view, it is characterised (uniquely)by a variety of independence relationships which makes it indisputably the referencemodel for expressing the non trivial idea of substantial independence for compositions.Indeed, its well known inadequacy as a general model for compositional data stemsfrom such an independence structure together with the poorness of its parametrisation.In this paper a new class of distributions (called Flexible Dirichlet) capable of handlingvarious dependence structures and containing the Dirichlet as a special case is presented.The new model exhibits a considerably richer parametrisation which, for example,allows to model the means and (part of) the variance-covariance matrix separately.Moreover, such a model preserves some good mathematical properties of the Dirichlet,i.e. closure under amalgamation and subcomposition with new parameters simplyrelated to the parent composition parameters. Furthermore, the joint and conditionaldistributions of subcompositions and relative totals can be expressed as simple mixturesof two Flexible Dirichlet distributions.The basis generating the Flexible Dirichlet, though keeping compositional invariance,shows a dependence structure which allows various forms of partitional dependenceto be contemplated by the model (e.g. non-neutrality, subcompositional dependenceand subcompositional non-invariance), independence cases being identified by suitableparameter configurations. In particular, within this model substantial independenceamong subsets of components of the composition naturally occurs when the subsetshave a Dirichlet distributionGeologische Vereinigung; Institut d’Estadística de Catalunya; International Association for Mathematical Geology; Càtedra Lluís Santaló d’Aplicacions de la Matemàtica; Generalitat de Catalunya, Departament d’Innovació, Universitats i Recerca; Ministerio de Educación y Ciencia; Ingenio 2010

Genetic differentiation, local adaptation and phenotypic plasticity in fragmented populations of a rare forest herb

Background Due to habitat loss and fragmentation, numerous forest species are subject to severe population decline. Investigating variation in genetic diversity, phenotypic plasticity and local adaptation should be a prerequisite for implementing conservation actions. This study aimed to explore these aspects in ten fragmented populations of Physospermum cornubiense in view of translocation measures across its Italian range. Methods For each population we collected environmental data on landscape (habitat size, quality and fragmentation) and local conditions (slope, presence of alien species, incidence of the herbivorous insect Metcalfa pruinosa and soil parameters). We measured vegetative and reproductive traits in the field and analysed the genetic population structure using ISSR markers (STRUCTURE and AMOVA). We then estimated the neutral (FST) and quantitative (PST) genetic differentiation of populations. Results The populations exhibited moderate phenotypic variation. Population size (range: 16–655 individuals), number of flowering adults (range: 3–420 individuals) and inflorescence size (range: 5.0–8.4 cm) were positively related to Mg soil content. Populations’ gene diversity was moderate (Nei-H = 0.071–0.1316); STRUCTURE analysis identified five different clusters and three main geographic groups: upper, lower, and Apennine/Western Po plain. Fragmentation did not have an influence on the local adaptation of populations, which for all measured traits showed PST < FST, indicating convergent selection. Discussion The variation of phenotypic traits across sites was attributed to plastic response rather than local adaptation. Plant translocation from suitable source populations to endangered ones should particularly take into account provenance according to identified genetic clusters and specific soil factors

A high protein diet is more effective in improving insulin resistance and glycemic variability compared to a mediterranean diet—a cross-over controlled inpatient dietary study

The optimal dietary pattern to improve metabolic function remains elusive. In a 21-day randomized controlled inpatient crossover feeding trial of 20 insulin-resistant obese women, we assessed the extent to which two isocaloric dietary interventions—Mediterranean (M) and high protein (HP)—improved metabolic parameters. Obese women were assigned to one of the following dietary sequences: M–HP or HP–M. Cardiometabolic parameters, body weight, glucose monitoring and gut microbiome composition were assessed. Sixteen women completed the study. Compared to the M diet, the HP diet was more effective in (i) reducing insulin resistance (insulin: Beta (95% CI) = −6.98 (−12.30, −1.65) µIU/mL, p = 0.01; HOMA-IR: −1.78 (95% CI: −3.03, −0.52), p = 9 × 10(−3)); and (ii) improving glycemic variability (−3.13 (−4.60, −1.67) mg/dL, p = 4 × 10(−4)), a risk factor for T2D development. We then identified a panel of 10 microbial genera predictive of the difference in glycemic variability between the two diets. These include the genera Coprococcus and Lachnoclostridium, previously associated with glucose homeostasis and insulin resistance. Our results suggest that morbidly obese women with insulin resistance can achieve better control of insulin resistance and glycemic variability on a high HP diet compared to an M diet