With large-scale database systems, statistical analysis of data, formed by probability distributions, become an important task in explorative data analysis. Nevertheless, due to specific properties of density functions, their proper statistical treatment still represents a challenging task in functional data analysis. Namely, the usual L 2 metric does not fully accounts for the relative character of information, carried by density functions; instead, their geometrical features are followed by Bayes spaces of measures. The easiest possibility of expressing density functions in L 2 space is to use centred logratio transformation, nevertheless, it results in functional data with a constant integral constraint that needs to be taken into account for further analysis. While theoretical background for reasonable analysis of density functions is already provided comprehensively by Bayes spaces themselves, preprocessing issues still need to be developed. The aim of this paper is to introduce optimal smoothing splines for centred logratio transformed density functions that take all their specific features into account and provide a concise methodology for reasonable preprocessing of raw (discretized) distributional observations. Theoretical developments are illustrated with a real-world data set from official statistics.
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.
A novel approach, based on Species sensitivity distribution (SSD), is proposed for the development of an index for classifying ecotoxicological pesticide risk in surface waters. In this approach, the concept of TER (Toxicity Exposure Ratio), commonly used in traditional risk indices, is substituted by the concept of PAF (Potentially Affected Fraction), which takes into account several species within the biological community of interest, rather than just a small number of indicator species assumed as being representative of the ecosystem. The procedure represents a probabilistic tool to quantitatively assess the ecotoxicological risk on biodiversity considering the distribution of toxicological sensitivity. It can be applied to assess chemical risk on generic aquatic and terrestrial communities as well as on site-specific natural communities. Examples of its application are shown for some pesticides in freshwater ecosystems. In order to overcome the problem of insufficient reliable ecotoxicological data, a methodology and related algorithms are proposed for predicting SSD curves for chemicals that do not have sufficient available data. The methodology is applicable within congeneric classes of chemicals and has been tested and statistically validated on a group of organophosphorus insecticides. Values and limitations of the approach are discussed.
BackgroundDue 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.MethodsFor 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.ResultsThe 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.DiscussionThe 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.
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