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The problem of clustering probability density functions is emerging in different scientific domains. The methods proposed for clustering probability density functions are mainly focused on univariate settings and are based on heuristic clustering solutions. New aspects of the problem associated with the multivariate setting and a model-based perspective are investigated. The novel approach relies on a hierarchical mixture modeling of the data. The method is introduced in the univariate context and then extended to multivariate densities by means of a factorial model performing dimension reduction. Model fitting is carried out using an EM-algorithm. The proposed method is illustrated through simulated experiments and applied to two real data sets in order to compare its performance with alternative clustering strategies.

Recently, different mixture models have been proposed for multilevel data, generally requiring the local independence assumption. In this work, this assumption is relaxed by allowing each mixture component at the lower level of the hierarchical structure to be modeled according to a multivariate Gaussian distribution with a non-diagonal covariance matrix. For high-dimensional problems, this solution can lead to highly parameterized models. In this proposal, the trade-off between model parsimony and flexibility is governed by assuming a latent factor generative model.

In the general classification context the recourse to the so-called Bayes decision rule requires to estimate the class conditional probability density functions. In this paper we propose a mixture model for the observed variables which is derived by assuming that the data have been generated by an independent factor model. Independent factor analysis is in fact a generative latent variable model whose structure closely resembles the one of ordinary factor model but it assumes that the latent variables are mutually independent and not necessarily Gaussian. The method therefore provides a dimension reduction together with a semiparametric estimate of the class conditional probability density functions. This density approximation is plugged into the classic Bayes rule and its performance is evaluated both on real and simulated data.

Summary The genetic identification of the population of origin of individuals, including animals, has several practical applications in forensics, evolution, conservation genetics, breeding and authentication of animal products. Commercial high-density single nucleotide polymorphism (SNP) genotyping tools that have been recently developed in many species provide information from a large number of polymorphic sites that can be used to identify population-/breed-informative markers. In this study, starting from Illumina BovineSNP50 v1 BeadChip array genotyping data available from 3711 cattle of four breeds (2091 Italian Holstein, 738 Italian Brown, 475 Italian Simmental and 407 Marchigiana), principal component analysis (PCA) and random forests (RFs) were combined to identify informative SNP panels useful for cattle breed identification. From a PCA preselected list of 580 SNPs, RFs were computed using ranking methods (Mean Decrease in the Gini Index and Mean Accuracy Decrease) to identify the most informative 48 and 96 SNPs for breed assignment. The out-of-bag (OOB) error rate for both ranking methods and SNP densities ranged from 0.0 to 0.1% in the reference population. Application of this approach in a test population (10% of individuals pre-extracted from the whole data set) achieved 100% of correct assignment with both classifiers. Linkage disequilibrium between selected SNPs was relevant (r2 > 0.6) only in few pairs of markers indicating that most of the selected SNPs captured different fractions of variance. Several informative SNPs were in genes/QTL regions that affect or are associated with phenotypes or production traits that might differentiate the investigated breeds. The combination of PCA and RF to perform SNP selection and breed assignment can be easily implemented and is able to identify subsets of informative SNPs useful for population assignment starting from a large number of markers derived by high-throughput genotyping platforms.

Background Carcass fatness is an important trait in most pig breeding programs. Following market requests, breeding plans for fresh pork consumption are usually designed to reduce carcass fat content and increase lean meat deposition. However, the Italian pig industry is mainly devoted to the production of Protected Designation of Origin dry cured hams: pigs are slaughtered at around 160 kg of live weight and the breeding goal aims at maintaining fat coverage, measured as backfat thickness to avoid excessive desiccation of the hams. This objective has shaped the genetic pool of Italian heavy pig breeds for a few decades. In this study we applied a selective genotyping approach within a population of ~ 12,000 performance tested Italian Large White pigs. Within this population, we selectively genotyped 304 pigs with extreme and divergent backfat thickness estimated breeding value by the Illumina PorcineSNP60 BeadChip and performed a genome wide association study to identify loci associated to this trait. Results We identified 4 single nucleotide polymorphisms with P≤5.0E-07 and additional 119 ones with 5.0E-07 Conclusions Further investigations are needed to evaluate the effects of the identified single nucleotide polymorphisms associated with backfat thickness on other traits as a pre-requisite for practical applications in breeding programs. Reported results could improve our understanding of the biology of fat metabolism and deposition that could also be relevant for other mammalian species including humans, confirming the role of neuronal genes on obesity.

Fatness in pigs is a complex trait for which a large number of genes are expected to be involved. Genetics of human obesity could take advantages from genetic information coming from the pig and vice versa. To these aims, a comprehensive candidate gene approach could be helpful. We catalogued all genes affecting fatness on both species, and identified in silico and by resequencing porcine SNPs on a large number of candidate genes. In addition, we applied a selective genotyping approach to identify markers associated with fat deposition in pigs. This approach was tested genotyping the IGF2 intron3-g.3072G>A mutation and novel markers in the PCSK1 and TBC1D1 genes. Polymorphisms in these genes resulted associated with back fat thickness in Italian Large White pigs.

In pigs, many production traits are known to vary among breeds or lines. These traits can be considered end phenotypes or external traits as they are the final results of complex biological interactions and processes whose fine biological mechanisms are still largely unknown. This study was designed to compare plasma and serum metabolomic profiles between animals of two heavy pig breeds (12 Italian Large White and 12 Italian Duroc), testing indirectly the hypothesis that different genetic backgrounds might be the determining factors of differences observed on the level of metabolites in the analyzed biofluids between breeds. We used a targeted metabolomic approach based on mass spectrometric detection of about 180 metabolites and applied a statistical validation pipeline to identify differences in the metabolomic profiles of the two heavy pig breeds. Blood samples were collected after jugulation at the slaughterhouse and prepared for metabolomics analysis that was carried out using the Biocrates AbsoluteIDQ p180 Kit, covering five different biochemical classes: glycerophospholipids, amino acids, biogenic amines, hexoses and acylcarnitines. A statistical pipeline that included the selection of the most relevant metabolites differentiating the two breeds by sparse Partial Least Squares Discriminant Analysis (sPLS-DA) was coupled with a stability test and significance test determined with leave one out and permutation procedures. sPLS-DA plots clearly separated the pigs of the two investigated breeds. A few metabolites (a total of five metabolites considering the two biofluids) involved in key metabolic pathways largely contributed to these differences between breeds. In particular, a higher level of the sphingomyelins SM (OH) C14:1 (both in plasma and serum), SM (OH) C16:1 (in serum) and SM C16:0 (in serum) were observed in Italian Duroc than in Italian Large White pigs and the inverse was for the biogenic amine kynurenine (in plasma). The level of another biogenic amine (acetylornithine) was higher in Italian Large White than in Italian Duroc pigs in both analysed biofluids. These results provided biomarkers that could be important to understand the biological differences between these two heavy pig breeds. In particular, according to the functional role played by sphingomyelins in obesity-induced inflammatory responses, it could be possible to speculate that a higher level of sphingomyelins in Italian Duroc might be related to the higher interrmuscular fat deposition of this breed compared with the Italian Large White. Additional studies will be needed to evaluate the relevance of these biomarkers for practical applications in pig breeding and nutrition.