Hastings' additivity counterexample via Dvoretzky's theorem

The goal of this note is to show that Hastings' counterexample to the additivity of minimal output von Neumann entropy can be readily deduced from a sharp version of Dvoretzky's theorem on almost spherical sections of convex bodies.Comment: 12 pages; v.2: added references, Appendix A expanded to make the paper essentially self-containe

Quantitative genetics theory for genomic selection and efficiency of genotypic value prediction in open-pollinated populations

ABSTRACT: Quantitative genetics theory for genomic selection has mainly focused on additive effects. This study presents quantitative genetics theory applied to genomic selection aiming to prove that prediction of genotypic value based on thousands of single nucleotide polymorphisms (SNPs) depends on linkage disequilibrium (LD) between markers and QTLs, assuming dominance and epistasis. Based on simulated data, we provided information on dominance and genotypic value prediction accuracy, assuming mass selection in an open-pollinated population, all quantitative trait loci (QTLs) of lower effect, and reduced sample size. We show that the predictor of dominance value is proportional to the square of the LD value and to the dominance deviation for each QTL that is in LD with each marker. The weighted (by the SNP frequencies) dominance value predictor has greater accuracy than the unweighted predictor. The linear × linear, linear × quadratic, quadratic × linear, and quadratic × quadratic SNP effects are proportional to the corresponding linear combinations of epistatic effects for QTLs and the LD values. LD between two markers with a common QTL causes a bias in the prediction of epistatic values. Compared to phenotypic selection, the efficiency of genomic selection for genotypic value prediction increases as trait heritability decreases. The degree of dominance did not affect the genotypic value prediction accuracy and the approach to maximum accuracy is asymptotic with increases in SNP density. The decrease in the sample size from 500 to 200 did not markedly reduce the genotypic value prediction accuracy

Genome-wide association and Mendelian randomisation analysis provide insights into the pathogenesis of heart failure

Heart failure (HF) is a leading cause of morbidity and mortality worldwide. A small proportion of HF cases are attributable to monogenic cardiomyopathies and existing genome-wide association studies (GWAS) have yielded only limited insights, leaving the observed heritability of HF largely unexplained. We report results from a GWAS meta-analysis of HF comprising 47,309 cases and 930,014 controls. Twelve independent variants at 11 genomic loci are associated with HF, all of which demonstrate one or more associations with coronary artery disease (CAD), atrial fibrillation, or reduced left ventricular function, suggesting shared genetic aetiology. Functional analysis of non-CAD-associated loci implicate genes involved in cardiac development (MYOZ1, SYNPO2L), protein homoeostasis (BAG3), and cellular senescence (CDKN1A). Mendelian randomisation analysis supports causal roles for several HF risk factors, and demonstrates CAD-independent effects for atrial fibrillation, body mass index, and hypertension. These findings extend our knowledge of the pathways underlying HF and may inform new therapeutic strategies

Heterogeneity of linalool chemotypes of Lippia alba (Mill.) N.E.Br., based on clonal half-sib progenies

Lippia alba (Mill.) N.E.Br. is an aromatic and medicinal shrub native to the American continent. Despite its potential as a source of essential oil for the pharmaceutical and cosmetics industries, few selection and genetic improvement studies have been carried out. The aim of this study was to provide genetic information on this species for breeding programs, showing its selection potential, by investigating clonal half-sib progenies. The following characteristics were evaluated per plant: leaf dry mass (LDM), total dry mass (TDM), leaf yield (LY), essential oil yield (EOY) and oil production (OP). Estimates were made for the several genetic parameters including absolute genetic gain at 30% selection intensity, correlations and relative contribution of additive and environmental effects to phenotypic correlation. Two experimental trials on 30 progenies were conducted: one in Campinas, state of São Paulo (SP), Brazil, with two harvests of the aerial part, and one in Monte Alegre do Sul, SP, Brazil, with only one harvest. The trials were conducted in a randomized block design consisting of subplots with three replications, each plot (progeny) consisting of 8 to 15 clonally-replicated plants with subplot harvesting. Variations were detected between progenies and harvests, as well as progeny/harvest interactions in the split plot experiment. High heritability and genetic gains were obtained at both sites for LDM, TDM and OP. The lowest variations among progenies were obtained for LY and EOY, highlighting selection problems. Negative additive genetic correlations were obtained for EOY × LDM, EOY × TDM, LY × TDM and LY × LDM. Selection for LDM resulted in increased oil production per plant (OP), even where there was a negative correlation between LDM × EOY