By their paternal transmission, Y-chromosomal haplotypes are sensitive markers of population history and male-mediated introgression. Previous studies identified biallelic single-nucleotide variants in the SRY, ZFY and DDX3Y genes, which in domestic goats identified four major Y-chromosomal haplotypes, Y1A, Y1B, Y2A and Y2B, with a marked geographical partitioning. Here, we extracted goat Y-chromosomal variants from whole-genome sequences of 386 domestic goats (75 breeds) and seven wild goat species, which were generated by the VarGoats goat genome project. Phylogenetic analyses indicated domestic haplogroups corresponding to Y1B, Y2A and Y2B, respectively, whereas Y1A is split into Y1AA and Y1AB. All five haplogroups were detected in 26 ancient DNA samples from southeast Europe or Asia. Haplotypes from presentday bezoars are not shared with domestic goats and are attached to deep nodes of the trees and networks. Haplogroup distributions for 186 domestic breeds indicate ancient paternal population bottlenecks and expansions during migrations into northern Europe, eastern and southern Asia, and Africa south of the Sahara. In addition, sharing of haplogroups indicates male-mediated introgressions, most notably an early gene

By its paternal transmission, Y-chromosomal haplotypes are sensitive markers of population history and male-mediated introgression. We used whole-genome sequences (WGSs) of 386 domestic goats from 75 modern breeds and 7 wild goat species generated by the VarGoats goat genome project. Phylogenetic analyses indicated five domestic haplogroups Y1AA, Y1AB, Y1B, Y2A and Y2B. Haplogroup distributions for 180 domestic breeds indicate ancient paternal population bottlenecks during the migration into northern Europe, southern Asia and Africa. Sharing of haplogroups reveals male-mediated introgressions: from Asia into Madagascar and, more recently, into the South-African Boer goat; then from this breed into other southeastern African goats; and from Europe into native Korean and Ugandan goats. This study illustrates the power of the Y-chromosomal variation for the reconstructing the history of domestic species with a wide geographic range.

Genome-wide association studies (GWAS) help identify polymorphic sites or genes linked to phenotypic variance, but a few identified genes and/or single nucleotide polymorphisms (SNPs) are unlikely to explain a large part of the phenotypic variability of complex traits. In this study, the focus was moved from single loci to functional units, expressed by the metabolic pathways as defined in the Kyoto Encyclopaedia of Genes and Genomes (KEGG) database. Consequently, the aim of this study was to estimate KEGG effects on stature in three Nordic dairy cattle breeds using SNP effects from GWAS as the dependent variable. The SNPs were annotated to genes, then the genes to KEGG pathways. The effects of KEGG pathways were estimated separately for each breed using a mixed linear model incorporating the similarity between pathways expressed by common genes. The KEGG pathway D-amino acid metabolism (map00473) was estimated to be significant for stature in two of the analysed breeds and revealed a borderline significance in the third breed. Thus, we demonstrate that the approach to statistical modelling of higher order functional effects on complex traits is useful, and provides evidence of the importance of D-amino acids for growth in cattle.

Quantile regression has emerged as a useful and effective tool in modeling survival data, especially for cases where noises demonstrate heterogeneity. Despite recent advancements, non‐smooth components involved in censored quantile regression estimators may often yield numerically unstable results, which, in turn, lead to potentially self‐contradicting conclusions. We propose an estimating equation‐based approach to obtain consistent estimators of the regression coefficients of interest via the induced smoothing technique to circumvent the difficulty. Our proposed estimator can be shown to be asymptotically equivalent to its original unsmoothed version, whose consistency and asymptotic normality can be readily established. Extensions to handle functional covariate data and recurrent event data are also discussed. To alleviate the heavy computational burden of bootstrap‐based variance estimation, we also propose an efficient resampling procedure that reduces the computational time considerably. Our numerical studies demonstrate that our proposed estimator provides substantially smoother model parameter estimates across different quantile levels and can achieve better statistical efficiency compared to a plain estimator under various finite‐sample settings. The proposed method is also illustrated via four survival datasets, including the HMO (health maintenance organizations) HIV (human immunodeficiency virus) data, the primary biliary cirrhosis (PBC) data, and so forth.