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Although research effort is being expended into determining the importance of epistasis and epistatic variance for complex traits, there is considerable controversy about their importance. Here we undertake an analysis for quantitative traits utilizing a range of multilocus quantitative genetic models and gene frequency distributions, focusing on the potential magnitude of the epistatic variance. All the epistatic terms involving a particular locus appear in its average effect, with the number of two-locus interaction terms increasing in proportion to the square of the number of loci and that of third order as the cube and so on. Hence multilocus epistasis makes substantial contributions to the additive variance and does not, per se, lead to large increases in the nonadditive part of the genotypic variance. Even though this proportion can be high where epistasis is antagonistic to direct effects, it reduces with multiple loci. As the magnitude of the epistatic variance depends critically on the heterozygosity, for models where frequencies are widely dispersed, such as for selectively neutral mutations, contributions of epistatic variance are always small. Epistasis may be important in understanding the genetic architecture, for example, of function or human disease, but that does not imply that loci exhibiting it will contribute much genetic variance. Overall we conclude that theoretical predictions and experimental observations of low amounts of epistatic variance in outbred populations are concordant. It is not a likely source of missing heritability, for example, or major influence on predictions of rates of evolution. EPISTATIC variance in quantitative traits arises from the interaction effects or epistasis between segregating genes at two or more loci that affect these complex traits. Such gene interaction is a common phenomenon because many factors have, for example, a regulatory role in a hierarchical system (Phillips 2008). The statistical theory of quantitative genetics following Fisher (1918) is based on a partition between average effects across loci, which contribute to the additive genetic variance, and to interactions within loci and between loci, which contribute to the dominance and epistatic variance, respectively (Cockerham 1954;Kempthorne 1954). The magnitudes of these components of the genotypic variance each depend on the frequencies, the effects, and the interactions among the contributing genes (see also Falconer and Mackay 1996;Lynch and Walsh 1998). The actual causal genetic factors are usually not known, but many quantitative genetic analyses, including selection on metric traits, have been applied successfully without such knowledge.Among quantitative geneticists, interest in epistasis continues, both to understand the genetic architecture and as a potential way to improve the genomic predictions of disease and quantitative traits, utilizing some of the unexplained parts of the genetic variation (e.g., Carlborg and Haley 2004;Nelson et al. 2013;Mackay 2014). Despite the obviou...

We herein report new evidence that the QTL effect on chromosome 20 in Finnish Ayrshire can be explained by variation in two distinct genes, growth hormone receptor (GHR) and prolactin receptor (PRLR). In a previous study in Holstein-Friesian dairy cattle an F279Y polymorphism in the transmembrane domain of GHR was found to be associated with an effect on milk yield and composition. The result of our multimarker regression analysis suggests that in Finnish Ayrshire two QTL segregate on the chromosomal region including GHR and PRLR. By sequencing the coding sequences of GHR and PRLR and the sequence of three GHR promoters from the pooled samples of individuals of known QTL genotype, we identified two substitutions that were associated with milk production traits: the previously reported F-to-Y substitution in the transmembrane domain of GHR and an S-to-N substitution in the signal peptide of PRLR. The results provide strong evidence that the effect of PRLR S18N polymorphism is distinct from the GHR F279Y effect. In particular, the GHR F279Y has the highest influence on protein percentage and fat percentage while PRLR S18N markedly influences protein and fat yield. Furthermore, an interaction between the two loci is suggested.

A whole genome scan of Finnish Ayrshire was conducted to map quantitative trait loci (QTL) affecting milk production. The analysis included 12 half-sib families containing a total of 494 bulls in a granddaughter design. The families were genotyped with 150 markers to construct a 2764 cM (Haldane) male linkage map. In this study interval mapping with multiple-marker regression approach was extended to analyse multiple chromosomes simultaneously. The method uses identified QTL on other chromosomes as cofactors to increase mapping power. The existence of multiple QTL on the same linkage group was also analyzed by fitting a two-QTL model to the analysis. Empirical values for chromosome-wise significance thresholds were determined using a permutation test. Two genome-wise significant QTL were identified when chromosomes were analyzed individually, one affecting fat percentage on chromosome (BTA) 14 and another affecting fat yield on BTA12. The cofactor analysis revealed in total 31 genome-wise significant QTL. The result of two-QTL analysis suggests the existence of two QTL for fat percentage on BTA3. In general, most of the identified QTL confirm results from previous studies of Holstein-Friesian cattle. A new QTL for all yield components was identified on BTA12 in Finnish Ayrshire. (Key words: cofactor, dairy cattle, interval mapping, quantitative trait) Abbreviation key: BTA = Bos taurus chromosome, DYD = daughter yield deviations, FY = fat yield, F% = fat percentage, MY = milk yield, PIC = polymorphic information content, PY = protein yield, P% = protein percentage.

A mapping population segregating for egg quality traits was created by a line cross between two egg layer lines and screened by a genome scan. The F2 generation consisted of 307 hens, which were scored for egg quality and production traits. The mapping population was genotyped for 99 microsatellite loci, spanning nine macrochromosomes and five small linkage groups. The linkage maps were used in mapping QTL affecting 14 traits, by using multiple markers and a least-squares approach. We detected 14 genomewide significant and six suggestive QTL that were located on chromosomes 2, 3, 4, 5, and, 8 and sex chromosome Z. A significant QTL affecting egg white thinning was found on chromosome 2. For eggshell strength, a significant QTL was found on chromosome Z. For production traits, the most interesting area was on chromosome 4, where highly significant QTL effects were detected for BW, egg weight, and feed intake in the same area. The most significant QTL explains 25.8% of the phenotypic variance in F2 of body weight. An area affecting the age at first egg, egg weight, and the number of eggs was located on chromosome Z.