In this paper an exact rejection algorithm for simulating paths of the coupled Wright–Fisher diffusion is introduced. The coupled Wright–Fisher diffusion is a family of multivariate Wright–Fisher diffusions that have drifts depending on each other through a coupling term and that find applications in the study of networks of interacting genes. The proposed rejection algorithm uses independent neutral Wright–Fisher diffusions as candidate proposals, which are only needed at a finite number of points. Once a candidate is accepted, the remainder of the path can be recovered by sampling from neutral multivariate Wright–Fisher bridges, for which an exact sampling strategy is also provided. Finally, the algorithm’s complexity is derived and its performance demonstrated in a simulation study.

Epistasis is a growing area of research in genome-wide studies, but the differences between alternative definitions of epistasis remain a source of confusion for many researchers. One problem is that models for epistasis are presented in a number of formats, some of which have difficult-to-interpret parameters. In addition, the relation between the different models is rarely explained. Existing software for testing epistatic interactions between single-nucleotide polymorphisms (SNPs) does not provide the flexibility to compare the available model parameterizations. For that reason we have developed an R package for investigating epistatic and penetrance models, Epi2Loc, to aid users who wish to easily compare, interpret, and utilize models for two-locus epistatic interactions. Epi2Loc facilitates research on SNP–SNP interactions by allowing the R user to easily convert between common parametric forms for two-locus interactions, generate data for simulation studies, and perform power analyses for the selected model with a continuous or dichotomous phenotype. The usefulness of the package for model interpretation and power analysis is illustrated using data on rheumatoid arthritis.

Epistasis is a growing area of research in genome-wide studies, but the differences between alternative definitions of epistasis remain a source of confusion for many researchers. One problem is that models for epistasis are presented in a number of formats, some of which have difficult-to-interpret parameters. In addition, the relation between the different models is rarely explained. Existing software for testing epistatic interactions between single-nucleotide polymorphisms (SNPs) does not provide the flexibility to compare the available model parameterizations. For that reason we have developed an R package for investigating epistatic and penetrance models, EpiPen, to aid users who wish to easily compare, interpret, and utilize models for two-locus epistatic interactions. EpiPen facilitates research on SNP-SNP interactions by allowing the R user to easily convert between common parametric forms for two-locus interactions, generate data for simulation studies, and perform power analyses for the selected model with a continuous or dichotomous phenotype. The usefulness of the package for model interpretation and power analysis is illustrated using data on rheumatoid arthritis.

The Val158Met polymorphism of the catechol-O-methyltransferase (COMT) gene may be related to individual differences in cognition, likely via modulation of prefrontal dopamine catabolism. However, the available studies have yielded mixed results, possibly in part because they do not consistently account for other genes that affect cognition. We hypothesized that COMT Met allele homozygosity, which is associated with higher levels of prefrontal dopamine, would predict better executive function as measured using standard neuropsychological testing, and that other candidate genes might interact with COMT to modulate this effect. Participants were 95 healthy, right-handed adults who underwent genotyping and cognitive testing. COMT genotype predicted executive ability as measured by the Trail-Making Test, even after covarying for demographics and Apolipoprotein E (APOE), brain-derived neurotrophic factor (BDNF), and ankyrin repeat and kinase domain containing 1 (ANKK1) genotype. There was a COMT-ANKK1 interaction in which individuals having both the COMT Val allele and the ANKK1 T allele showed the poorest performance. This study suggests the heterogeneity in COMT effects reported in the literature may be due in part to gene–gene interactions that influence central dopaminergic systems. (JINS, 2011, 17, 1–7)

Decline in fertility of high-producing dairy cattle has become a global challenge to the dairy industry. Because of low heritability and complexity, it is difficult to find genetic markers for fertility traits in cattle. Here, we report the use of an in vitro fertilization (IVF) system and candidate gene approach to test genetic associations of a single-nucleotide polymorphism (SNP) in bovine placental lactogen (bPL), and its interactions with SNPs in the prolactin receptor (PRLR) and growth hormone receptor genes with fertility traits in an IVF system. The associations suggest a possible involvement of genetic interactions between bPL and PRLR in the fertilization and embryonic development processes, and the potential for application in a marker-assisted selection program.

We study the k-epistasis of a fitness function over a search space. This concept is a natural generalization of that of epistasis, previously considered by Davidor, Suys and Verschoren and Van Hove and Verschoren [Y. Davidor, in: Foundations of genetic algorithms, Vol. 1, (1991), pp. 23–25; D. Suys and A. Verschoren, ‘Proc Int. Conf. on Intelligent Technologies in Human-Related Sciences (ITHURS’96), Vol. II (1996), pp. 251–258; H. Van Hove and A. Verschoren, Comput. Artificial Intell.14 (1994), 271–277], for example. We completely characterize fitness functions whose k-epistasis is minimal: these are exactly the functions of order k. We also obtain an upper bound for the k-epistasis of nonnegative fitness functions.