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Assuming random mating and random sampling of pedigrees, the likelihood of a set of pedigree data is developed in terms of: (1) the population distribution of the different genotypes; (2) the phenotypic distributions for the different genotypes, and (3) the genotypic distribution of offspring given the parents’ genotypes. This last is given for any number of unlinked autosomal loci, two linked autosomal loci, an X-linked locus, and combinations of these possibilities. Methods are given for using this likelihood to test specific genetic hypotheses and for genetic counselling.

By impairing both function and survival, the severe reduction in oxygen availability associated with high-altitude environments is likely to act as an agent of natural selection. We used genomic and candidate gene approaches to search for evidence of such genetic selection. First, a genome-wide allelic differentiation scan (GWADS) comparing indigenous highlanders of the Tibetan Plateau (3,200-3,500 m) with closely related lowland Han revealed a genome-wide significant divergence across eight SNPs located near EPAS1. This gene encodes the transcription factor HIF2α, which stimulates production of red blood cells and thus increases the concentration of hemoglobin in blood. Second, in a separate cohort of Tibetans residing at 4,200 m, we identified 31 EPAS1 SNPs in high linkage disequilibrium that correlated significantly with hemoglobin concentration. The sex-adjusted hemoglobin concentration was, on average, 0.8 g/dL lower in the major allele homozygotes compared with the heterozygotes. These findings were replicated in a third cohort of Tibetans residing at 4,300 m. The alleles associating with lower hemoglobin concentrations were correlated with the signal from the GWADS study and were observed at greatly elevated frequencies in the Tibetan cohorts compared with the Han. High hemoglobin concentrations are a cardinal feature of chronic mountain sickness offering one plausible mechanism for selection. Alternatively, as EPAS1 is pleiotropic in its effects, selection may have operated on some other aspect of the phenotype. Whichever of these explanations is correct, the evidence for genetic selection at the EPAS1 locus from the GWADS study is supported by the replicated studies associating function with the allelic variants.chronic mountain sickness | high altitude | human genome variation | hypoxia | hypoxia-inducible factor

The determination of gene-by-gene and gene-by-environment interactions has long been one of the greatest challenges in genetics. The traditional methods are typically inadequate because of the problem referred to as the "curse of dimensionality." Recent combinatorial approaches, such as the multifactor dimensionality reduction (MDR) method, the combinatorial partitioning method, and the restricted partition method, have a straightforward correspondence to the concept of the phenotypic landscape that unifies biological, statistical genetics, and evolutionary theories. However, the existing approaches have several limitations, such as not allowing for covariates, that restrict their practical use. In this study, we report a generalized MDR (GMDR) method that permits adjustment for discrete and quantitative covariates and is applicable to both dichotomous and continuous phenotypes in various population-based study designs. Computer simulations indicated that the GMDR method has superior performance in its ability to identify epistatic loci, compared with current methods in the literature. We applied our proposed method to a genetics study of four genes that were reported to be associated with nicotine dependence and found significant joint action between CHRNB4 and NTRK2. Moreover, our example illustrates that the newly proposed GMDR approach can increase prediction ability, suggesting that its use is justified in practice. In summary, GMDR serves the purpose of identifying contributors to population variation better than do the other existing methods.

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