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**1 - 4**of**4**### Population structure and cryptic relatedness in genetic association studies

- Statistical Science
, 2009

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### BMC Bioinformatics BioMed Central Methodology article Global haplotype partitioning for maximal associated SNP pairs

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### On measures of association among genetic variables

"... Summary Systems involving many variables are important in population and quantitative genetics, for example, in multi-trait prediction of breeding values and in exploration of multi-locus associations. We studied departures of the joint distribution of sets of genetic variables from independence. Ne ..."

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Summary Systems involving many variables are important in population and quantitative genetics, for example, in multi-trait prediction of breeding values and in exploration of multi-locus associations. We studied departures of the joint distribution of sets of genetic variables from independence. New measures of association based on notions of statistical distance between distributions are presented. These are more general than correlations, which are pairwise measures, and lack a clear interpretation beyond the bivariate normal distribu-tion. Our measures are based on logarithmic (Kullback-Leibler) and on relative ‘distances’ between distributions. Indexes of association are developed and illustrated for quantitative genetics settings in which the joint distribution of the variables is either multivariate normal or multivariate-t, and we show how the indexes can be used to study linkage disequilibrium in a two-locus system with multiple alleles and present applications to systems of correlated beta distributions. Two multivariate beta and multivariate beta-binomial processes are examined, and new distributions are introduced: the GMS-Sarmanov multivariate beta and its beta-binomial counterpart.

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, 2012

"... Linkage disequilibrium (LD) and the persistence of its phase across populations are important for genomic selection as well as fine scale mapping of quantitative trait loci (QTL). However, knowledge of LD in beef cattle, as well as the persistence of LD phase between crossbreds (C) and purebreds, is ..."

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Linkage disequilibrium (LD) and the persistence of its phase across populations are important for genomic selection as well as fine scale mapping of quantitative trait loci (QTL). However, knowledge of LD in beef cattle, as well as the persistence of LD phase between crossbreds (C) and purebreds, is limited. The objective of this study was to understand the patterns of LD in Angus (AN), Charolais (CH), and C beef cattle based on 31,073, 32,088, and 33,286 SNP in each population, respectively. Amount of LD decreased rapidly from 0.29 to 0.23 to 0.19 in AN, 0.22 to 0.16 to 0.12 in CH, 0.21 to 0.15 to 0.11 in C, when the distance range between markers changed from 0–30 kb to 30–70 kb and then to 70–100 kb, respectively. Breeds and chromosomes had significant effects (P < 0.001) on LD decay. There was significant interaction between breeds and chromosomes (P < 0.001). Correlations of LD phase were high between C and AN (0.84), C and CH (0.81), as well as between AN and CH (0.77) for distances less than or equal to 70 kb. These dropped when the distance increased. Estimated effective population sizes for AN and CH were 207 and 285, respectively, for 10 generations ago. Given a useful LD of at least 0.3 between pairs of SNPs, the LD phase between any pair of the three