Functional Quantitative Genetics and the Missing Heritability Problem
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In classical quantitative genetics, the correlation between the phenotypes of individuals with unknown genotypes and a known pedigree relationship is expressed in terms of probabilities of IBD states. In existing models of the inverse problem where genotypes are observed but pedigree relationships are not, probabilities and correlations have either a Bayesian or a hybrid interpretation. We introduce the IBF (Identity by Function) model based on the classic infinite allele mutation process. Describing genetic resemblance in terms of functional states defines a genetic architecture for a trait without reference to specific alleles or a population, treating a gene-scale functional region, rather than a SNP, as a QTL, and emphasizing locus weights and patterns of dominance over multiple alleles. This allows the reconciliation of bottom-up (genome sequence based) and (pedigree/population) calculations of heritability, as well as phenotype and gene effect prediction. We perform these calculations with simulated, pig, and human traits. For related computational problems, we describe an algorithm for the estimation in large scale variance components problems by matrix decomposition methods techniques related to the Sparse Bayesian Learning/Relevance Vector Machine framework. Additionally, we describe a combinatorial framework for decomposing nonlinear genetic effects due to dominance and epistasis, and a method for adjusting the Genomic Relationship Matrix for linkage disequilibrium by SNP selection and weighting.
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