The Theory of Genetic Interactions and its Application to the Problem of Missing Heritability. A. Young1, R. Durbin2 1) Wellcome Trust Centre for Human Genetics, University of Oxford, Oxford, United Kingdom; 2) Wellcome Trust Sanger Institute, Hinxton, Cambridgeshire.

   Twin studies have estimated high heritabilities for complex traits in humans, yet genome wide association studies have failed to identify variants that collectively explain much of the estimated heritability. Insufficient power to detect genetic interactions leaves their contribution largely unknown. It is known, however, that genetic interactions upwardly bias heritability estimators. Quantifying the influence of genetic interactions will therefore lead to a better understanding of the problem of missing heritability. This quantification will become more precise with increasing sample sizes and play an important role in modelling the relation between genotype and phenotype. A theoretical framework is built to provide a basis for quantifying the influence of genetic interactions on phenotypic correlations and heritability estimators. The genetic correlations between individuals in a population isolate are derived in terms of identity-by-descent sharing. The covariance structure of a general trait in a diploid population with an arbitrary ancestral size is derived. This shows the relation between patterns of phenotypic similarity and patterns of identity-by-descent sharing dependent on genetic architecture. Existing heritability estimators are derived as consequences of the general theory. The general theory and the estimators are summarised in an elegant graphical representation. This shows how estimator bias changes dependent on genetic architecture and suggests novel estimators. The theory is illustrated by an application to data from the Northern Finland Birth Cohort. Using identity-by-descent sharing patterns, the covariance structure is fitted to estimate the narrow sense heritability of height, high density lipoprotein levels, and mean cell haemoglobin count in the Northern Finland Birth Cohort.".

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