Realized Genome Sharing in Random Effects Models for Quantitative Genetic Traits

Bowen Wang

Advisor: Elizabeth Thompson

Genes inherited from the same ancestral copy by related individuals are said to be identical by descent (IBD). In quantitative genetics, correlation of trait values between relatives has often been modeled as a function of the kinship coefficient, a parameter that summarizes pairwise IBD sharing either at a locus or at the genome level. Pedigree kinship, the expectation of locus/genome-wide kinship over realizations of descent in the pedigree, is a deterministic function of the pedigree relationship. However, realized (actual) genome-wide kinship varies widely around this expected value, and even more so for locus level kinship. The availability of better and denser genetic marker data has made it possible to estimate both local and genome-wide IBD sharing very accurately. This is further supported by my recent work on efficient estimation of realized genome-wide kinship from genetic marker data. It is natural to use accurate estimates of realized genome-wide kinship in place of pedigree kinship to capture genetic correlation between relatives in random effects models for estimation or testing of variance parameters. A question of interest is how much difference would this make in the analyses, taking into account the specific relationship types/pedigree structures involved.

Starting with maximum likelihood estimation of variance parameters in a simple random effects model with only the additive genetic random effects and random residuals, I investigate the statistical properties of the parameter estimates when the correlation structure of the additive genetic effects is a function of the realized genome-wide kinship. Under this assumed true trait model, I show that fitting a model with pedigree kinship to capture genetic correlation still yields consistent point estimates of the variance parameters. Between using pedigree kinship or realized genome-wide kinship for model fitting, the asymptotic sampling variance of the parameter estimates may or may not differ, depending on the distributions of eigenvalues of the corresponding kinship matrices. Extreme eigenvalues, particularly those at the lower end of the spectrum are most influential in reducing asymptotic sampling variances of the parameter estimates. These analytical conclusions are supported by extensive simulation studies. My findings are also in agreement with relevant results from the literature. Next, I will extend my analysis to estimation as well as hypothesis testing of variance parameters under more complex random effects models.

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