Efficient Estimation of Realized Kinship from Single Nucleotide Polymorphism Genotypes.

Realized kinship is a key statistic in analyses of genetic data involving relatedness of individuals or structure of populations. There are several estimators of kinship that make use of dense SNP genotypes. We introduce a class of estimators, of which some existing estimators are special cases.

Combinatorial Methods for Epistasis and Dominance.

We develop computational tools for the analysis of nonlinear genotype-phenotype relationships with epistasis among multiple loci or dominance interactions among multiple alleles within the same locus. Theory distinguishes between separable traits, with removable epistasis, and traits with essential epistasis. Separable traits can be transformed to a natural scale where additive methods apply.

Identity-by-descent graphs offer a flexible framework for imputation and both linkage and association analyses.

We demonstrate the flexibility of identity-by-descent (IBD) graphs for genotype imputation and testing relationships between genotype and phenotype. We analyzed chromosome 3 and the first replicate of simulated diastolic blood pressure. IBD graphs were obtained from complete pedigrees and full multipoint marker analysis, facilitating subsequent linkage and other analyses.

Estimating and adjusting for ancestry admixture in statistical methods for relatedness inference, heritability estimation, and association testing.

It is well known that genetic association studies are not robust to population stratification. Two widely used approaches for the detection and correction of population structure are principal component analysis and model-based estimation of ancestry. These methods have been shown to give reliable inference on population structure in unrelated samples.

Correlation between relatives given complete genotypes: from identity by descent to identity by function.

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 approaches to the inverse problem where genotypes are observed but pedigree relationships are not, dependence between phenotypes is either modeled as Bayesian uncertainty or mapped to an IBD model via inferred relatedness parameters. Neither approach yields a relationship between genotypic similarity and phenotypic similarity with a probabilistic interpretation corresponding to a generative model.