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. Within this class, we derive properties of the estimators and determine an optimal estimator. Additionally, we introduce an alternative marker weighting that takes allelic associations [linkage disequilibrium (LD)] into account, and apply this weighting to several estimators. In a simulation study, we show that improved estimators are obtained (1) by optimal weighting of markers, (2) by taking physical contiguity of genome into account, and (3) by weighting on the basis of LD.

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. The methods we present solve for the natural scale, exactly when possible and approximately when not. Through graph methods, our methods allow for enumeration, counting, or sampling of distinct trait architectures satisfying constraints from the separability theory. A tool is provided for diagnosing which separability constraints are violated by a given nonseparable architecture. For genetic traits controlled by limited numbers of loci and alleles, our algorithm enumerates all possible trait structures and finds exact or error-minimizing linearizing transformations by formulating a constrained optimization program. We find that the fraction of possible distinct genetic traits satisfying simple criteria that can be fully or approximately linearized is high for small systems and falls as the number of alleles or loci increases.

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. We evaluated these two approaches in Mexican American pedigrees provided by the Genetic Analysis Workshop 18. We also estimated identity-by-descent sharing probabilities and kinship coefficients, with adjustment for ancestry admixture, to confirm documented pedigree relationships as well as to identify cryptic relatedness in the sample. We also estimated the heritability of the first simulated replicate of diastolic blood pressure (DBP). Finally, we performed an association analysis with simulated DBP, comparing the performance of an association method that corrects for population structure but does not account for relatedness to a method that adjusts for both population and pedigree structure. Analyses with simulated DBP were performed with knowledge of the underlying trait model.

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. For rare alleles, pedigree-based imputation using these IBD graphs had a higher call rate than did population-based imputation. Combining the two approaches improved call rates for common alleles. We found it advantageous to incorporate known, rather than estimated, pedigree relationships when testing for association. Replacing missing data with imputed alleles improved association signals as well. Analyses were performed with knowledge of the underlying model.

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. We introduce a generative model for diploid allele effect based on the classic infinite allele mutation process. This approach motivates the concept of IBF (Identity by Function). The phenotypic covariance between two individuals given their diploid genotypes is expressed in terms of functional identity states. The IBF parameters define a genetic architecture for a trait without reference to specific alleles or population. Given full genome sequences, we treat a gene-scale functional region, rather than a SNP, as a QTL, modeling patterns of dominance for multiple alleles. Applications demonstrated by simulation include phenotype and effect prediction and association, and estimation of heritability and classical variance components. A simulation case study of the Missing Heritability problem illustrates a decomposition of heritability under the IBF framework into Explained and Unexplained components.