A genealogical estimate of genetic relationships.

The application of genetic relationships among individuals, characterized by a genetic relationship matrix (GRM), has far-reaching effects in human genetics. However, the current standard to calculate the GRM treats linked markers as independent and does not explicitly model the underlying genealogical history of the study sample. Here, we propose a coalescent-informed framework, namely the expected GRM (eGRM), to infer the expected relatedness between pairs of individuals given an ancestral recombination graph (ARG) of the sample. Through extensive simulations, we show that the eGRM is an unbiased estimate of latent pairwise genome-wide relatedness and is robust when computed with ARG inferred from incomplete genetic data. As a result, the eGRM better captures the structure of a population than the canonical GRM, even when using the same genetic information. More importantly, our framework allows a principled approach to estimate the eGRM at different time depths of the ARG, thereby revealing the time-varying nature of population structure in a sample. When applied to SNP array genotypes from a population sample from Northern and Eastern Finland, we find that clustering analysis with the eGRM reveals population structure driven by subpopulations that would not be apparent via the canonical GRM and that temporally the population model is consistent with recent divergence and expansion. Taken together, our proposed eGRM provides a robust tree-centric estimate of relatedness with wide application to genetic studies.