Estimating variance components in population scale family trees

The rapid digitization of genealogical and medical records enables the assembly of extremely large pedigree records spanning millions of individuals and trillions of pairs of relatives. Such pedigrees provide the opportunity to investigate the sociological and epidemiological history of human populations in scales much larger than previously possible. Linear mixed models (LMMs) are routinely used to analyze extremely large animal and plant pedigrees for the purposes of selective breeding. However, LMMs have not been previously applied to analyze population-scale human family trees. Here, we present Sparse Cholesky factorIzation LMM (Sci-LMM), a modeling framework for studying population-scale family trees that combines techniques from the animal and plant breeding literature and from human genetics literature. The proposed framework can construct a matrix of relationships between trillions of pairs of individuals and fit the corresponding LMM in several hours. We demonstrate the capabilities of Sci-LMM via simulation studies and by estimating the heritability of longevity and of reproductive fitness (quantified via number of children) in a large pedigree spanning millions of individuals and over five centuries of human history. Sci-LMM provides a unified framework for investigating the epidemiological history of human populations via genealogical records.Author summary: The advent of online genealogy services allows the assembly of population-scale family trees, spanning millions of individuals and centuries of human history. Such datasets enable answering genetic epidemiology questions on unprecedented scales. Here we present Sci-LMM, a pedigree analysis framework that combines techniques from animal and plant breeding research and from human genetics research for large-scale pedigree analysis. We apply Sci-LMM to analyze population-scale human genealogical records, spanning trillions of relationships. We have made both Sci-LMM and an anonymized dataset of millions of individuals freely available to download, making the analysis of population-scale human family trees widely accessible to the research community. Together, these resources allow researchers to investigate genetic and epidemiological questions on an unprecedented scale.