Inferring Transmission Histories of Rare Alleles in Population-Scale Genealogies.

Learning the transmission history of alleles through a family or population plays an important role in evolutionary, demographic, and medical genetic studies. Most classical models of population genetics have attempted to do so under the assumption that the genealogy of a population is unavailable and that its idiosyncrasies can be described by a small number of parameters describing population size and mate choice dynamics. Large genetic samples have increased sensitivity to such modeling assumptions, and large-scale genealogical datasets become a useful tool to investigate realistic genealogies. However, analyses in such large datasets are often intractable using conventional methods. We present an efficient method to infer transmission paths of rare alleles through population-scale genealogies. Based on backward-time Monte Carlo simulations of genetic inheritance, we use an importance sampling scheme to dramatically speed up convergence. The approach can take advantage of available genotypes of subsets of individuals in the genealogy including haplotype structure as well as information about the mode of inheritance and general prevalence of a mutation or disease in the population. Using a high-quality genealogical dataset of more than three million married individuals in the Quebec founder population, we apply the method to reconstruct the transmission history of chronic atrial and intestinal dysrhythmia (CAID), a rare recessive disease. We identify the most likely early carriers of the mutation and geographically map the expected carrier rate in the present-day French-Canadian population of Quebec.