ArticleTheoretical population biology2014
A renewal theory approach to IBD sharing.
Article in Theoretical population biology, 2014. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 17 papers.
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Who cites it
17 citing papers in PubMed.
- The Length of Haplotype Blocks and Signals of Structural Variation in Reconstructed Genealogies.Molecular biology and evolution · 2025Article
- Modeling the effects of consanguinity on autosomal and X-chromosomal runs of homozygosity and identity-by-descent sharing.G3 (Bethesda, Md.) · 2024Article
- Exact Decoding of a Sequentially Markov Coalescent Model in Genetics.Journal of the American Statistical Association · 2024Article
- Ultrafast genome-wide inference of pairwise coalescence times.Genome research · 2023Article
- Demographic inference for spatially heterogeneous populations using long shared haplotypes.bioRxiv : the preprint server for biology · 2023Article
- Genome-wide data from medieval German Jews show that the Ashkenazi founder event pre-dated the 14Cell · 2022Article
- Limiting distribution of X-chromosomal coalescence times under first-cousin consanguineous mating.Theoretical population biology · 2022Article
- The distribution of waiting distances in ancestral recombination graphs.Theoretical population biology · 2021Article
- Parental relatedness through time revealed by runs of homozygosity in ancient DNA.Nature communications · 2021Article
- The effect of consanguinity on coalescence times on the X chromosome.Theoretical population biology · 2021Article
- Variance and limiting distribution of coalescence times in a diploid model of a consanguineous population.Theoretical population biology · 2021Article
- Article
- Exact limits of inference in coalescent models.Theoretical population biology · 2019Article
- Estimating recent migration and population-size surfaces.PLoS genetics · 2019Article
- Rapidly Registering Identity-by-Descent Across Ancestral Recombination Graphs.Journal of computational biology : a journal of computational molecular cell biology · 2016Article
- Atlas of Cryptic Genetic Relatedness Among 1000 Human Genomes.Genome biology and evolution · 2016Article
- Article
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4 authors.
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Abstract
A long genomic segment inherited by a pair of individuals from a single, recent common ancestor is said to be identical-by-descent (IBD). Shared IBD segments have numerous applications in genetics, from demographic inference to phasing, imputation, pedigree reconstruction, and disease mapping. Here, we provide a theoretical analysis of IBD sharing under Markovian approximations of the coalescent with recombination. We describe a general framework for the IBD process along the chromosome under the Markovian models (SMC/SMC'), as well as introduce and justify a new model, which we term the renewal approximation, under which lengths of successive segments are independent. Then, considering the infinite-chromosome limit of the IBD process, we recover previous results (for SMC) and derive new results (for SMC') for the mean number of shared segments longer than a cutoff and the fraction of the chromosome found in such segments. We then use renewal theory to derive an expression (in Laplace space) for the distribution of the number of shared segments and demonstrate implications for demographic inference. We also compute (again, in Laplace space) the distribution of the fraction of the chromosome in shared segments, from which we obtain explicit expressions for the first two moments. Finally, we generalize all results to populations with a variable effective size.
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