%0 Journal Article %1 surviving-blocks %A Baird, S. J. E. %A Barton, N. H. %A Etheridge, A. M. %D 2003 %J Theoretical Population Biology %K ancestral_blocks branching_processes haplotype_length recombination IBD %N 4 %P 451-471 %T The distribution of surviving blocks of an ancestral genome %U http://dx.doi.org/10.1016/S0040-5809(03)00098-4 %V 64 %X What is the chance that some part of a stretch of genome will survive? In a population of constant size, and with no selection, the probability of survival of some part of a stretch of map length y < 1 approaches y / log(yt/2) for logyt >> 1. Thus, the whole genome is certain to be lost, but the rate of loss is extremely slow. This solution extends to give the whole distribution of surviving block sizes as a function of time. We show that the expected number of blocks at time t is 1+yt and give expressions for the moments of the number of blocks and the total amount of genome that survives for a given time. The solution is based on a branching process and assumes complete interference between crossovers, so that each descendant carries only a single block of ancestral material. We consider cases where most individuals carry multiple blocks, either because there are multiple crossovers in a long genetic map, or because enough time has passed that most individuals in the population are related to each other. For species such as ours, which have a long genetic map, the genome of any individual which leaves descendants approximately 80\% of the population for a Poisson offspring number with mean two is likely to persist for an extremely long time, in the form of a few short blocks of genome.

@article{surviving-blocks, abstract = {What is the chance that some part of a stretch of genome will survive? In a population of constant size, and with no selection, the probability of survival of some part of a stretch of map length y < 1 approaches y / log(yt/2) for logyt >> 1. Thus, the whole genome is certain to be lost, but the rate of loss is extremely slow. This solution extends to give the whole distribution of surviving block sizes as a function of time. We show that the expected number of blocks at time t is 1+yt and give expressions for the moments of the number of blocks and the total amount of genome that survives for a given time. The solution is based on a branching process and assumes complete interference between crossovers, so that each descendant carries only a single block of ancestral material. We consider cases where most individuals carry multiple blocks, either because there are multiple crossovers in a long genetic map, or because enough time has passed that most individuals in the population are related to each other. For species such as ours, which have a long genetic map, the genome of any individual which leaves descendants approximately 80\% of the population for a Poisson offspring number with mean two is likely to persist for an extremely long time, in the form of a few short blocks of genome.}, added-at = {2009-01-27T17:55:35.000+0100}, author = {Baird, S. J. E. and Barton, N. H. and Etheridge, A. M.}, biburl = {https://www.bibsonomy.org/bibtex/25904243f50d870e009165f62a1090e45/peter.ralph}, interhash = {4cac91971b7dcaf3ff96230a413a12a2}, intrahash = {5904243f50d870e009165f62a1090e45}, journal = {Theoretical Population Biology}, keywords = {ancestral_blocks branching_processes haplotype_length recombination IBD}, number = 4, pages = {451-471 }, timestamp = {2015-01-20T22:35:53.000+0100}, title = {The distribution of surviving blocks of an ancestral genome }, url = {http://dx.doi.org/10.1016/S0040-5809(03)00098-4}, volume = 64, year = 2003 }