%0 Book Section %1 griffiths1997ancestral %A Griffiths, Robert C. %A Marjoram, Paul %B Progress in population genetics and human evolution (Minneapolis, MN, 1994) %C New York %D 1997 %I Springer %K ARG coalescent_theory original recombination %P 257--270 %T An ancestral recombination graph %U http://www.math.canterbury.ac.nz/~r.sainudiin/recomb/ima.pdf %V 87 %X This paper describes a model of a gene as a continuous length of DNA represented by the interval 0,1. The ancestry of a sample of genes is complicated by possible recombination events, where a gene can have two parent genes. An analogue of Kingman's coalescent process, in which the ancestry of a sample of genes at a single locus is described by a stochastic binary tree, is a stochastic ancestral recombination graph, with vertices wehre coalescent or recombination events occur. All the information about ancestry is contaned in this graph. The sample DNA lengths have marginal ancestral trees at each point in 0,1 which are imbedded in the graph. An upper bound is found for the number of distinct most recent common ancestors of these trees, and the expected minimum waiting time to these ancestors.

@incollection{griffiths1997ancestral, abstract = {This paper describes a model of a gene as a continuous length of DNA represented by the interval [0,1]. The ancestry of a sample of genes is complicated by possible recombination events, where a gene can have two parent genes. An analogue of Kingman's coalescent process, in which the ancestry of a sample of genes at a single locus is described by a stochastic binary tree, is a stochastic ancestral recombination graph, with vertices wehre coalescent or recombination events occur. All the information about ancestry is contaned in this graph. The sample DNA lengths have marginal ancestral trees at each point in [0,1] which are imbedded in the graph. An upper bound is found for the number of distinct most recent common ancestors of these trees, and the expected minimum waiting time to these ancestors.}, added-at = {2012-09-17T19:37:47.000+0200}, address = {New York}, author = {Griffiths, Robert C. and Marjoram, Paul}, biburl = {https://www.bibsonomy.org/bibtex/2d60d21cbcdf8d4328d26446b0ea3bee8/peter.ralph}, booktitle = {Progress in population genetics and human evolution ({M}inneapolis, {MN}, 1994)}, description = {See refs for earlier work on such models.}, interhash = {21b9c7d0f1ae7ffed602bc57edaa44da}, intrahash = {d60d21cbcdf8d4328d26446b0ea3bee8}, keywords = {ARG coalescent_theory original recombination}, mrclass = {92D20 (60K99 92D15)}, mrnumber = {1493031}, pages = {257--270}, publisher = {Springer}, series = {IMA Vol. Math. Appl.}, timestamp = {2012-09-17T19:41:38.000+0200}, title = {An ancestral recombination graph}, url = {http://www.math.canterbury.ac.nz/~r.sainudiin/recomb/ima.pdf}, volume = 87, year = 1997 }