%0 Journal Article %1 MR770050 %A Tavaré, Simon %D 1984 %J Theoret. Population Biol. %K coalescent_theory genealogies %N 2 %P 119--164 %T Line-of-descent and genealogical processes, and their applications in population genetics models %U http://www.cmb.usc.edu/people/stavare/STpapers-pdf/T84a.pdf %V 26 %X The principal aim of this paper is to demonstrate the importance and simplicity of genealogical Markov chains in the theory of classical selectively neutral population genetics models. An overview of the WrightFisher and Moran multiple-allele single-locus models and an introduction to genealogical Markov chains for discrete-time finite population size situations is given. A continuous-time process is then used to approximate Kingman's coalescent process which describes the family tree of a sample of individuals and their ancestors. A process is introduced which takes the effects of mutation into account. By considering lines of descent an approximating diffusion time-scale process, which has the structure of a Markovian death process, is introduced and applied to discrete reproduction mechanisms. Properties of these processes are established. Applications of line-of-descent and ancestral processes are given, looking at loss of alleles and coalescent, bivariate genealogical processes. Also, the infinite alleles model and infinite sites models are discussed.

@article{MR770050, abstract = {The principal aim of this paper is to demonstrate the importance and simplicity of genealogical Markov chains in the theory of classical selectively neutral population genetics models. An overview of the Wright\mhy Fisher and Moran multiple-allele single-locus models and an introduction to genealogical Markov chains for discrete-time finite population size situations is given. A continuous-time process is then used to approximate Kingman's coalescent process which describes the family tree of a sample of individuals and their ancestors. A process is introduced which takes the effects of mutation into account. By considering lines of descent an approximating diffusion time-scale process, which has the structure of a Markovian death process, is introduced and applied to discrete reproduction mechanisms. Properties of these processes are established. Applications of line-of-descent and ancestral processes are given, looking at loss of alleles and coalescent, bivariate genealogical processes. Also, the infinite alleles model and infinite sites models are discussed. }, added-at = {2009-09-28T23:01:04.000+0200}, author = {Tavar{\'e}, Simon}, biburl = {https://www.bibsonomy.org/bibtex/2646c4279665ca5bd93e96d19ad0308e8/peter.ralph}, coden = {TLPBAQ}, description = {MR: Publications results for "MR Number=(770050)"}, fjournal = {Theoretical Population Biology. An International Journal}, interhash = {8138d949c06b382c5b961bc40e1dd8e9}, intrahash = {646c4279665ca5bd93e96d19ad0308e8}, issn = {0040-5809}, journal = {Theoret. Population Biol.}, keywords = {coalescent_theory genealogies}, mrclass = {92A10 (60J10 60J70)}, mrnumber = {MR770050 (86f:92017)}, mrreviewer = {Klaus Hinkelmann}, number = 2, pages = {119--164}, timestamp = {2012-04-23T01:33:10.000+0200}, title = {Line-of-descent and genealogical processes, and their applications in population genetics models}, url = {http://www.cmb.usc.edu/people/stavare/STpapers-pdf/T84a.pdf}, volume = 26, year = 1984 }