%0 Journal Article %1 griffiths1980lines %A Griffiths, R.C. %D 1980 %J Theoretical Population Biology %K Wright-Fisher_diffusion coalescent_theory diffusion_approximation site_frequency_spectrum %N 1 %P 37 - 50 %R 10.1016/0040-5809(80)90013-1 %T Lines of descent in the diffusion approximation of neutral Wright-Fisher models %U http://www.sciencedirect.com/science/article/pii/0040580980900131 %V 17 %X This paper studies lines of descent in the diffusion approximation of neutral Wright-Fisher models where the mutation rate away from each gene per generation is the same. Here a line of descent begins with a single gene and has branches at each generation where genes are reproduced from a parent in the line. New mutations are not included in a line of descent but are considered to begin a new line. The joint distribution of the number of lines of descent surviving in a population from time 0 to time t and the frequencies in these lines is derived. Expected times between loss of lines of descent are found. The distribution of the number of lines of descent in a sample from the population is derived. This leads to the distribution of the number of types in a sample from a nonstationary infinite alleles population.

@article{griffiths1980lines, abstract = {This paper studies lines of descent in the diffusion approximation of neutral Wright-Fisher models where the mutation rate away from each gene per generation is the same. Here a line of descent begins with a single gene and has branches at each generation where genes are reproduced from a parent in the line. New mutations are not included in a line of descent but are considered to begin a new line. The joint distribution of the number of lines of descent surviving in a population from time 0 to time t and the frequencies in these lines is derived. Expected times between loss of lines of descent are found. The distribution of the number of lines of descent in a sample from the population is derived. This leads to the distribution of the number of types in a sample from a nonstationary infinite alleles population.}, added-at = {2013-01-30T20:09:15.000+0100}, author = {Griffiths, R.C.}, biburl = {https://www.bibsonomy.org/bibtex/2390bdb41c34267c5eb1165a43862beb1/peter.ralph}, doi = {10.1016/0040-5809(80)90013-1}, interhash = {c796fbc6c0f73ed9c1124fb94c3a175f}, intrahash = {390bdb41c34267c5eb1165a43862beb1}, issn = {0040-5809}, journal = {Theoretical Population Biology}, keywords = {Wright-Fisher_diffusion coalescent_theory diffusion_approximation site_frequency_spectrum}, number = 1, pages = {37 - 50}, timestamp = {2013-01-30T20:09:15.000+0100}, title = {Lines of descent in the diffusion approximation of neutral {Wright}-{Fisher} models}, url = {http://www.sciencedirect.com/science/article/pii/0040580980900131}, volume = 17, year = 1980 }