%0 Journal Article %1 sawyer1977asymptotic %A Sawyer, Stanley %B Advances in Applied Probability %D 1977 %I Cambridge University Press %K dispersal_estimation isolation_by_distance malecots_formula %N 2 %P 268-282-- %R DOI: 10.2307/1426386 %T Asymptotic properties of the equilibrium probability of identity in a geographically structured population %U https://www.cambridge.org/core/article/asymptotic-properties-of-the-equilibrium-probability-of-identity-in-a-geographically-structured-population/C0CF01AE8F9C680E8186014CFB7A05ED %V 9 %X Let I(x, u) be the probability that two genes found a vector distance x apart are the same type in an infinite-allele selectively-neutral migration model with mutation rate u. The creatures involved inhabit an infinite of colonies, are diploid and are held at N per colony. Set in one dimension and in higher dimensions, where σ2 is the covariance matrix of the migration law (which is assumed to have finite fifth moments). Then in one dimension, in two dimensions, and in three dimensions uniformly for Here C0 is a constant depending on the migration law, K0(y) is the Bessel function of the second kind of order zero, and are the eigenvalues of σ2. For symmetric nearest-neighbor migrations, in one dimension and log mi in two. For is known in one dimension and C0 does not appear. In two dimensions, These results extend and make more precise earlier work of Malécot, Weiss and Kimura and Nagylaki.

@article{sawyer1977asymptotic, abstract = {Let I(x, u) be the probability that two genes found a vector distance x apart are the same type in an infinite-allele selectively-neutral migration model with mutation rate u. The creatures involved inhabit an infinite of colonies, are diploid and are held at N per colony. Set in one dimension and in higher dimensions, where σ2 is the covariance matrix of the migration law (which is assumed to have finite fifth moments). Then in one dimension, in two dimensions, and in three dimensions uniformly for Here C0 is a constant depending on the migration law, K0(y) is the Bessel function of the second kind of order zero, and are the eigenvalues of σ2. For symmetric nearest-neighbor migrations, in one dimension and log mi in two. For is known in one dimension and C0 does not appear. In two dimensions, These results extend and make more precise earlier work of Malécot, Weiss and Kimura and Nagylaki.}, added-at = {2019-01-13T21:16:14.000+0100}, author = {Sawyer, Stanley}, biburl = {https://www.bibsonomy.org/bibtex/25ba9ba7316538023dc127d2a761d0863/peter.ralph}, booktitle = {Advances in Applied Probability}, doi = {DOI: 10.2307/1426386}, interhash = {88c187ef36266d3a779aefcf947682bf}, intrahash = {5ba9ba7316538023dc127d2a761d0863}, issn = {00018678}, keywords = {dispersal_estimation isolation_by_distance malecots_formula}, number = 2, pages = {268-282--}, publisher = {Cambridge University Press}, timestamp = {2019-01-13T21:16:14.000+0100}, title = {Asymptotic properties of the equilibrium probability of identity in a geographically structured population}, url = {https://www.cambridge.org/core/article/asymptotic-properties-of-the-equilibrium-probability-of-identity-in-a-geographically-structured-population/C0CF01AE8F9C680E8186014CFB7A05ED}, volume = 9, year = 1977 }