### Abstract

A recurring problem with the use of migration matrix models of genetic differentiation has to do with their convergence properties. In practice, predictions can be drawn from these models only at equilibrium; but in the case of the standard predictors (most of which are modifications of Wright's F_{ST}), it can take an unrealistically large number of generations to approach equilibrium. An alternative set of predictors, the set of all pairwise genetic distances among the populations that define the rows and columns of the migration matrix, is investigated here. These distances are shown analytically to converge much more rapidly than the more commonly used predictors. In an application of the model to migration data on a human population from Papua New Guinea, it takes only about three to four generations for the pairwise distances to converge, in contrast to more than 100 generations for one of the standard predictors. In this case, moreover, the distances predicted by the model at equilibrium are similar to those calculated from the available genetic data.

Original language | English (US) |
---|---|

Pages (from-to) | 209-219 |

Number of pages | 11 |

Journal | American Journal of Physical Anthropology |

Volume | 71 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1986 |

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### All Science Journal Classification (ASJC) codes

- Anatomy
- Anthropology

### Cite this

*American Journal of Physical Anthropology*,

*71*(2), 209-219. https://doi.org/10.1002/ajpa.1330710208

}

*American Journal of Physical Anthropology*, vol. 71, no. 2, pp. 209-219. https://doi.org/10.1002/ajpa.1330710208

**Convergence of genetic distances in a migration matrix model.** / Wood, James William.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Convergence of genetic distances in a migration matrix model

AU - Wood, James William

PY - 1986/1/1

Y1 - 1986/1/1

N2 - A recurring problem with the use of migration matrix models of genetic differentiation has to do with their convergence properties. In practice, predictions can be drawn from these models only at equilibrium; but in the case of the standard predictors (most of which are modifications of Wright's FST), it can take an unrealistically large number of generations to approach equilibrium. An alternative set of predictors, the set of all pairwise genetic distances among the populations that define the rows and columns of the migration matrix, is investigated here. These distances are shown analytically to converge much more rapidly than the more commonly used predictors. In an application of the model to migration data on a human population from Papua New Guinea, it takes only about three to four generations for the pairwise distances to converge, in contrast to more than 100 generations for one of the standard predictors. In this case, moreover, the distances predicted by the model at equilibrium are similar to those calculated from the available genetic data.

AB - A recurring problem with the use of migration matrix models of genetic differentiation has to do with their convergence properties. In practice, predictions can be drawn from these models only at equilibrium; but in the case of the standard predictors (most of which are modifications of Wright's FST), it can take an unrealistically large number of generations to approach equilibrium. An alternative set of predictors, the set of all pairwise genetic distances among the populations that define the rows and columns of the migration matrix, is investigated here. These distances are shown analytically to converge much more rapidly than the more commonly used predictors. In an application of the model to migration data on a human population from Papua New Guinea, it takes only about three to four generations for the pairwise distances to converge, in contrast to more than 100 generations for one of the standard predictors. In this case, moreover, the distances predicted by the model at equilibrium are similar to those calculated from the available genetic data.

UR - http://www.scopus.com/inward/record.url?scp=0022444676&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0022444676&partnerID=8YFLogxK

U2 - 10.1002/ajpa.1330710208

DO - 10.1002/ajpa.1330710208

M3 - Article

C2 - 3799824

AN - SCOPUS:0022444676

VL - 71

SP - 209

EP - 219

JO - American Journal of Physical Anthropology

JF - American Journal of Physical Anthropology

SN - 0002-9483

IS - 2

ER -