### Abstract

Models of genetic differentiation which incorporate migration matrices generally assume that the recorded rates of migration between subdivisions of an solate have persisted for a very long time. A technique derived from the stability theory of linear differential equations is presented which can be used to test this assumption. The technique involves a simple transformation of the original migration matrix. If the transformed matrix possesses at least one eigenvalue with a positive real part, no set of equilibrium subdivision population sizes can be associated with the recorded migration rates, in which case it can be concluded that the rates have not existed for an indefinite period of time. This technique is applied to migration data from Papua New Guinea that have already been used in an analysis of genetic differentiation. The transformed data yield an eigenvalue of 0.016 which, though positive real, does not appear to be significantly different from zero. Therefore, it can be tentatively concluded that these data were appropriate for the migration matrix analysis that was carried out on them.

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

Pages (from-to) | 309-320 |

Number of pages | 12 |

Journal | Human Biology |

Volume | 49 |

Issue number | 3 |

State | Published - 1977 |

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### All Science Journal Classification (ASJC) codes

- Agricultural and Biological Sciences(all)
- Ecology, Evolution, Behavior and Systematics
- Genetics
- Genetics(clinical)

### Cite this

*Human Biology*,

*49*(3), 309-320.

}

*Human Biology*, vol. 49, no. 3, pp. 309-320.

**A stability test for migration matrix models of genetic differentiation.** / Wood, J. W.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A stability test for migration matrix models of genetic differentiation

AU - Wood, J. W.

PY - 1977

Y1 - 1977

N2 - Models of genetic differentiation which incorporate migration matrices generally assume that the recorded rates of migration between subdivisions of an solate have persisted for a very long time. A technique derived from the stability theory of linear differential equations is presented which can be used to test this assumption. The technique involves a simple transformation of the original migration matrix. If the transformed matrix possesses at least one eigenvalue with a positive real part, no set of equilibrium subdivision population sizes can be associated with the recorded migration rates, in which case it can be concluded that the rates have not existed for an indefinite period of time. This technique is applied to migration data from Papua New Guinea that have already been used in an analysis of genetic differentiation. The transformed data yield an eigenvalue of 0.016 which, though positive real, does not appear to be significantly different from zero. Therefore, it can be tentatively concluded that these data were appropriate for the migration matrix analysis that was carried out on them.

AB - Models of genetic differentiation which incorporate migration matrices generally assume that the recorded rates of migration between subdivisions of an solate have persisted for a very long time. A technique derived from the stability theory of linear differential equations is presented which can be used to test this assumption. The technique involves a simple transformation of the original migration matrix. If the transformed matrix possesses at least one eigenvalue with a positive real part, no set of equilibrium subdivision population sizes can be associated with the recorded migration rates, in which case it can be concluded that the rates have not existed for an indefinite period of time. This technique is applied to migration data from Papua New Guinea that have already been used in an analysis of genetic differentiation. The transformed data yield an eigenvalue of 0.016 which, though positive real, does not appear to be significantly different from zero. Therefore, it can be tentatively concluded that these data were appropriate for the migration matrix analysis that was carried out on them.

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UR - http://www.scopus.com/inward/citedby.url?scp=0017729663&partnerID=8YFLogxK

M3 - Article

C2 - 892757

AN - SCOPUS:0017729663

VL - 49

SP - 309

EP - 320

JO - Human Biology

JF - Human Biology

SN - 0018-7143

IS - 3

ER -