**Appendix 2: Multilocus F-statistics
(as it appears in the DOS version 3.4 documentation written by Francois Rousset) **

F_{is} may be defined as , where the *Q*Õs are probability of identity in state of pairs of genes either within (*Q _{1}*>) or between (

With several loci, such an analysis is performed for each locus *i.* However, there is no single obvious way to compute multilocus F-statistics. Weir and Cockerham's (1984) multilocus estimators are defined from sums of intermediate statistics *a*, *b*, and *c* for each locus. The numerator of F_{st }of Weir and Cockerham (1984) is the sum over alleles of the *a* terms, . WeirÕs (1996) estimators are defined from sums of intermediate statistics S_{1}, S_{2}, and S_{3}. The numerator of Weir (1996) is the sum over alleles of the S_{1 }terms which are whereis an average over all loci. The 1984 and 1996 estimators slightly differ, but both give the same weight to the estimates of the Õs for a locus typed at 5 individuals in each subpopulation as for a locus typed at 50 individuals in each subpopulation..

Genepop uses yet other formulas. The multilocus estimator of Genepop has numerator , which will give 10 time more weight to the *Q* estimates for the more intensively typed locus. Explicit formulas for the estimators are (the estimators are sometimes expressed in terms of ,, and ):

.

The following example (due to A.J. Gharrett) illustrates the results obtained by the different methods for the data shown here.

Estimate | Fis | Fst | Fit |

Loc1 | -0.0483 | 0.5712 | 0.5505 |

Loc2 | -0.1161 | 0.8560 | 0.8393 |

Loc3 | 0.0051 | -0.0023 | 0.0028 |

Multilocus (1984 a,b,c method) | -0.0286 | 0.5606 | 0.5480 |

Multilocus (1996 S_{1},S_{2},S_{3} method) |
-0.0286 | 0.5633 | 0.5508 |

Multilocus (Genepop v3.3 and later) | -0.0275 | 0.5436 | 0.5310 |

Most of the time the different estimators yield close values.

Note that options 5.2 and 5.3 also return unweighted averages of *MSG* over loci.

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