## Appendix 3

(excerpts from the DOS version 4.0 documentation written by Francois Rousset)

### 1. Microsatellite allele sizes, R_{ST}, and r_{ST}

Following Slatkin (1995), statistics based on allele size have been widely used.
The parameters r_{IS}, r_{ST} and r_{IT} and their estimators are defined by replacing any by the expected square difference in allele size between the genes compared (Rousset, 1996) in all formulas above, and any by the observed mean square difference (more formulas are given in Michalakis & Excoffier, 1996). Then
the estimators become plain ANOVA estimators of intraclass correlation for allele size; if there are only two alleles, , but Slatkin's .

### 2. Robertson and Hill's estimator of F_{IS}

This estimator, reported in options 1 and 5, was designed to have lower variance
than the ANOVA estimator and no small-sample bias when F_{IS} is low, assuming
a probability model for sample probabilities (Robertson & Hill, 1984). The score
test computed in heterozygote excess and deficiency sub-options of option 1 is
equivalent to this estimator for testing purposes.

### 3. Bootstraps

Option 6 constructs approximate bootstrap confidence (ABC) intervals (DiCiccio & Efron, 1996), assuming that each locus is an independent realization of genealogical and mutation processes. The bootstrap is a general methodology with
different incarnations. The ABC methods were chosen because they balance moderate
computation needs with good accuracy compared to alternatives. Bootstrap
methods are approximate, and simulation tests of their performance (a too rare
deed in statistical population genetics) for the present application are reported in
Leblois et al. (2003) and Watts et al. (2007).
The ABC method is also applied over individuals in option 8 to compute confidence intervals for null allele frequency estimates.

*Last Modified on
April 14, 2010
by Eleanor Morgan*

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