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.