On the evolutionary mutation rate at Y-chromosome STRs: comments on paper by Di Giacomo et al. (2004)

Appendix

Proof of line 3

The average number of repeats at STRs in the J-haplogroup, estimated from the data of the Appendix at the paper of Di Giacomo et al. (2004), is 15.21, whereas that in haplogroups C2 and H1 in populations with known history, viz., the Bulgarian Gypsy populations (without the Musicians) and the Maori, as used for the estimation of effective mutation rate by Zhivotovsky et al. (2004) is 14.88, with the difference of Δ=0.33 repeats. Now, let us estimate to what extent this difference can increase the effective mutation rate. The data available from the paper of Dupuy et al. (2004) do not provide details on the way in which STR-mutation rate grows as a function of repeat score. Moreover, the presence of mutational changes with more than one repeat (Forster et al. 1998; Kayser et al. 2000; Nebel et al. 2001; Dupuy et al. 2004) argues for the need of an effective mutation rate (the product of mutation rate itself by mutational variance), because it determines evolutionary rate at STRs under mutation and genetic drift and, in particular, is linearly related to the variance in repeat score and to genetic distances (Slatkin 1995; Zhivotovsky and Feldman 1995).

The rate of increase in the variance in repeat score with increase in allele size can be inferred from the recent study of Kayser et al. (2004). It follows from the regression lines in Fig. 5 of Kayser et al. (2004) that an average linear increase of one repeat leads to the increase of roughly 0.25 in the repeat variance between haplogroups. Since each haplogroup in the study of Kayser et al. (2004) was represented by one individual, this estimate actually includes both the between- and within-haplogroup variance. Since the approaches to dating in Semino et al. (2004), Di Giacomo et al. (2004), and Zhivotovsky et al. (2004) are based on within-haplogroup repeat variation, we need to know the value of the intra-class correlation coefficient to estimate the fraction of the 0.25 that corresponds to the increase in repeat variance within a haplogroup.

In order to estimate the between- and within-haplogroup variance in the repeat score, we analyzed available STR data on the following five haplogroups: Hg-Q from north Asia and America (Zegura et al. 2004), Hg-J from Europe, Near East, and northern Africa (Semino et al. 2004), and Hg-E3a8 in native sub-Saharan Africans, Hg-C2 in Polynesians, and Hg-H1 in Bulgarian Gypsies (Zhivotovsky et al. 2004) with loci DYS19, DYS388, DYS389I, DYS390, DYS391, and DYS392 available for all five haplogroups, DYS389II and DYS393 in four haplogroups, DYS439 in three haplogroups, and DYSA7.2 in two haplogroups. The one-way variance analysis gives 2.29 and 0.33 for the between- and within-haplogroup repeat variances, respectively, or 0.33/(2.29+0.33)≈0.13 for the fraction of within-haplogroup repeat variance.

Therefore, the difference in repeat score, Δ=0.33, will give an excess in within-haplogroup variance of 0.33×0.25×0.13≈0.01. From the data of Di Giacomo et al. (2004), the average repeat variance weighted across loci and haplogroups is 0.44. Therefore, taking the above point estimate of 0.72×10⁻³ for the five loci, the larger-allele-size argument can be justified for an effective mutation rate of (1+0.01/0.44)×0.72×10⁻³≈0.74×10⁻³, which is very close to 0.69×10⁻³ and far less than 2.6×10⁻³.