Earlier this year, we discovered that an extreme age estimate for a Y chromosomal haplotype (237 000–581 000 years ago) by Mendez *et al*^{1} was based on analytical choices that consistently inflated its value.^{2}

As stated in our original criticism,^{2} estimating divergence time is not different, in principle, from estimating the time it takes two cars traveling in opposite directions at known speeds to reach a certain distance from each other. The time inferences will be overestimated if the distance between the two cars is overestimated, or if the speed of either car is underestimated. Similarly, a divergence time estimate will seem larger than the actual divergence time if the genetic distances between sequences are overestimated and/or the rates of substitution are underestimated.

Let us consider a very simple estimation model for the time of divergence,

where *t* is the divergence time, *d* is the genetic distance, and *r* is the substitution rate per unit time. To overestimate *t*, one needs to overestimate *d* and/or underestimate *r*. *d* is usually estimated by dividing the number of differences between two sequences, *n*, by the length of the aligned sequences, *l*, and correcting for multiple hits and the like

*d* can, thus, be overestimated by either overestimating *n* or underestimating *l*. The unit time for *r* is years. However, *r* is often derived from data on number of substitutions per generation. *r* can, thus, be overestimated by assuming that the generation time, *t*_{g}, is larger than it really is.

In selecting values for *d*, *r*, *n*, *l*, and *t*_{g}, Mendez *et al*^{1} consistently and without exception chose values that led to overestimating the time of divergence.

In Elhaik *et al*,^{2} we discussed many such choices. In the following we will focus on two choices left unexplained by Mendez *et al.*^{3} The first choice concerns the substitution rate used in the calculation of the TMRCA. Using an estimate based on Y-chromosome substitution rate (1 × 10^{–9} substitutions per nucleotide per year)^{4} we can calculate divergence times of 43/240 000/10^{−9}≈179 000 years and 45/180 000/10^{−9}≈250 000 years, for an average of 214500 years, very similar to the TMRCA obtained using a likelihood-based method: 209 500 (95% CI: 168 000–257 400) years.^{2} Not surprisingly, by employing an autosomally derived value of 0.617 × 10^{–9} as the mutation rate constant, which is 1.6 times smaller, Mendez *et al*^{1} obtained a divergence time 1.6 times higher than that estimate of 290 000–404 000 years, with an average value of 347 000 years. More appropriate choices would have resulted in a much lower estimate. Mendez *et al*^{1} other choices, such as the unprecedented 40 years for human generation time, resulted in overestimating the time of divergence by 20–130%.

The second choice concerns the irregular and questionable comparison of mutation numbers based on sequences of unequal lengths. Mendez *et al*^{3} compared 240 000 bases of the A00 Y-chromosome that contained 43 mutations with 180 000 bases of the A0 Y-chromosome that contained 45 mutations. In other words, they used data from two segments, in which one segment was smaller than the other by about 25%. In response to Mendez *et al*’s^{3} allegations of ‘misunderstanding of population genetic theory,’ we challenge the authors to come up with one example in the evolutionary literature in which the branches on a phylogenetic tree were estimated by using pairwise distances based on alignments of different lengths. We note that textbooks in molecular evolution (for example, Graur and Li^{5}) specifically caution against such practices.

### References

- Mendez FL, Krahn T, Schrack B
*et al*. An African American paternal lineage adds an extremely ancient root to the human Y chromosome phylogenetic tree. Am J Hum Genet 2013; 92: 454–459. | Article | PubMed | ISI | CAS | - Elhaik E, Tatarinova TV, Klyosov AA, Graur D: The ‘extremely ancient’ chromosome that isn’t: a forensic bioinformatic investigation of Albert Perry’s X-degenerate portion of the Y chromosome. Eur J Hum Genet 2014; 22: 1111–1116. | Article | PubMed | ISI | CAS |
- Mendez FL, Veeramah KR, Thomas MG, Karafet TM, Hammer MF: Reply to “The ‘extremely ancient’ chromosome that isn’t” by Elhaik et al. Am J Hum Genet 2014.
- Xue Y, Wang Q, Long Q
*et al*. Human Y chromosome base-substitution mutation rate measured by direct sequencing in a deep-rooting pedigree. Curr Biol 2009; 19: 1453–1457. | Article | PubMed | ISI | CAS | - Graur D, Li W-H. Fundamentals of Molecular Evolution. Sinnauer Associates: Sunderland, MA, USA, 2000.