The following is from Human Y Chromosome Mutation Rate: Problems and Perspectives
Note that Jeanson does reference some of these papers, but diverges wildly from the accepted range of mutation rate.
Table 1. Methodology used, number of Mb analysed, mutation rate in bp-1y-1 and TMRCA in thousand years of age, in some relevant studies on human Y chromosome.
Reference Methodology n° of Mb Mutation Rate TMRCA
Thomson et al. 2000 [37] chimp/human 0.064 1.24×10-9 bp-1y-1, 50 ky
Kuroki et al. 2006 [62] chimp/human 13 1.50×10-9 bp-1y-1, n.a
Xue et al. 2009 pedigree 10.15 1.00×10-9 bp-1y-1, n.a
Mendez et al. 2013 pedigree 0.24 0.62×10-9 bp-1y-1, 338 ky
Francalacci et al. 2013 archaeology 8.97 0.53×10-9 bp-1y-1, 180-200 ky
Poznik et al. 2013 archaeology 10 0.82×10-9 bp-1y-1, 120-156 ky
Helgason et al. 2015 pedigree 23.1 0.87×10-9 bp-1y-1, n.a
Karmin et al. 2015 aDNA 10.8 0.74×10-9 bp-1y-1, 150 ky
Trombetta et al. 2015 aDNA 1.5 0.72×10-9 bp-1y-1, 291 ky
What I note in above table is that the estimates for TMRCA run from 50 to 291 thousand years, as opposed to ~4,500 years per Jeanson.
More recent relevant papers include The Divergence of Neandertal and Modern Human Y Chromosomes where Mendez reports the time to the most recent common ancestor of modern humans and Neandertals as ~588 thousand years ago, two orders of magnitude greater than Jeanson’s result. A preprint from this spring, The evolutionary history of Neandertal and Denisovan Y chromosomes may be of interest.