From the paper:
When the tree is calibrated with a mutation rate estimate of 0.76 × 10-9 mutations per base pair per year9, the time to the most recent common ancestor (TMRCA) of the tree is ~190,000 years, but we consider the implications of alternative mutation rate estimates below. Of the clades resulting from the four deepest branching events, all but one are exclusive to Africa, and the TMRCA of all non-African lineages (that is, the TMRCA of haplogroups DE and CF) is ~76,000 years (Fig. 1, Supplementary Figs. 18 and 19, Supplementary Table 10, and Supplementary Note). We saw a notable increase in the number of lineages outside Africa ~50–55 kya, perhaps reflecting the geographical expansion and differentiation of Eurasian populations as they settled the vast expanse of these continents. Consistent with previous proposals14, a parsimonious interpretation of the phylogeny is that the predominant African haplogroup, haplogroup E, arose outside the continent. This model of geographical segregation within the CT clade requires just one continental haplogroup exchange (E to Africa), rather than three (D, C, and F out of Africa). Furthermore, the timing of this putative return to Africa—between the emergence of haplogroup E and its differentiation within Africa by 58 kya—is consistent with proposals, based on non–Y chromosome data, of abundant gene flow between Africa and nearby regions of Asia 50–80 kya15.
I've long argued for the Y-chromosome haplogroup E migration into Africa and it is nice to see this common-sense interpretation finally adopted. Too much focus has been placed on figuring out which routes modern humans took out of Africa, and not at all to figure out how Eurasian males came to overwhelm the African Y-chromosome gene pool so decisively. The Eurasian migration into Africa must have taken place in the ~70-60kya window, constrained by the D/E split and  the deepest intra-African E splits. I think that the Out-of-Arabia scenario I outlined in 2012 continues to make a lot of sense. It would be awesome to get data from the first Later Stone Age people from Africa which are probably the best bet to trace this migration from Eurasia into Sub-Saharan Africa.

Nature Genetics (2016) doi:10.1038/ng.3559

Punctuated bursts in human male demography inferred from 1,244 worldwide Y-chromosome sequences

G David Poznik et al.

We report the sequences of 1,244 human Y chromosomes randomly ascertained from 26 worldwide populations by the 1000 Genomes Project. We discovered more than 65,000 variants, including single-nucleotide variants, multiple-nucleotide variants, insertions and deletions, short tandem repeats, and copy number variants. Of these, copy number variants contribute the greatest predicted functional impact. We constructed a calibrated phylogenetic tree on the basis of binary single-nucleotide variants and projected the more complex variants onto it, estimating the number of mutations for each class. Our phylogeny shows bursts of extreme expansion in male numbers that have occurred independently among each of the five continental superpopulations examined, at times of known migrations and technological innovations.

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