There is greater selection pressure acting on the y chromosome, thereby limiting the retention of y lineages, by a mechanism separate from the effective (reproducing) male population. This finding is so important because it means that a greater diversity of mtdna, over ydna, does not imply greater continuity of female populations.
So, take this into account when considering gender biased migrations.
Key finding from abstract: Here we show that neutral models with unequal male and female effective population sizes are not consistent with observed genome-wide diversity on autosomes, X, Y and mtDNA across completely sequenced males. Instead, a model including selection is needed to explain the departure of observed Y diversity from expectations.