Looking for Nm* values for humans I stumbled across an interesting paper, Estimating sex-specific processes in human populations: Are XY-homologous markers an effective tool?:
…To test this idea, we analyzed XY-homologous microsatellite diversity in 33 human populations from Africa, Asia and Europe. Interpopulation comparisons suggest that the generally discordant pattern of genetic variation observed for X- and Y-linked markers could be an outcome of sex-specific migration processes (mfemales/mmales ~ 3) or sex-specific demographic processes (Nfemales/Nmales ~ 11) or a combination of both….
Basically the authors were looking at diversity on homologous markers on the X & Y chromosomes. Previously researchers had compared mtDNA (female) and Y (male) lineages, but the authors point out that the comparison using these two regions of the genome might be problematic (e.g., mtDNA is subject to its own peculiarities such as high mutational rate, and might not be as neutral as we assume). The diversity across the markers that they focused on implied two general dynamics:
1) female biased migration or 2) female biased sex ratios
The authors do note data which is locally contradictory, but the overall trends fit our expectations from other data, males usually exhibit more reproductive skew which drives their effective population down vis-a-vis females. Additionally, both common chimpanzees and H. sapiens seem to exhibit a tendency toward patrilocality & patrilineality which is somewhat anomalous among mammals (think of the matrilineages which are focus of social life among whales and elephants). But what is the balance between the two? The models above were presented as extreme cases, holding sex ratio or male and female migration even. It seems that a skew of 1 to 11 is a bit high for most populations, so likely the female migration rate is somewhat higher than the male one. But if history is a guide it may also be that male and female migration tend to follow different tracks, the former being rarer long distance movements and the latter much more common deme-to-deme exchanges. The Arab enslavement of women from black Africa is the main example I can think of long distance migration of females as opposed to males (black males in much of the Arab world were castrated). In contrast, we have many cases of groups of males founding new hybrid populations. The mestizo populations of the New World and the peoples of Madagascar are two prominent cases where males traveled over long distances and left a dominant genetic imprint (in the case of Madagascar the female lineages tend to be from the adjacent African continent).
* N = population size and m migration rate between populations.