Ignoring the 800lb Polygynous Ashkenazi Gorilla In the Room

In Natural History of Ashkenazi Intelligence G. Cochran, J. Hardy and H. Harpending write:

A selective force that only affects a tiny fraction of the population can never be strong enough to cause important evolutionary change in tens of generations.

Yes it can.

Our intrepid scientists have failed to recognize the 800lb alpha gorilla in the room:

Polygamy

There is extensive evidence of Jewish polygamy, or more precisely -- polygyny, throughout history up to and even after the proscription by Rabbi Gershom circa 1000AD. Moreover the ecologically imposed monogamy of northern Europe had long since given way to socially imposed monogamy of Christianity by the time the Ashkenazim definitively appear some hundreds of years before Gershom. The reason for this change from ecological to social imposition of monogamy can be easily seen in the change from monogamy to polygyny that characterizes the transition from hunter gatherer to agricultural societies: Caloric availability of agriculture removes the ecological restraints on polygyny.

How much more does the presence of urban centers, the specialized habitat of the Ashkenazim, concentrate caloric availability and hence the ecological support for polygyny?

The answer: For elites -- at least an order of magnitude.

Grain stores for transport and trade are concentrated most in urban centers hence the opportunity for elites to benefit from caloric availability far more than even neolithic farmers such as the Bantu's displacing the Saan and other hunter gatherers with a polygynous culture. (See Destro-Bisol G, Donati F, Coia V et al: Variation of female and male lineages in Sub-Saharan populations: the importance of sociocultural factors. Mol Biol Evol 2004; 21: 1673– 1682.)

Is it known what the harem sizes tended to be prior to the Ashkenazim proscription on polygynous practices?

Is it known over what time the Ashkenazim practiced polygyny among northern Europeans?

Is it known that they actually ceased practicing de facto polygyny (we must not lightly discount routes to fertility other than marriage) when they said? Although it is easy to accuse indigenous northern Europeans of mere hysteria, a common theme in antisemitism has been concern about one-way gene flow out of the Ashkenazim while maintaining the Ashkenazim lineages. How do we verify that this was mere hysteria rather than a reaction to de facto polygyny among the Ashkenazim?

Fortunately, we don't need to engage in debate of these questions -- we can answer them with a generalization of the technique used by Michael J. Wade and Stephen M. Schuster in Estimating the Strength of Sexual Selection from Y-Chromosome and Mitochondrial DNA Diversity (Evolution, 58(7), 2004, pp. 1613–1616). The generalization revolves around the fact that we know the mutation rate for the Y-Chromosome is high enough that we have reasonable temporal resolution on when various mutations appeared. From that we can have some idea of what the reproductive harem sizes were of the Ashkenazim elites through various points of time.

There are two questions left:

1. Who has the most detailed collection of Ashkenazim mtDNA and Y-Chromosome data?
   
2. Are those who have this collection, themselves Ashkenazim hence in a problematic ethnic position for doing this study?