Benjamin W. Domingue
Institute of Behavioral Science and
1440 15th St, Boulder, CO 80309
Dear Sir:
Please find enclosed a DVD (Windows 10 Word) with three files, one a video and the others my accumulated references on fertility and kinship in 2 different formats.  A friend who knows my interest in kinship/population size – fertility/infertility recommended “Genetic and educational assortative mating among US adults,” and I have read it with great interest.  I take it that when you say, regarding genetic assortative mating (GAM), “several different approaches have converged on an estimate of residual GAM between 0.02 and 0.03” which makes me think somewhere around 0.025 would be an acceptable guess and it appears from the Helgason study in Iceland (remember, references on that disc), that would indicate an average kinship on the order of 9th cousin or closer, which implies a fertility of less than replacement.
Herein lies, I think, an opportunity you may like.  You exclude non-whites and non-straight couples, which of course affect the impact of the kinship you have measured on the general population; immigrants have a precipitous decline in fertility over their first few generations.  I understand that the Hispanic fertility in Los Angeles county is already below replacement.  Survival appears to depend on the choices of the majority.  Helgason makes it clear that generally the closer the kinship of a couple the more children and grandchildren they have.  His data admit little effect on fertility of anything but kinship.  This is made explicit in the Laboraou study in Denmark.
You’ll have to do some reading and put up with a lot of handwaving, but the evidence is that the driver of kinship enhanced fertility is not genetic but epigenetic.  And there is your prize.  The DVD has evidence that fertility/infertility is epigenetic, but you don’t need me.  The Sibly curve of kinship/population size against fertility/infertility shows that it should be possible for a population size to oscillate around a balance point while the European vole study shows that actually happening.
You have already done the hard work.  You have a defined population of couples and their kinship by shared genes.  Split them into generations as the Iceland study does and compare the actual number of babies with what you would expect.  The Iceland study show fertility “normalized,” compared with the country as a whole.  For many years Iceland has been pretty close to the replacement number of 2.1 children per women so their zero level should be about there, but you might want to check with Helgason to be sure.
Now you can compare the fertility predicted by the Iceland data with what actually happened – I’m sure fertility is in your data base.  If the numbers are identical, then you can be assured that the fertility of your couples is due to real – genealogical – kinship.  If the number of actual babies is less than predicted, then the difference is, as you suggest, due to mutual attraction by shared genes.  Of course epigenetic differences could be visible somatic difference, and that is a limitation.
The more-than-expected marriage between kin falls right in line with Bateson study of Japanese quail attraction, and the last time I checked Wikipedia on Bateson, he was quite aware that this enhanced fertility. 
So there is a paper for you at the cost of a couple of hours with pen and envelope.  Who can afford to write grant proposals, eh.
One favor I ask.  If I have misinterpreted your paper, do let me know.  I am likely to quote you and I don’t want to use your name in vain.

Linton Herbert MD. 

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