Family size is largest at the 4 and 5th cousin degree of separation

I have been doing a fair amount of genealogical research in the past five years, building on work done by my mother.  It is interesting history.

My mother's family is basically Puritan/Pilgrim with a later intermixing with Tidewater Virginians.  My father's is Tidewater Virginians and Scotch Irish with light roots in New England.  

The Pilgrims/Puritan record is much more complete than those in the Tidewater.

The size of all these families, Pilgrim/Puritan and Tidewater tended towards the 5-15 children.  Big families.  While the records are more complete for the Pilgrim/Puritans, their tendency to perpetuate first names in families combined with the size of those families means that by the third or fourth generation there are a lot of people with the same name in the same geographic area which is something of a challenge.   

An initial migration of some 20,000 people in perhaps 5,000 family units into a small geographic area across only about 20 years also means that there is an almost inherent high degree of consanguinity.  First cousin marriages were forbidden and second cousin marriages strongly discouraged.

However, researching in the 2020s back to families arriving in the 1620s-40s, you can't avoid seeing all the cross family connections.  I run across few instances of second cousin marriage but good grief, there are a lot of third and fourth cousin marriages.  Somehow they managed, in their scattered and small communities, to avoid those first and second cousin marriages but perforce virtually every family was related by marriage to every other family.  

For social and genetic purposes, third and fourth cousins are essentially strangers.  The probability of a person today knowing their own second-cousins is close to zero much less their third and fourth cousins.  

Historians almost uniformly attribute the large Puritan family sizes (compared to their peers in Britain) to cultural values and the assumption that life in low density New England was healthier and the land more fertile and therefore farmers more prosperous.  And those factors are true and probably most of the story.  

However, I came across this research suggesting that it might not be the whole story.  From An Association Between the Kinship and Fertility of Human Couples by Agnar Helgason, Snæbjörn Pálsson, Daníel F. Guðbjartsson, Þórður Kristjánsson and Kári Stefánsson.  From the Abstract (emphasis added):

Previous studies have reported that related human couples tend to produce more children than unrelated couples but have been unable to determine whether this difference is biological or stems from socioeconomic variables. Our results, drawn from all known couples of the Icelandic population born between 1800 and 1965, show a significant positive association between kinship and fertility, with the greatest reproductive success observed for couples related at the level of third and fourth cousins. Owing to the relative socioeconomic homogeneity of Icelanders, and the observation of highly significant differences in the fertility of couples separated by very fine intervals of kinship, we conclude that this association is likely to have a biological basis.

Perhaps, in addition to lower density and higher prosperity among the Puritan settlers, there is now a further explanation for large Puritan family sizes.  By the 5 and 6th generation of Puritans, most Puritans in North America were 3-4th cousins of one another.  Sufficiently different from one another to be social and genetic strangers but sufficiently close to optimize large families as reflected in the Icelandic research.