Passing on your fertility to your kids

From the NY Times earlier this spring, a profile of a New York woman with an exceptional legacy:

WHEN Yitta Schwartz died last month at 93, she left behind 15 children, more than 200 grandchildren and so many great- and great-great-grandchildren that, by her familys count, she could claim perhaps 2,000 living descendants.

The story talks about her history and how she came to have such a large family. By itself, having 15 children would be unremarkable except that the children and grandchildren themselves all went on to have large families (“Like many Hasidim, Mrs. Schwartz considered bearing children as her tribute to God.”). After a couple of generations, it adds up to a lot of descendants.

I don’t think the story is all that unique. Within the United States there are many communities, like the Hutterites, Old Order Amish, and Hasidic Jews, where large family sizes are the norm. Probably hundreds of women on earth can claim more than a thousand living descendants, and thousands more have only to wait until they are old enough, while their children and grandchildren’s families continue to grow.

You can get there by having 10 children, each of which has 10, and each grandchild has 10 – that adds up to 1110, giving some extra for different generation times and losses. Of course, it’s a trick to live long enough to see the 1000 great-grandchildren, but the early ones should already have given you a fraction of your 10000 great-great-grandchildren.

What’s surprising here? Not the family sizes themselves – big families are common in most human populations. The high offspring numbers are not as apparent in populations that have high juvenile and infant mortality, but many pregnancies was the norm prior to the industrial transition.

No, what’s surprising about huge numbers of living descendants is the correlation between generations. In these cases, the correlation is driven by religion and various social proscriptions related to religious observance.

I often talk about models and real human population structures in my classes. One obviously unrealistic aspect of the Wright-Fisher population model is its reproductive variance. In the Wright-Fisher model, reproductive variance is binomial – every gene in an offspring population is equally likely to descend from each gene in the parental generation. In the model, it is possible – albeit extraordinarily unlikely – for a single parent to give rise to the entire offspring generation. That just can’t happen in a real population, certainly not in humans. The effect of that unrealistic assumption of the model is not great, however, because even in the model the chances have having more than 10 offspring, while possible in theory, are negligible. If anything, the Wright-Fisher model is too conservative about the variance of offspring number – real human populations have a non-negligible fraction of women who have 10 or more live births.

I get more concerned about other deficiencies of simple models, which are sometimes harder to deal with. One of those is the correlation of offspring number between generations. If there is even a slight correlation, women tending to have more children because they came from larger families, it has a major effect on the amount of inbreeding in the population.

You can think about it genealogically. Suppose you live in a small town with a few big families. The chances that you yourself were born into one of those big families is small. But if today’s big families tended to come from yesterday’s big families, with each generation we go back in time, it becomes more and more likely that one of your ancestors came from one of those big families. Still looking backward in time, your genealogy becomes captured by those big families, branch by branch. Since there are few big families in the town, once two or more lines of your ancestry trace to them, those lines will rapidly share a common ancestor. That’s inbreeding, from the perspective of your genealogy.

In small towns, that process isn’t inevitable because people move in from elsewhere. Most of the lines of your genealogy will probably come from other towns within a few generations. But if we consider the human species as a small town, well, there’s nowhere else to move in from. If the population structure of our species has included a strong correlation of offspring number between generations, it will have massively reduced our genetic variation.

Since we have low genetic variation as a species, you can see why this is potentially interesting.

Masatoshi Nei and Motoi Murata back in 1966 worked out a relation between intergenerational correlation in offspring number and effective population size. That’s before the days of computer models, for you simulation jocks out there. The “effective” size of a population, as I’ve noted here many times, is the one parameter of a Wright-Fisher model, as estimated from the genetic variation within a population. It’s a statement about how inbred the population looks, assuming that its evolution followed a random-mating model throughout its history. Now, that model is wrong in pretty much every interesting case, and so there are various mathematical transformations that attempt to account for the effects of different mating structures.

In the case of intergenerational correlation of offspring number, Nei and Murata derived an expression to predict the reduction of effective size to be expected from this correlation, assuming a model in which the variance in offspring number is distributed in a certain way. The solution isn’t general – if offspring number were distributed in some other way, the effect of the same measured correlation may be quite different. And in their model, they were concerned with the case where the correlation of offspring number is influenced by genes that determine fitness – in other words, genes under selection in the population. So it’s not a complete answer, but it’s a start.

Nei and Murata cited empirical data from several earlier studies that showed a correlation of 0.20 to 0.40 between generations of human offspring number. Under the assumption of their model, a correlation of 0.30 would causes a reduction of the effective size by roughly half.

That’s a big effect. We already expect a reduction of effective size compared to the census count of a human population, because human populations include many non-reproductive individuals – kids and postreproductive adults make up half to two-thirds of small-scale foragers. If big families have an additional effect of half, it means that the effective size of the population starts out at a fourth to a sixth the census count. So that an effective size of 10,000 really means 40,000 to 60,000 people on the ground.

Still low, but as one factor among many it may be very important – and possibly the distribution of variance caused a further decline. It’s much worth investigation.

A correlation of offspring number between populations can be caused by many ecological or cultural factors. Nei and Murata (1966) had considered the case where fitness itself is inherited, because of the presence of selected genes. But in humans, a more pervasive force is cultural inheritance. This factor was discussed in 1976 by the demographer Samuel Preston, attending to the importance of cultural preferences in contemporary populations:

Since children of each generation are drawn disproportionately from families of women with high fertility achievements in the past, it may be expected that a pronatalist selective bias operates each generation with respect to the transmission of "tastes" for children. It has also been suggested that personality traits which may affect fertility achievement, such as the ability to defer gratification, may be transferred to some extent between parent and child (Kantner and Potter, 1954). It is also reasonable to suggest that biological fecundability is partially inherited. The positive correlation between the social classes of parent and child implies that economic constraints impinging on the childbearing process tend to be similar for the two generations (Preston 1976:110).

In small-scale societies, these forces are somewhat different. But I wouldn’t expect them to be less – indeed, the social competition between families is probably more intense. The entire “Macchiavellian intelligence” model of cognitive evolution implies that these kin-level effects were pervasive throughout human evolution over the past 2 million years or more. A strong cultural inheritance of fitness is really necessary for selection on genes that influence prosocial kin-related behaviors.

How intense? Seems like a good question to investigate, as it may have a lot of importance to understanding genetic variation in our ancestors – including our common ancestors with the Neandertals, whose genetic variation was limited just as much as our own.

On the subject of effective population size, I’ll be posting next week about chimpanzees and bonobos. More genetically variable than us? Well, some of them…

References:

Preston SH. 1976. Family sizes of children and family sizes of women. Demography 13:105-114.

Nei M, Murata M. 1966. Effective population size when fertility is inherited. Genet Res 8:257-260.