## And now for something completely different.

02/26/2012

I'll continue with the "Skiing Black Diamond Down Demographic Trails" series next week. This week, I'm changing gears.

For the past 20 years or so, scientists have used sophisticated mathematical models to demonstrate unity among three, previously separate fields: demography, population genetics, and cultural anthropology. Reams and reams of peer-reviewed paper with meaningful Greek symbols and mathematical operators on them show that that the manner in which ideas and social norms are transmitted between minds--that is, culture--is analogous to the way genes are transmitted among organisms.  What's more, the two transmission mechanisms can influence one another.

For these reasons, you can study the evolutionary fates of ideas using similar mathematical tools as you would to study the fates of genes or species. These tools employ demographic measures at their base. Sweet, right? So I was fresh out of being indoctrinated into this dual-inheritance way of thinking when I took a course in formal demography.

One thing I learned in that class is that, unless all mothers in a population complete their reproductive careers with the same number of children, you will always calculate a smaller average family size when asking post-menopausal mothers about the number of children they've had than if you had asked their children about how many kids their moms had. Here's a good reference by one of the authors of my demography course's textbook.

People use this fact to warn against collecting data from offspring about their parents' completed fertility, or to devise means of correcting it. Others note that the two measures have different social effects. I think this bias might also be significant to the cultural transmission of family size norms and the evolution of some reproductive behaviors.
"Oh, okay, I see where you're goi--whaaaaaaaaaa?"

I'll explain, starting with the reason for the bias. Say you've got two mothers, a blue one and a green one. The blue mother has three blue babies because she just loves children. The green mother is like, "Ef that," and sticks with one.
Compute the average number of babies per mother. You should get 2 as your answer. So the average family size from the moms' "perspectives" is two babies.

Okay. Now let's let the babies grow up and ask them how many babies their moms had.
Look at 'em. All grown up!
Now compute the average number of babies in the thought bubbles above to get the average family size from the kids' "perspectives". The answer is 2.5 kids on average, half a kid more than we calculated from the moms' "perspectives". Might not sound like much, but in developed countries, 2 children per woman would eventually lead to population decline (curious why?) while 2.5 kids per woman is significantly higher than any national total fertility rate recorded in the United States since the Baby Boom ended and The Pill began. So demographically speaking, the difference is huge.

Now let's compare the two images to see what's going on:
Three blue babies got to grow up and say their mom had three babies, but only one green baby grew up to say her mom had one baby. The family size of the blue family is sampled three times, but the family size of the green family is sampled only once.

So the general problem is that when you ask kids about their family size, you oversample the bigger families. There's a formal mathematical relationship between the two calculated family sizes:
 (nifty formula 1)
The "C" with a bar over it is the average family size from the kids' "perspectives", the "P" with a bar over it is the same but from the moms' "perspectives", and the squiggly thing with a two over it is  variance in the moms' average family size. For a bonus point, you can check and see if the formula works in my simple example.

It's clear  from nifty formula 1 above that the greater the variance in the number of kids a woman has (that is, the more diverse family size is from the mothers' "perspectives"), the greater the difference between the two "perspectives". Only if there is no variance (i.e., all women have the same number of children) are the two calculations the same.

Okay, now that we've got the basics down, just what the Hell does any of this have to do with cultural transmission, much less the evolution of reproductive behavior? I don't really know yet, but I have some half-cocked ideas that I hope will provoke discussion. Here is one of them. Another will come soon, but it is even less ripe than...

## ...half-cocked idea #1: cultural transmission

Scholars of cultural transmission have defined types of cultural transmission in relation to the generations to which the senders and recipients of cultural information belong. Vertical transmission is when ideas pass between parents and offspring. We usually assume transmission from parent to offspring, but obviously the opposite can happen, too (but not likely when it comes to completed family size!). Oblique transmission is the passing of ideas between any member of the parent generation and any member of the offspring generation. Horizontal transmission is the passing of ideas within the same generation. There are other types of cultural transmission, and heated debates about whether these categories are meaningful. Let's ignore them for now.

Cultural transmission theory also distinguishes between two types of learning: social learning, which is basically a dependence upon culturally transmitted ideas, and individual learning. In this case, when I talk about individual learning, I mean individual sampling of a local social norm regarding family size by observing the number of kids people have.

Okay. Suppose that people's reproductive decisions (thus their completed family size) depends in part on their perception of the normal (i.e., average) family size. Perhaps knowledge of this average family size is a cue about the quality of the environment. Most people aren't demographers, and certainly nobody was a demographer 200 thousand years ago. Group sizes were small in the distant past, so maybe you could just get a sense of the normal family size by looking around. But perhaps one would benefit more by having knowledge of family sizes in other groups to get a better estimate of the quality of the environment, which makes the count more labor-intensive. Furthermore, evolution did not stop 12 thousand years ago, when groups became larger as people became more sedentary. Who has time to sit down and count babies?

(Answer: human behavioral ecologists...sorry, it's an old joke about my own discipline.)

So, if you want to know about the average family size, you'd best utilize several sources of information: your own observations of yours and others' family sizes (individual learning), and information you get from others (social learning). The degree to which you depend on individual versus social learning depends on the costs of social learning, so the peer-reviewed literature says.

If you depended only on individual learning, and assuming you randomly sampled your observations of people's family sizes, you would have an unbiased estimate of average family size.

What if you relied solely on social learning? If your social learning relied solely on vertical transmission, you would have have an estimate of average family size biased toward the size of your own family. If you relied solely on oblique transmission, you would again have an unbiased measure because you'd be randomly sampling from the parent generation. Yet if you relied solely on horizontal transmission, you would overestimate average family size because, as in my simple example, you'd over-sample large families.

So if natural selection could independently tune the squelches on each of these types of social learning and modes of cultural transmission, and if an accurate estimate of average family size promotes evolutionary fitness, then you would expect humans to favor a mixture of oblique transmission and individual learning. The degree of individual versus social learning would again depend on the cost of individual learning.

There is, however, reason to believe that there are limits to the fine-tuning that natural selection will allow. Learning is a complex trait, especially in humans. While flexible, it is also general. We use it for many tasks every day, and we have a finite amount of energy to spend on optimizing the way we learn to each and every context. In addition, humans tend to socialize within age groups. Paired with the fact that individual learning is costly, our general reliance on social learning within peer groups might infect our estimate of average family size with the bias I discussed above...another example of how cultural transmission can lead to maladaptive behavior.

I'll talk about my other half-cocked idea soon, which applies to the family size bias problem and the evolution of reproductive behaviors. For now...

## What?

My n of 3 tells the true (and sometimes fictional) story of an anthropologist and Fulbrighter who (kind of) became what his doctoral dissertation is about: a migrant trying to maintain his ties with family back home. This is a dissertation blog that often lapses into current science news commentary and coverage of various side projects.

## Who?

Brash Equilibrium's is a Phd student in anthropology at the University of Washington. His real name is Benjamin Chabot-Hanowell. He lives with his wife, daughter, mother-in-law, and brother-in-law in Seattle. He's also the creator of Malark-O-Meter, which statistically analyzes fact checker rulings to make comparative judgments about the factuality of politicians, and to measure uncertainty in those judgments.