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August 19, 2004

Fear of a brown planet

A slight thought experiment, which I have alluded to before, but never been totally explicit about. Take a population, say 1,000 females of the black race and 1,000 males of the white race. Allow them to interact, isolated from the distractions of the outside world. In a few years, little brown children are born....

Moving into the world of 'make believe,' imagine that the phenotype 'white' is controlled by the same locus as the phenotype 'black.' One who expresses a black phenotype has the genotype BB while one who expresses the white genotype has the genotype bb. In the world of generation 1, blacks are jet black, while whites lack pigment at all (are albinos).

Assume that the density of melanin is proportional to the number copies of the B allele one carries. So, the density of melanin of blacks is 2x (1 copy of B is proportional to x), while for whites it is 0. In generation 2, all carry copies of both alleles. That is:

BB X bb = Bb, in that all matings were between a BB and bb individual in the parental generation.

Since density of melanin in the skin is proportional to the number of copies of B one carries, the generation 2 offspring are all 'brown,' fairer than their mothers, darker than their fathers.

So we live in a brown planet, right? Blacks and whites banished forever?

Not really. Assume random mating and Hardy-Weinberg proportions will quickly ensue (ignore random genetic drift and selection). That is, p2 + 2pq + q2. Since the allele frequencies are 50/50, about half of the population expresses the Bb phenotype, while 1/4 is homozygous for the black and white phenotypes (that is, p = .5 & q = .5, so, substitue into the equation above).

But let's throw in a twist, rule: like mates with like whenever possible after generation 1. That is, people who express the black phenotype marry other blacks, browns prefer browns and whites only pair up with whites.

In generation 2, this is a moot point, only browns exist, ergo, browns pair up with browns. But, in generation 3 whites and blacks will reappear as homozygous offspring of their heterozygous parents. Since like mates with like, blacks and whites will pair up with each other in generation 3. Since they are homozygous, they will have black and white offspring only.

The browns also prefer each other. Because they are heterozygous they will give birth to mostly heterozygous offspring (1/2 within the population of the children of brown parents). But they will also give birth to white and black children (1/4 of each).

Iterate.

The process (assortive mating) clearly mitigates against the perpetuation of brown people. Perhaps a mild form of this happened in Brazil in the recent past?

I say this because a team of Brazilian researchers suggested that the lineages of Brazilian whites were highly confounded with non-white Brazilians. That is, though both groups were of distinct phenotype, their ancestry was far less pure than physique might have suggested.

Going back to the world of make believe, in generation x, where x >> 1, if the rule I state holds, you have a population that has been cleaved into two. Yet, aside from the color locus, the two populations are equally white and black, though you wouldn't guess that from glancing at their butt cheeks.

No wonder such a simple idea like Mendelianism did not gain traction until well into the 20th century (see R. A. Fisher's seminal paper that showed how continuous traits emerged out of Mendelian principles, resolving the 'dispute' between the Mendelians and the biometricians). Human beings are the products of millions of years of evolution. We have predispositions and tendencies, and our fine pattern detection sensors come preloaded with biases shaped by our past. Everyone understands genetics on the intuitive level in what it does, the principle of heredity is an atomic & foundational element of human nature. It is expected that a mother and father should birth offspring that resemble them, we do not attain this position via reason, rather our own cognitive modules come loaded with a few basic understandings, triggered and molded by our experience.

That being said, we do not have an instinctive understanding of Mendelianism. Humans know what genetics does, but have little grasp of how it does it. People speak in broad inclusive typologies of race, tribe or family, but these are ultimately fuzzy emergent concepts fixed upon the reality that we are all but a commune of genes and their protein slaves.

In the EEA family and tribe were restricted in space, and genes were exchanged at a tepid pace, from hillock to valley and hillock over the generations. Today, a man born in Ghana can become Secreatary General of the United Nations and wed a Swedish woman. Granted, the majority of the human race does not consist of mobile cosmopolitans, but mobile cosmopolitans are an influential segment of humanity. Additionally, in places like Latin America one can see the impact of hundreds of years of mixing between lineages, indigenous and foreign.

We are slowly stepping outside the land of make believe. Our intuition might not always lead us to the right path, and the principles that we could neglect because the sun always rose in the east must now be examined with greater care and attention.

Posted by razib at 08:38 PM