Heterogeneity suppresses recombination:
There is a trend in our historical data we have been ignoring so far, and there is a well known genetic fact that we have not mentioned along with a fairly obscure one. When we try to reconcile the three facts, we shall find it is not quite straightforward. The obscure fact will not be of much use to us.
The trend is that as a civilization (or a regime or a dynasty or a historical period or however you wish to characterize an urbanized population) approaches its 300th birthday, it faces a precipitous decline of its chance of surviving farther. We have seen this graphed a few times. Generally I tend to describe the descent (and to think of it) as inherently linear. It looks like a combination of a linear drop, in which new civilizations are recruited at random with respect to their history of urbanization, and a squared drop, in which the chance of surviving stays very high for about 300 years and then drops straight down, which implies that the new civilization (or dynasty or whatever) always begins with a population of village people, peasants, primary producers or however you wish to characterize a population with a restricted mating pool size.
This average of two effects accounts quite satisfactorily for the curves we have seen, but at a casual glance the averaging is just a little bit too good. The shape of the curve in the Mesopotamian experience, the Egyptian experience and the pooled Roman, Mayan and Chacoan experience looks too similar to be a coincidence. It might be coincidence, but it makes one suspicious.
So here is the well known genetic fact. There is something called “recombination” or “crossing over.” I use the terms interchangeably. Since recombination will interest us in the future, I shall describe it now,
Consider 9 genes (in the most general sense of bits of DNA) lined up together on a chromosome. We have two versions of most of our chromosomes. These will be what we consider. Let us say that the genes line up on the two chromosomes like this, sketched parallel to each other.
1,2,3,4,5,6,7,8,9.
1,2,3,4,5,6,7,8,9.
As one begins to talk about genes and chromosomes, one is generally careful not to be offensive to anybody’s politics. So we will go straight to a political analogy. We will say that every gene has three forms: a Republican form, a Democratic form and an anarchist form, which we will represent as red, blue and black. Technically speaking the “1” represents a locus on the chromosomes and the red 1 is a republican allele, the blue 1 the democratic allele and the black 1 the anarchist allele, any of which can reside at the 1 locus. So here are our original pure lines of Republican, Democrat and Anarchist: (These are only names, of course. The same arrangement would also apply in non-political animals.)
1,2,3,4,5,6,7,8,9.
1,2,3,4,5,6,7,8,9.
1,2,3,4,5,6,7,8,9.
1,2,3,4,5,6,7,8,9.
1,2,3,4,5,6,7,8,9.
1,2,3,4,5,6,7,8,9.
Now suppose we have a mating between a Democrat and a Republican. The offspring gets one chromosome from each parent so that offspring has a pair of chromosomes that look like this:
1,2,3,4,5,6,7,8,9.
1,2,3,4,5,6,7,8,9.
We take it as axiomatic that genes are fine tuned to each other. So let us suppose that the red 1 allele is tuned to the red 9 allele but not necessarily to the blue 9 allele. The blue 1 allele is tuned to the blue 9 allele.
Initially there should be no problem. Each allele is on a chromosome to which it has been tuned and although the result may be slightly less advantageous than the straight Republican scheme or the straight Democratic scheme, it ought to work out all right.
But sometimes, during one pair of cell divisions per generation, (dubbed meiosis) the chromosomes get together while preparing to form gametes and actually to approach each other intimately, twisting around each other. When that happens, they can break and rejoin. The event is called recombination and the result looks like this:
1,2,3,4,5,6,7,8,9.
1,2,3,4,5,6,7,8,9.
Of course if this event happened when both chromosomes were straight Democrat or straight republican, there would be no change to notice.
Each chromosome goes to a different gamete. If that chromosome is passed to the next generation, and the matching (homologous) chromosome is straight republican, the result is this:
1,2,3,4,5,6,7,8,9.
1,2,3,4,5,6,7,8,9.
We have one matched pair of red 1 and 9, and an unmatched pair of red 1 and blue 9.
If we cross a Democrat with an anarchist, we could get – after a recombination event – this:
1,2,3,4,5,6,7,8,9.
And if that chromosome gets paired with one from the first recombination event, we could get this:
1,2,3,4,5,6,7,8,9.
1,2,3,4,5,6,7,8,9.
Now nothing matches. So because of recombination, the detuning process can accumulate over a number of generations.
The obscure genetic fact, so obscure that I find it hard to put my hand to the reference, but no matter, this is going to be a futile exercise anyway, is that heterogeneity suppresses recombination.
In other words this pair of DNA lengths:
1,2,3,4,5,6,7,8,9.
1,2,3,4,5,6,7,8,9.
is less likely to undergo a recombination event than this pair:
1,2,3,4,5,6,7,8,9.
1,2,3,4,5,6,7,8,9.
Now it turns out to be the case that having genes strung together on chromosomes permits an organism to endure a greater number of mutations each generation than if the genes were all sorting out at random. So if heterogeneity reduces crossing over, it has the chance to improve the organism’s resistance to further mutation. That would be a lucky good thing. And in that case, the curve of the survival of a population (or the persistence of a historical political regime) should improve somewhat with time. In other words, this effect would produce just the opposite curve from what we see.
Besides, the curve tends to level off as fertility drops in the computer model, and the computer model does not permit any recombination at all. So the curve of fertility against population density in animals and so forth is accounted for already without invoking recombination being suppressed by heterogeneity.
Recombination may be important, but it appears that suppressing recombination with heterogeneity is not. For now I just wanted to take a moment to describe recombination or crossing over in case you slept through that part of your high school biology class.
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