A Closer Look at the Numbers: I have said, and I’ll stick by it, that the results of the computer program should not be considered as the absolute numbers, but their pattern.

But it is interesting to look at the numbers from the model and compare them with the numbers from the Iceland study all the same. 

Where the model predicts a population of 5 will die out from inbreeding, the study does not go as low as first cousin marriages.  Since at equilibrium, a clutch of first cousins would number 4, their prudence and the program’s prediction match well.  But it is not so simple.  They have calculated relatedness by going back 10 generation and counting how many common ancestors the couple have.  By that approach, a population of 5 would all have the same ancestors.  So the match is imperfect but tantalizing.

Their best fertility in terms of grandchildren is at third and fourth cousins.  A clutch of third cousins would be 16 individuals and fourth cousins would number 32.  The maximal growth rate of the model is at a population size of 20.  So that fits, too. 

The maximum stability seems to be at about fifth or sixth cousins, meaning clutches of 64 and 128.  We did not test these levels, but a population of 200 seems to be very stable.  So again, acknowledging that the comparison is not perfect, the model seems to be right on the money. 

In the model, the statistics are not good and the line is not smooth as things become unstable, but the size of the population that just about is able to replace itself is somewhere around 600 or 800 just by eyeball.  In the Iceland study, that line is crossed around sixth or seventh cousins, or about 128 to 256 individuals in a clutch.  Stretching it, you might say that there is disagreement only by a factor of 2, but that is not so impressive.

Beyond that, populations are dwindling and unstable both in the model and in real life.

If you go out to a population size of 20,000 in the model, there is predictable extinction.  That number was not chosen at random.  Years ago I read a little blurb in a highly regarded journal that remarked that workers had done genetic studies in Iceland and determined the effective population size.  They expected that since Iceland was homogenous in its population that the size should be smaller than elsewhere.  They were disappointed because they found a population size of 20,000 (if I remember the words) “… just like everybody else.”  There was no reference, so I couldn’t use it as proof of anything, but two things struck me.  The first was that if “everybody,” and I assumed they meant every other rich nation, had the same population size, then that was proof of the principle right there.  In all the great cities the population had hit a ceiling above which it did not rise.  Now one of the basic assumptions of science is that if something always happens then it must happen.  It is a law of science even if there is no known mechanism.  But here, at least, it was clear that the explanation had to be genetic.  The second thing that struck me was that if I knew the information existed, I could find it.

I have done battle with PubMed, the search engine for medical and scientific studies, and have come home beaten and bowed.  I can’t find any reports of any effective population sizes anywhere.  I suspect that the information is out there, and a better searcher can find it. 

But I decided that I would model a population of 20,000.  The version of the program I had at the time did not go above, I think it was 2,000.  I got out my flensing knife (that was what they used to use to take blubber of whales) and streamlined the program until it would model a population that big.  And properly tweaked, that population fails when a population of 200 does fine. 

But that leaves a problem.  Civilizations take about 10 generations from takeoff to collapse.  A farming community or band of hunter-gatherers tends to be about 200.  If you are building a great city starting with rural people in villages with an effective population size of 200, you gather many such populations and let them mate at random.  The effective population size should double every generation.  Double a number 10 times and the result is 1,024 times your original number, or about 1,000 times it.  So we ought to be seeing effective population sizes of about 200,000.  Instead, populations don’t appear to go over 20,000 effective, even though cities have populations in the millions. 

The implication is that the effective population of a small village is in fact a great deal smaller than the actual number who live there even after the situation has equilibrated over a very long time.

On the other hand, the critical number may not be the average population size but the range.  As a successful population begins to lose fertility because of excess genetic size and diversity, those that already started out with the highest rate of outbreeding should vanish first, followed in later generations by those who had less and less.  The final offspring should be descendants of those who started out with the smallest effective population size.  That might not be far from twenty.  It would be interesting to see the numbers pertaining to effective genetic population sizes both in great cities and in tiny subsistence bands.

So far the numbers look close enough to reality to be intriguing.  With such a crude model so severely limited by available computing power, the surprise is that the model’s numbers are even in the right ballpark. 

But the match is not as good as I have suggested so far.  If indeed all urban population sizes are about 20,000, and since urban populations are known to be infertile and fertility is getting worse, that ceiling becomes the most important number it history.  In fact, by and large it has determined history.  A look back at the survival record of civilizations suggests that there is not much else going on.  A society simply flourishes until it reaches the forbidden limit and then collapses.  And the model predicts that it should collapse.  The difficulty is this:  I did a series of runs in which I limited the population to 10,000 instead of 20,000.  They all went extinct after surviving 91, 83, 167, 89, 195, 250, 573, 81, 163 and 78 generations. 

So far as the program with these particular parameters can predict, there is nothing magical about the number 20,000.  But populations can last the test distance if restricted to 2,000, so perhaps we are within an order of magnitude of being right after all. 

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