August 27, 2012
to be posted on

Peter Turchin
University of Connecticut
75 N. Eagleville Road, U-43
Storrs, CT 06269-3043
(860) 486-3603
Fax: (860) 486-6364

Dear Peter Turchin:
I read the recent article about you (Laura Spinney History as Science NATURE vol. 488 no. 7409 page 24 August 2, 2012) and had to resist shouting “Yes!  Yes!”  Our paths have been quite divergent, I studying and practicing medicine and arriving at mathematical modeling of population fertility and history by an indirect approach and you taking an interest through more traditional channels, with appropriate credentials, at least one colleague and publications. 

Of course we differ on important points.  But we do agree that this is important stuff.  I suspect (indeed I would stake my on life it, but not my good manners) that population growth follows mating strategy.  As there is an ideal degree of diversity for the major histocompatibility group complex – too much diversity is bad for the immune system as is too little – so there is a degree of diversity for high fertility.  Since I have been working on this, a few papers have emerged that establish this particular point I think beyond reasonable doubt. 

(On the Regulation of Populations of Mammals, Birds, Fish and Insects, Richard M. Sibly, Daniel Barker, Michael C. Denham, Jim Hope and Mark Pagel SCIENCE vol. 309 July 22, 2005 page 609 AND An Association between Kinship and Fertility of Human Couples Agnar Helgason et al. SCIENCE vol. 329 no. 5864 February 8, 2008 page 813 – 816 AND Human Fertility Increases with marital radius. Rodrigo Labourian and Antonio Amorim.  GENETICS volume 178 January 2008 page 603 AND Comment on “An Association Between the Kinship and Fertility of Human Couples,” Rodrigo Labouriau and António Amorim SCIENCE vol. 322, page 1634b December 12, 2008)

The references of course are beginning to drop off the edge of the five year cliff, after which people are unimpressed.  Sorry about that.

So taking it from the top I cite the work of Robin Fox, most recently in the Tribal Imagination, but as an abiding topic ever since he burst onto the scene with Kinship and Marriage, throughout almost all of history just about everybody married kin, pretty much at the degree called by Patrick Bateman “optimal outbreeding,” which is pretty close to inbreeding. 

So there were lots of babies, were it for good or ill, but overall successful in a pre-industrial society.

So we introduce the city.  The urban environment is not conducive to the kind of marital discipline that can be enforced (and I’m sure it is usually quite onerous) in a tiny village or band.  Generally I think people have been happy with this.  The down side is, of course, that eventually the population is far from optimal outbreeding and fertility declines.

I have suspected that unrest – wars or regime changes – have occurred during times of falling birth rate.  I think you have noticed the same thing, arriving at the conclusion that there is a phase difference: a dense population predisposes to warfare but after a delay. 

What I do know is that regime changes alone follow a stereotyped pattern.  Here is a graph of the experience of Mesopotamian civilizations.  I divided the Ottoman Empire into two phases when then method of recruiting Janissaries changed.  After all, we are talking about populations.

graph shows empires dying more as they age
Information taken from R. H. Carling THE WORLD HISTORY CHART International Timeline Inc. Vienna, VA 1985.  The experience of Southern Mesopotamia.  The vertical axis is The chance of an empire of any age continuing to rule locally for another 50 years.  The horizontal axis is the ages of the empires. 
I think that’s pretty good for being predictable.  If what took out a civilization was a characteristic of a civilization, the line should go up at some point because of selective effects.  If civilizations fell because of climate change or other outside forces, the line would be horizontal.  The line goes down, so the culprit is neither inside the population nor outside of it.  It can only be the fact of a big population.  Falling fertility would do it, wouldn’t it?  And there would be a lag between peak population and unrest.  The elite, the administrators, the guys who make things work have the broadest social horizon.  Lose them and the society collapses. 
There is more information at
But you get the general picture. 
According to the article, you have found a cycle of civil unrest in America.  So we are in agreement with the existence of cycles.  I have cudgeled my brain, but I cannot come up with a fifty year cycle.  So your data require more explanation than I can offer. 
And a serious weakness of my model is that I cannot identify a starting point.  The end is easy.  It’s a regime change.  They line up all the old elite and liquidate them.  Blessedly this did not happen in Russia with the end of communism, but it happened at the beginning.  Everyone remembers the Terror of the French Revolution. 
Clearly there is a sort of brick wall as a civilization reaches 300 years.  So it is probably about ten generations from leaving the village structure and founding an urban culture.  That would mean a maximum population of about a thousand before trouble sets in.  Looking at the decline of fertility with kinship in the Helgason study, nature puts the breaks on the population by the time kinship falls that low.  So it all kind of works out.  But it still leaves the question of how you identify the start.  Would it be 1776 for America? 
If so, the end should come in 2076.  I imagine that the end is reached when the society – at least the administrative segment – consists only of people over fifty.  So the last baby born to the original population of the United States would be close to 2026 or 14 years from now.  If the mother of that last baby were going to be 40, she would be 26 by now and have no offspring.  We would have noticed that, for sure.  So that doesn’t seem to be the time we would be looking at for a regime change based on infertility.  The soonest it would come would be if the youngest mother to be were 12, where there are not that many pregnancies anyway.  Would leave the last baby being born in 2050 and collapse occurring toward the end of the century.
You have looked carefully, and I think brilliantly, at civil unrest and find a 50 year cycle expected to recur in 2020.  I do not challenge your prediction.  I think my own idea just does not apply.  But I thought that since you are interested in population dynamics and history, you’d like to see my evidence.  As I said, the relationship between kinship and fertility is established.  What nobody has done in print is say, “Hey.  If this happens to everybody, then it happens to the whole population, doesn’t it?”  I don’t see why that leap is difficult, but apparently it is.

M. Linton Herbert MD 

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