August 17, 2011
Open letter to be posted on

Ronald Lee
Department of Demography
University of California at Berkeley
2232 Piedmont Avenue
Berkeley, California 94720

Dear Ronald Lee:

I read with care your excellent piece on future population growth.  (Ronald Lee, The Outlook for Population Growth SCIENCE vol. 333 no. 6042 July, 29, 2011 page 569)  You call for a grand theory of demographics.   Let me give you one.  This might be kind of fun.  If it’s not fun, skip down to the evidence.  Elements of the theory are: 1) Evolution has been around a long time.  2) Evolution cannot go far without speciation.  2) If two populations are separated for 2,000 years, when brought back to together they will not have adequately fertile offspring or the line will die out from hybrid breakdown.  (Actual number is negotiable but not by much.)  3) A chromosome or a part of a chromosome is represented twice in an individual (not considering sex chromosomes.)  4) There are 2,000 chromosomes of each type in a population of 1,000.  5) On average, two sibling chromosomes will take 2,000 generations to get back together.  6) So far as their function is concerned, it is the same as if the populations were separated; no fully fertile offspring or hybrid breakdown ensues.  7) Since this is true of every chromosome in every individual in the population, the whole population dies.  8) 2,000 generations is a long time; it is improbable that the local population can be kept in air tight isolation so long, so the whole species faces the same problem and is in danger of extinction.  9) Although 2,000 generations is a long time for an individual, it is not a very long time for evolution.  10) Evolution must then have developed a fix.  11) For the fix to work, a running census of the population must be maintained and the population be eliminated before it reaches 1,000.  12) If an individual has no shared ancestors back for 10 generations, the ceiling has been breached and that individual must be effectively eliminated, usually along with the rest of the population, since they are all in the same situation.  13) So there must be some mechanism which evaluates the kinship of a couple and denies them normal fertility if that kinship is insufficient, that is if the 1,000 ancestor rule has been violated.  14) If the details of the effect are known, and if the mating selection strategy and size of any population is known, it is possible to predict fertility generations before the event.  15) Arguing only from first principles, the infertility could be pre-zygotic, post-zygotic or both.  Only looking at evidence regarding a particular species can tell.  16)  10 generations is fairly long, but is far too fast for DNA mutations to be the mechanism of infertility.  17) If it is not DNA (that is genes) the mechanism must be epigenetic which can be faster.  18) The most commonly found epigenetic mechanism is methylation of DNA, which suppresses the function of the relevant gene, if there is one.  19) In vitro fertilization causes a degree of demethylation. 20) Therefore in vitro fertilization should be expected to run afoul of the census protocol, masking kinship even if it should exist.  21) In vitro fertilization bypasses any pre-zygotic control, but if there is a post-zygotic element, the offspring should be even less fertile than the parents, who were already too infertile to achieve pregnancy by ordinary means.  22) Offspring of in vitro fertilization should be expected to be absolutely infertile even by in vitro fertilization.  23) Such offspring should be counted in any attempt to estimate birth rate and be eliminated from any projected descendant population. 

Now tell me that wasn’t fun.


There is a great deal of evidence in support, which I have piled up on my web site  However at this point there is one crucial paper that gives the details of the relationship between kinship and fertility in humans, as in “14” above.

The study was done in Iceland and compared kinship with fertility in both the first generation


and the second generation.

An Association Between Kinship And Fertility of Human Couples.  Agnar Helgason, Snaebjoern Palsson, Daniel F. Guobjartsson, Pordur Kristjansson and Karl Stefanson, SCIENCE vol 329 8 February 2008 page 813 figure 3 C. 

Obviously the relationship between kinship and fertility is very strong.  Those error bars are two standard deviations.  There is essentially room for nothing else, since most of the variability in the second generation is accounted for by differences in the first generation, and most of the variation in the first generation is determined by prior generation.  The mechanism runs its census, makes its allocation, and that is that.

Next notice that there are obviously pre-zygotic effects and post-zygotic effects, and the intensity and shape are very similar except for very near relatives.  That goes along with in vitro fertilization outcomes.  Success, is about fifty percent.  The pre-zygotic mechanism is bypassed and the post-zygotic mechanism is untouched.  And sure enough, as would have to be the case, by the time you are out to ninth cousin, fertility is and has been below replacement. 

But some issues remain.  Compare those graphs with your own history of fertility in four populations.

Ronald Lee, The Outlook for Population Growth SCIENCE vol. 333 no. 6042 July, 29, 2011 figure 1.

For the most part it all makes sense.  In most of the world, people no longer marry kin so that in the least developed countries and in the most developed countries, Japan and Europe, fertility goes down like a brick.  What we see in India is the experience when villages and traditional mating strategies were very strong.  She does just fine.

But in Japan and in the most developed countries generally there is a trifling up tick not predicted by the Iceland studies.  I suspect this is due to in vitro fertilization and does not represent an authentic contribution to the population since one must expect them to be infertile as outlined in “16” through “23” above.  Convergence of fertility at 2.1 offspring per woman is either wishful thinking or worse. 

The other thing that is missing from the Iceland study is any hint of extinction.  The curve descends ominously at first but soon begins to level off, and by the time 8th cousin is reached is trolling along serenely at below replacement level, but not disastrously so.  One might be forgiven for thinking that there is no impending disaster.  We will just experience a genteel decline and then some day maybe have enough children for an enduring society.

But while fertility does fall below replacement before the tenth generation, in keeping with theory, we are looking for where extinction could be hiding.  The analysis does not go out past 8th cousins or 9 generations.  Maybe there is a further decline in the next couple of generations.  And just maybe there simply isn’t anybody out there 9th cousins to analyze.  Sure 8th cousins are having children, if very few, but that is 8th cousins or closer.  Maybe, but I don’t believe it.  Children of Montezuma married into noble Spanish families and their descendents survive in the present.  Spanish and New World lines had been separate for over a thousand generations.  If hybrid breakdown were going to have happened, it would long since have done so.  There must be something else going on.  I suspect post-zygotic infertility takes generations to accumulate.  A single shock can be accommodated if earlier and subsequent matings are prudent.  It is the sequential violation of the thousand member rule that is the danger.  This effect is not visible in the Iceland data we have.  The mechanism probably evaluates each of the couple; if each proves to be the product of 32 individuals, then the sum would only be 64, or roughly sixth cousins, which appears to be a viable combination. 

If you like, I can offer more evidence, or you can dig it out of the web site at your leisure.  But let me just offer one more graph now.  This is the survival experience of Mesopotamian empires. 

This oversimplifies matters, but there it is.  My how they topple as they approach 10 generations.  We sort of act as if history had just started and as if nothing in the past were going to be of importance in the future.  That doesn’t seem to be the case.  We are oozing down the usual siphon.

Let me know what you think. 

M. Linton Herbert MD

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