December 8, 2012
to be posted on

Jeremy Grantham
Grantham Foundation for the protection of the Enviornment
Boston, Massachusetts

Dear Jeremy Grantham:
This is a fan letter so do not let it distract you from more important things.  I read with due alarm your article (Jeremy Grantham BE Persuasive.  Be Brave. Be Arrested (if necessary) NATURE vol. 401 nol. 7424 November 15, 2012 page 303).  I take it that our attitude toward environmental degradation should be more like panic and less like bemused silence.  As if to drive the point home, a couple of other articles in the same issue (Thinning Ice More Fragile and Mobile on page 304 and Killer Fungus Claims UK Ash Trees) add to the impression, were more input needed.  Thank you for your efforts.  All I have to offer is this mention on my own web site.

In a manner of speaking, we have been trying to lift both ends of the same piano.  The obvious fact is that there must be a balance between what humans need and what the environment can support.  But things are worse than that.  The environment is not only finite; it is unstable.  That makes the future hazardous beyond reckoning.  In order to achieve anything like stability, what we put into the environment must be well within the world’s ability to digest it and what we take out must be renewable.  Everything else will need to be recycled.  Obviously there is much to be done.

My own issue is the population size.  Alas, that, too, is not just excessive, it is unstable.  Most people probably carry a little equation around in their heads:

((Men + women X sex) – birth control) X average life expectancy = population. 

That seems pretty good.  Birth rates are lowest in the rich world, where birth control is most available.  And birth control seems to be the one factor one can tamper with.  But birth rates in the rich world are not just low; for a generation they have been unsustainably low.  And in the poor world they are unsustainably high.  So the situation is dynamically unstable.  Even if the environment could be stabilized, things would remain out of hand.

The problem is that the equation appears to be wrong.  The evidence is quite massive.  Birth rate appears to be a consequence of consanguinity; birth control only permits people to do pleasantly what they were going to do anyway. 

Before I introduce the published evidence and try to trace out the implications, let me hasten to agree on one point.  The environment is more important than people.  Were the environment to degrade to the point that it could not sustain intelligent life, we would go extinct.  Were we to go extinct and leave behind an acceptable environment that environment might produce intelligent life again; it did so before.  So at the extreme, environment trumps population.  Of course neither of the dire events seems plausible, but when things are unstable unexpected things can happen. 

Here are my best references:

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

An Association between Kinship and Fertility of Human Couples Agnar Helgason et al. SCIENCE vol. 329 no. 5864 February 8, 2008 page 813 – 816

Human Fertility Increases with marital radius. Rodrigo Labouriau and António Amorim.  GENETICS volume 178 January 2008 page 603

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

Were some kind spirit to move you sufficiently, and I do not expect it, you might look at least at the Helgason article.  In it the authors graph consanguinity against birth rate, both children and grandchildren.  Their birth rate is “normalized,” meaning it is compared with the average for Iceland at the time.  They calculated consanguinity by going back in the exhaustive Icelandic genealogy for 10 generations and then translating into second cousin or closer, third cousin or closer and so forth.  So what they show does not really translate exactly to comparing degree of cousin with number of children, but they are the best game in town.  What follows is approiximate.

It appears that for children, the greater the consanguinity the more children.  The error bars are so tight that it seems no other factor is effective.  As consanguinity drops so does fertility and then it levels off. 

For grand children it is more complicated.  At high levels of consanguinity there is low reproductive success.  Reproductive success rises as consanguinity falls, then levels off, then falls, then levels off again.

Alas the study does not investigate the third generation.  From what I can tell, things get more extreme there but let us stick with the devil we know.

People tend to express everything they think about consanguinity in terms of “inbreeding,” which is destructive by definition.  A few brave souls will also refer to “outbreeding,” by which they tend to mean “no inbreeding.”  Patrick Bateson has gone so far as to coin the phrase “optimal outbreeding,” by which he means an optimal balance.  For instance the best immune system depends on something called the “major histocompatibility group complex.”  With either too much consanguinity or too little, the immune system is compromised. 

But from what I see (and I have been groping my way toward this for a long time) there are in fact five biologically distinct degrees of consanguinity.  Here’s what I mean. 

If average consanguinity is close to sibling marriage, there is inbreeding and the population is unstable. 

If average consanguinity is a bit past first cousin marriage, there is a degree of inbreeding depression and the number of grandchildren is pretty close to two per couple.  The population is potentially stable.

If average consanguinity is about third cousin marriage, then the number of grandchildren is maximal.  This is Bateson’s “optimal outbreeding.  It is optimal in that it maximizes reproductive success but it is inherently unstable; no finite environment could sustain it indefinitely. 

If average consanguinity is about seventh cousin then fertility falls to just about sustainable.  This is stable again.  At this level of consanguintity there is no inbreeding depression.

If average consanguinity is about ninth cousin or more distant, then fertility falls below sustainable and the situation is again unstable.  This is what one might reasonably call “oubreeding.” 

Five levels of kinship: five biological outcomes.   Two of them are stable.  If you ran the zoo, you would prefer that regime that promises stability with no threat of inbreeding depression, but that is not the only winning strategy. 

Even this is a gross oversimplification.  As I said, available evidence suggests that the third generation is much more strongly depressed by outbreeding than is the second.  By generation five, unless consanguinity be restored by an extreme contraction of the local population, the dance – the jig – is probably over. 

Reaching a stable population would probably require as much effort as reaching a stable environment.  Again, thank you for what you are doing.  I sure wish there were more talent of your caliber on this side of the problem.


M. Linton Herbert MD 

There have been 73,061 visitors so far.

Home page