September 14, 2009
Marten Sheffer
Department of Environmental Sciences
Wageningen University
PO Box 47
6700 Wageningen
The Netherlands
Dear Marten Sheffer:
I read Early-warning signals for critical transitions, Marten Scheffer, Jordi Bascompte, William A. Brock, Victor Brovkin, Stephen R. Carpenter, Vasilis Dakos, Hermann Held, Egbert H. van Nes, Max Rietkerk and George Sugihara, NATURE vol. 461 no. 7260 September 3, 2009 page 53 with great interest. I am hoping to interest you in another kind of crisis, and in fact I am putting this letter on my web site nobabies.net in case anybody else cares to think about it, but your team seems the best qualified.
You point out very astutely that there can be early warning signs that a system which is in equilibrium is close to changing abruptly to another equilibrium, including such observations that the endangered system recovers more slowly from a small perturbation than it would if it were at a safe distance from a tipping point and a large and non-reversing change.
I am sure everybody has his own impending crisis to worry about. In fact it was refreshing to read your measured approach. It was sort of, “Some crises are more critical than others, and if you keep your composure you may be able to tell them apart.” So I am hoping you will worry about this one.
The issue is that the fertility of a couple, or the growth rate of a population, depends on the kinship of the couple, which is as much as to say the size of the population. In fact it appears in humans to depend on very little else. And the same curve, relating kinship with fertility, has been found in human and animal populations as the norm. (1 On the Regulation of Populations of Mammals, Birds, Fish, and Insects. Richard M. Sibly, Daniel Barker, Michael C. Denham, Jim Hone, Mark Pagel SCIENCE VOL 309 22 JULY 2005 page 609
2 An Association between Kinship And Fertility of Human couples Agnar Helgason, Snaedbjoern Palsson, Daniel F. Guobjartsson, Pordur Kristjansson and Karl Stefanson, SCIENCE vol 319 8 February 2008 page 813
3 Comment on “An Association Between the Kinship and Fertility of Human Couples,” Rodrigo Labourai and António Amorim, SCIENCE vol 322 12December 2008 page 1634b)
The curve always looks about like this. In the vicinity of A it is a small inbred population with low fertility. (The drawing is crude. The line actually should continue to drop down and to the left.) Here the population is in crisis. As you say, a small change in the population downward will recover slowly because fertility is low. If the population falls far enough so that fertility drops below the break even level, the population will in all likelihood crash and go extinct.
In the vicinity of B, there is a region, or as you say a basin, of stability. If the population rises, fertility falls and the population moves back toward B. If the population falls, there is a rapid rise in fertility and the population again seeks its equilibrium point.
This is good news. Populations tend to stabilize. And this is without respect to things like free choice or environment. The many animal species that display this effect have no way of making an informed choice. And the human populations were in Denmark and Iceland, where environmental limitations are not currently felt. It’s purely genetic.
Indeed I have written a program in C language that makes some reasonable assumptions and applies Mendelian genetics to a population. The program shows the same curve as is seen in real populations.
The problem arises when the population is at C. By eyeball, it should simply roll back to B. But I can set up the parameters of the program so that it goes straight back to A where it has a high probability of dropping to zero. The thing is that just about every time I have been able to look at real human populations that are isolated from immigration and have numbers in the thousands, that is what I get. Extinction. The evidence is indirect except in one case, but it is very consistent and follows a stereotyped time course. I think it’s the truth.
For warning to be “early” it would have to come fairly soon after the population rose above B. By the time it is at C and falling, every line of evidence suggests danger, even though the fall may be rapid and predictable.
I am sending along a copy of the C language program and a summary of the findings for you to look at. If you want more, I will try to present more evidence as efficiently as I can. If you want to dig through the bulk of it, it is at my web site.
Hope you take an interest. This is important stuff.
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