A critical appraisal of July 2, 2008:
I was delighted to receive an email the other day.  I don’t get that much response, although the traffic level is gratifying.  Lack of feedback of course has problems.  How am I doing?  Then there is, What do you know that I don’t?  And most important there is, What have you thought of that I haven’t?

In this case, when I went back and looked at the post (over the four years I had kind of forgotten it) my purpose was to try to figure out what sort of algebraic formula might account for the data I then had.  The posting is monumentally tedious.  I was much impressed that the person who was referring to it had managed to wade through.  It mostly consisted of defining terms and belaboring the obvious so as to be able to speculate on what form an equivalent equation might take.

When I wrote him I asked permission to name the fellow.  I think he deserves credit for his analysis.  And I was going to post his whole letter.  But he has not responded, so of course I am wondering whether he has simply lost interest or is exasperated beyond words with me or has found my explanation so clear and vivid that he does not want to pursue it.

I was keying off the Iceland data (An Association between Kinship and Fertility of Human Couples Agnar Helgason et al. SCIENCE vol. 329 no. 5864 February 8, 2008 page 813 – 816), which gives such a nice clean relationship between kinship and fertility both in the first and second generation.  I was hoping that given suitable equations for those relationships it might be possible to use them to predict the time course of the birth rate of a population of unlimited size.  That would mean applying the equations in successive generations.

What he pointed out was that I had written then in order for a population to grow, the number of offspring had to be greater than the population.  That would mean that the number of children in a population should be greater than the entire population in real life.  That was indeed a strange thing to imply. 

What I had failed to make clear was that I meant in a mathematical model the number off offspring in any one generation must outnumber the prior generation in order for the population to grow.

Increasing data has indeed revealed a stereotyped time course, but I don’t think there is much hope for an algebraic model.  I think a digital model holds more promise and offers a better line on what the mechanism might be.  So I would not encourage you to go back and read the old article. 

On the other hand I definitely encourage you to write to info@nobabies.net and give me a frank opinion, as did he.  I make no claim to have a thick skin, but this is important and feedback would be much appreciated even if, as I would anticipate, it is mostly negative.

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