>I was
>ruminating on the passing convergence of two "family trees", that then drift
>apart. One line eventually dies, the other prospers. It doesn't sound that
>far different from the archaeological record, without overly stressing the
>exegesis. I'd have to give it a lot more thought before I was willing to
>push it further than that. As I said, it's just a thought.
Note from Bruce N. Lundberg:
Of related interest here is a model, common in stochastic
processes textbooks, for the probability of the eventual extinction of
family lines. (For original literature see:
A. J. Lotka, The extinction of families, Journal of the Washington Academy
of Sciences, vol. 21, No. 16, October 4, 1931, pages 377-380.
The above uses data on United States family trees to estimate parameters in the model
developed by H. W. Watson in 1889 (who followed Francis Galton).
See: Francis Galton, Natural Inheritance, London, Macmillan & Co. (an NY.) 1889. Appendix F:
Probable Extinction of Families, pp. 241-249. The latter is a slightly revised reprint from
the Journ. Anthropol. Inst., 1888.)
In short, the estimate from the model with US data is that about 88% of all family lines
eventually become extinct.
Regards,
Bruce N. Lundberg
Department of Mathematics
University of Southern Colorado
2200 Bonforte Blvd.
Pueblo, Colorado 81001-4901
phone: (719) 549-2482 Fax: (719) 549-2732
email: lundberg@meteor.uscolo.edu