×

Vertical transmission of culture and the distribution of family names. (English) Zbl 0984.92516

Summary: A stochastic model for the evolution of a growing population is proposed, in order to explain empirical power-law distributions in the frequency of family names as a function of the family size. Preliminary results show that the predicted exponents are in good agreement with real data. The evolution of family-name distributions is discussed in the frame of vertical transmission of cultural features.

MSC:

92D25 Population dynamics (general)

References:

[1] Mandelbrot, B., Fractals and Scaling in Finance (1997), Springer: Springer New York · Zbl 1005.91001
[2] Bouchaud, J. P.; Potters, M., Theory of Financial Risks: From Statistical Physics to Risk Management (2000), Cambridge University Press: Cambridge University Press Cambridge
[3] Axelrod, R., The Complexity of Cooperation (1997), Princeton University Press: Princeton University Press Princeton
[4] Cavalli-Sforza, L. L.; Feldman, M. W.; Chen, K. H.; Dornbusch, S. M., Science, 218, 19-27 (1982)
[5] Cavalli-Sforza, L. L.; Feldman, M. W., Cultural Transmission and Evolution: A Quantitative Approach (1981), Princeton University Press: Princeton University Press Princeton · Zbl 0357.92015
[6] Legay, J.-M.; Vernay, M., Pour la Science, 255, 58-65 (1999)
[7] Miyazima, S.; Lee, Y.; Nagamine, T.; Miyajima, H., Physica A, 278, 282-288 (2000)
[8] Simon, H. A., Models of Man (1957), Wiley: Wiley New York
[9] Zipf, G. K., Human Behavior and the Principle of Least Effort (1949), Addison-Wesley: Addison-Wesley Cambridge
[10] Dewdney, A. K., Sci. Am., 254, 12-16 (1986)
[11] Dzierzawa, M.; Omero, M.-J., Physica A, 287, 321-333 (2000)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.