Self-similarity in population dynamics: surname distributions and genealogical trees

by Paolo Rossi (Dipartimento di Fisica “E. Fermi” - Universit`a di Pisa)

Tuesday 23 Sept 2014, 16:00 → 18:00 Europe/Rome

Aula Careri (Dip. di Fisica - Edificio G. Marconi)

The frequency distribution of surnames turns out to be a relevant issue not only historical demography but also in population biology, and especially in genetics, since surnames tend to behave like neutral genes and propagate like Y chromosomes. A brief review of the century-long studies on surname distributions and on the related issues of isonymy, consanguinity and migration dynamics is presented.
The stochastic dynamics leading to the observed scale-invariant distributions has been studied as a Yule process, as a branching phenomenon and also by field-theoretical Renormalization Group (RG) techniques, always obtaining the same prediction for the dependence of the power-law exponents from mutation and migration coefficients.
In special cases (absence of mutations) the theoretical models are in good agreement with empirical evidence; however in many concrete instances there is a still unexplained discrepancy between the theoretical and the empirically measured exponents.
Hints for the possible origin of such discrepancy are presented and discussed, with some emphasis on the difference between the asymptotic frequency distribution of a full population and the frequency distributions observed in its samples. We show how to construct large sets of measurable quantities whose expectation value is independent of the sample size.
It is also theoretically promising to explore the connection between the above mentioned results and the statistical properties of genealogical trees, which may be investigated theoretically by RG techniques thanks to the obvious self-similarity of the trees, but can also be studied empirically by exploiting the very large online genealogical databases presently available, especially concerning many families of the European nobility, for which records of birth and marriage referring to several generations have been consistently preserved.
Some statistical results are presented and discussed, based on the study of the family links of more than 12,500 individuals belonging to the rather compact and closed social group formed by the German Hochadel in the Modern Age (1500-1800).