Abstract
The frequency distribution of surnames turns out to be a relevant issue not only in historical demography but also in population biology, and especially in genetics, since surnames tend to behave like neutral genes and propagate like Y chromosomes. 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 techniques. In the absence of mutations the theoretical models are in good agreement with empirical evidence, but when mutations are present a discrepancy between the theoretical and the experimental exponents is observed. Hints for the possible origin of the mismatch are discussed, with some emphasis on the difference between the asymptotic frequency distribution of a full population and the frequency distributions observed in its samples. A precise connection is established between surname distributions and the statistical properties of genealogical trees. Ancestors tables, being obviously self-similar, may be investigated theoretically by renormalization group techniques, but they can also be studied empirically by exploiting the large online genealogical databases concerning European nobility.
Highlights
Introduction and Historical BackgroundThe frequency distribution of family names has been an interesting issue in human biology since the last quarter of the nineteenth century
George Darwin analyzed marriage isonymy as a tool for the evaluation of inbreeding in the English society [1], while Galton and Watson started the theory of branching processes by computing the probability of surname extinction, a phenomenon perceived as a signal of physical decline in English aristocracy [2]
The treatment of critical phenomena based on the renormalization group techniques may very well apply to the description of evolutionary models, despite the still controversial status of self-organized criticality intended as a universal explanation for evolutionary dynamics [27,28,29,30]
Summary
The frequency distribution of family names has been an interesting issue in human biology since the last quarter of the nineteenth century. The most important recent contribution to phenomenological description and model building was offered in 2007 by the master equation approach of Baek, Kiet and Kim, whose formal solution allows for the (statistical) prediction of the surname distribution as a function of time once the initial distribution is given and the four above mentioned rates are assigned [19].
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