Evolution of surname distribution under gender-equality measurements

We consider a model for the evolution of the surnames distribution under a gender-equality measurement presently discussed in the Spanish parliament (the children take the surname of the father or the mother according to alphabetical order). We quantify how this would bias the alphabetical distribution of surnames, and analyze its effect on the present distribution of the surnames in Spain.

💡 Research Summary

The paper investigates the demographic impact of a proposed Spanish law that would assign a child’s surname based on alphabetical order when parents do not reach an agreement on whether to use the father’s or mother’s name. The authors construct a minimal stochastic model to capture the essential dynamics of surname transmission. Starting with a population of 2N individuals (N males and N females), each person carries a surname drawn from an initial distribution p(n,0), where n indexes surnames in alphabetical order. In each generation, random mating keeps the total population constant. With probability a, parents reach an agreement and the child’s surname is chosen randomly between the two parental surnames; with probability 1‑a, no agreement is reached and the child inherits the surname that appears earlier alphabetically. By defining the proportion p(n,t) of individuals bearing the nth‑alphabetical surname at time t (measured in generations) and its cumulative distribution P(n,t), the authors derive a differential equation ∂P/∂t = (1‑a) P (1‑P). This logistic equation yields the solution P(n,t) = P(n,0) e^{(1‑a)t} /