Galton–Watson process

The Galton–Watson process, also called the Bienaymé-Galton-Watson process or the Galton-Watson branching process, is a branching stochastic process arising from Francis Galton's statistical investigation of the extinction of family names. The process models family names as patrilineal (passed from father to son), while offspring are randomly either male or female, and names become extinct if the family name line dies out (holders of the family name die without male descendants).

Galton's investigation of this process laid the groundwork for the study of branching processes as a subfield of probability theory, and along with these subsequent processes the Galton-Watson process has found numerous applications across population genetics, computer science, and other fields.