Galton–Watson process

The Galton–Watson 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). This is an accurate description of Y chromosome transmission in genetics, and the model is thus useful for understanding human Y-chromosome DNA haplogroups. Likewise, since mitochondria are inherited only on the maternal line, the same mathematical formulation describes transmission of mitochondria. The formula is of limited usefulness in understanding actual family name distributions, since in practice family names change for many other reasons, and dying out of name line is only one factor. There was concern amongst the Victorians that aristocratic surnames were becoming extinct. In 1869, Galton published Hereditary Genius, in which he treated the extinction of different social groups. Galton originally posed a mathematical question regarding the distribution of surnames in an idealized population in an 1873 issue of The Educational Times:A large nation, of whom we will only concern ourselves with adult males, N in number, and who each bear separate surnames colonise a district. Their law of population is such that, in each generation, a0 per cent of the adult males have no male children who reach adult life; a1 have one such male child; a2 have two; and so on up to a5 who have five. Find what proportion of their surnames will have become extinct after r generations; and how many instances there will be of the surname being held by m persons.The Reverend Henry William Watson replied with a solution. Together, they then wrote an 1874 paper titled "On the probability of the extinction of families" in the Journal of the Anthropological Institute of Great Britain and Ireland (now the Journal of the Royal Anthropological Institute).

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Galton–Watson process

Surname

A surname, family name, or last name is the mostly hereditary portion of one's personal name that indicates one's family. It is typically combined with a given name to form the full name of a person. Depending on culture, the surname may be placed at either the start of a person's name, or at the end. The number of surnames given to an individual also varies: in most cases it's just one, but in many Spanish-speaking countries, two surnames are used for legal purposes.

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