Galton watson process1/6/2024 ![]() As before, reproduction of different couples are considered to be independent of each other. ( Bisexual in this context refers to the number of sexes involved, not sexual orientation.) In this process, each child is supposed as male or female, independently of each other, with a specified probability, and a so-called "mating function" determines how many couples will form in a given generation. (Likewise, if mitochondrial transmission is analyzed, only women need to be considered, since only females transmit their mitochondria to descendants.)Ī model more closely following actual sexual reproduction is the so-called "bisexual Galton–Watson process", where only couples reproduce. This effectively means that reproduction can be modeled as asexual. In the classical family surname Galton–Watson process described above, only men need to be considered, since only males transmit their family name to descendants. ![]() Suppose the number of a man's sons to be a random variable distributed on the set For a detailed history see Kendall (19).Īssume, for the sake of the model, that surnames are passed on to all male children by their father. ![]() Galton and Watson appear to have derived their process independently of the earlier work by I. 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). Galton originally posed a mathematical question regarding the distribution of surnames in an idealized population in an 1873 issue of The Educational Times, and the Reverend Henry William Watson replied with a solution. There was concern amongst the Victorians that aristocratic surnames were becoming extinct.
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