GaltonWatsonin
GaltonWatsonin is a probabilistic model of reproduction across generations, commonly known as the Galton–Watson branching process. It is a classical model in probability theory named after Francis Galton and the Reverend Henry William Watson, who studied the extinction of family names in the 19th century. The model describes a population where each individual in generation n produces a random number of offspring in generation n+1, independently of others, according to a fixed offspring distribution.
Formally, if X denotes the number of offspring produced by a single individual with distribution {p_k}, and
If m < 1 (subcritical) or m = 1 (critical), extinction occurs with probability 1, though the distribution