In probability theory, a branching process is a Markov process that models a population in which each individual in generation?n produces some random number of individuals in generation?n?+?1, according, in the simplest case, to a fixed probability distribution that does not vary from individual to individual. Branching processes are used to model reproduction; for example, the individuals might correspond to bacteria, each of which generates?0,?1,?or?2 offspring with some probability in a single time unit.