branching process

Haccou P & Iwasa Y 1996 Establishment probability in fluctuating environments: a branching process model. Theor Popul Biol 50:254-280.

• it is assumed that individuals reproduce asexually during discrete reproduction periods
• individuals have (independent) Poisson distributed numbers of offspring
• the expected numbers of offspring per individual are independently identically distributed over the periods

• many evolutionary stability concepts are defined in terms of invasion probability (Maynard Smith, 1982; Charlesworth, 1994)
• this is usually modelled by means of branching processes or birth-and-death processes
• it is assumed that the environment is constant between generations (Goel and Richter-Dyn, 1972; Eshel, 1981, 1984; Charlesworth, 1994)