A stochastic model of mutant growth

Integrals of birth and death processes

Population processes under the influence of disasters occurring independently of population size

Markov branching processes and in particular birth-and-death processes are considered under the influence of disasters that arrive independently of the present population size. For these processes we derive an integral equation involving a shifted and rescaled argument. The main emphasis, however, is on the (random) probability of extinction. Its distribution density satisfies an equation which can be solved numerically at least up to a multiplicative constant. In an example it is also found by simulation.

The linear birth and death process under the influence of independently occurring disasters

A population developing according to a time homogeneous linear birth and death process is subjected to an independently occurring random sequence of disasters. Using an embedded Galton-Watson process with random environments explicit results about the probability of extinction and the asymptotic behavior of the process are obtained.

Quasi Competition — a New Aspect

The model of quasi competition put forward in 1967 is reinvestigated under the aspect that only large (N ∞) populations are considered. Under this new angle the conclusion that myomas develop from single cells seems better justified than the original discussion indicated.