A stochastic model of mutant growth

1987

Integrals of birth and death processes

1980

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

1989

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

1989

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

1978

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.