Simulating the Branching Process

number of generations

1

2

3

4

5

6

new simulation

20

distribution of the number of descendants

Bernoulli type

Poisson

geometric type

P(fission) (Bernoulli)

0.7

P(0 descendants) (geometric)

0.4825

P(success) (geometric)

0.4107

mean number of descendants (Poisson)

1.4

This Demonstration shows up to six simulated generations of a branching process. The distribution of the number of descendants of each member of the population can be either a Bernoulli type distribution, the Poisson distribution, or a geometric type distribution; the parameters of these distributions can be set with sliders. From the three figures, the left one shows the simulated branching process, the upper-right one shows the probability of ultimate extinction as a function of a parameter of the distribution, and the lower-right one shows the probabilities of the size of the population at the selected generation.