File:Galton Watson survival Poisson.png

Summary
Plot of Galton-Watson survival rates for Poisson processes with Poisson constants 0.9, 1.0, 1.05, 1.1; illustrating the zero limiting survival probability if the Poisson rate <= 1, and the perhaps surprisingly low survival probabilities even if the population as a whole is increasing exponentially with a Poisson rate > 1.

Created in the R statistics environment, exported as PNG.