Evaluating dispersion strategies in growth models subject to geometric catastrophes

We consider stochastic growth models to represent population dynamics subject to geometric catastrophes. We analyze different dispersion schemes after catastrophes, to study how these schemes impact the population viability and comparing them with the scheme where there is no dispersion. In the schemes with dispersion, we consider that each colony, after the catastrophe event, has $d$ new positions to place its survivors. We find out that when $d = 2$ no type of dispersion considered improves the chance of survival, at best it matches the scheme where there is no dispersion. When $d = 3$, based on the survival probability, we conclude that dispersion may be an advantage or not, depending on its type, the rate of colony growth and the probability that an individual will survive when exposed to a catastrophe.