Colonization and Collapse

ALEA, Lat. Am. J. Probab. Math. Stat. 14, 719-731 (2017) Many species live in colonies that thrive for a while and then collapse. Upon collapse very few individuals survive. The survivors start new colonies at other sites that thrive until they collapse, and so on. We introduce spatial and non-spatial stochastic processes for modeling such population dynamic. Besides testing whether dispersion helps survival in a model experiencing large fluctuations, we obtain conditions for the population to get extinct or to survive.