Stability classification of a Ricker model with two random parameters

We consider a stochastic version of the Ricker model describing the density of an unstructured isolated population. In particular, we investigate the effects of independently varying the per capita growth rate and the parameter governing density dependent feedback. We derive conditions on the distributions sufficient to guarantee different forms of stochastic stability such as null recurrence or positive recurrence. We find, for example, that null recurrence appears in two widely different scenarios: when there is a mean-zero growth rate or via a growth-catastrophe behaviour.