Minimisation of extinction probabilities in reproducing populations

In an attempt to explain variability in clutch size among laying birds of the same species, models are considered in which birds have to choose a randomised strategy for clutch size in the face of random environments in order to minimise a probability of extinction. Three models emerge, depending upon whether this is the probability of extinction of the whole species or that of an individual line of descent, and whether change of strategy from one generation to the next is allowed. In two of these models an asymptotically optimal strategy, which typically is randomised, is predicted for large populations.