Consistency and fluctuation theorems for discrete time structured population models having demographic stochasticity

In this paper we prove a consistency theorem (law of large numbers) and a fluctuation theorem (central limit theorem) for structured population processes. The basic assumptions for these theorems are that the individuals have no statistically distinguishing features beyond their class and that the interaction between any two individuals is not too high. We apply these results to density dependent models of Leslie type and to a model for flour beetle dynamics. Received: 24 February 1999 / Revised version: 23 July 1999 / Published online: 14 September 2000