Steinar Engen, Russell Lande, Bernt-Erik Sæther and Henri Weimerskirch, *Extinction in relation to demographic and environmental stochasticity in age-structured models*, ** Mathematical Biosciences**,

__Volume 195, Issue 2__, June 2005, Pages 210-227.

### Abstract

The demographic variance of an age-structured population is defined. This parameter is further split into components generated by demographic stochasticity in each vital rate. The applicability of these parameters are investigated by checking how an age-structured population process can be approximated by a diffusion with only three parameters. These are the deterministic growth rate computed from the expected projection matrix and the environmental and demographic variances. We also consider age-structured populations where the fecundity at any stage is either zero or one, and there is neither environmental stochasticity nor dependence between individual fecundity and survival. In this case the demographic variance is uniquely determined by the vital rates defining the projection matrix. The demographic variance for a long-lived bird species, the wandering albatross in the southwestern part of the Indian Ocean, is estimated. We also compute estimates of the age-specific contributions to the total demographic variance from survival, fecundity and the covariance between survival and fecundity.

**Keywords: **Demographic stochasticity; Environmental stochasticity; Age-structure; Leslie matrix; Stochastic growth rate; Stochastic population models