A modified model for projecting age-structured populations in random environments

A discrete-time age-structured population model with vital rates linked to a stochastic environmental process was developed as a generalization of an existing model by making the explicit link between variability in the vital rates and variability in the environment more flexible. This modified model uses biologically relevant probability distributions for the vital rates, and allows for temporal autocorrelation and an arbitrary covariance structure between vital rates. Through simulations, the properties of the projected population in the short-term were investigated and compared to analytical approximations. The distribution of the total population size did not quickly approach lognormality under all conditions. Furthermore, the sensitivity of the vital rates to the environmental process had a strong effect on the variance and distribution of the projected population size. These results suggest that short-term projections need to be carried out through simulation methods, as the analytical approximations technically apply only to the long-run asymptotic behavior. Techniques for parameter estimation were considered; recommendations depend on the form of the data available. The approach described allows the empirical calculation of the probability distribution for predicted population size, a quantity relevant to the use of formal decision analysis in natural resource management.