Temporal changes in parameters describing stochastic population dynamics

Abstract

The solution of a stochastic differential equation with temporally dependent parameters is the basis for the following analysis of stochastic population dynamics with temporal changes in the parameters. A discrete density regulated population model is compared with the diffusion approximation and the latter can readily incorporate sampling error and/or missing values in the population data. From these models, the dynamics of populations with temporal changes in parameters are studied. Estimation of parameters is investigated extensively, both by maximum likelihood and MCMC methods. The estimates form the basis for constructing population prediction intervals used in assessing extinction risk. Isotonic regression is presented as an alternative to parametrization of the temporally dependent parameters, with only an assumption of an increase or decrease in parameter values. The different models and methods are compared and applied to real data sets.