State-space models for the dynamics of wild animal populations

We develop a unified framework for jointly defining population dynamics models and measurements taken on a population. The framework is a state-space model where the population processes are modelled by the state process and measurements are modelled by the observation process. In many cases, the expected value for the state process can be represented as a generalisation of the standard population projection matrix: each sub-process within the state process may be modelled by a separate matrix and the product of these matrices is a generalised Leslie matrix. By selecting appropriate matrices and their ordering, a wide range of models may be specified. The method is fully flexible for allowing stochastic variation in the processes. Process parameters may themselves be modelled as functions of covariates. The structure accommodates effects such as density dependence, competition and predator–prey relationships, and metapopulations are readily modelled. Observations on the population enter through an observation process model, and we show how likelihood functions can be built that reflect both demographic stochasticity (which appears in the state process) and stochastic errors in the observations. Parameter estimation and estimation of state process variables can be conducted using sequential Monte Carlo procedures.