Density-dependent state-space model for population-abundance data with unequal time intervals

The Gompertz state-space (GSS) model is a stochastic model for analyzing time-series observations of population abundances. The GSS model combines density dependence, environmental process noise, and observation error toward estimating quantities of interest in biological monitoring and population viability analysis. However, existing methods for estimating the model parameters apply only to population data with equal time intervals between observations. In the present paper, we extend the GSS model to data with unequal time intervals, by embedding it within a state-space version of the Ornstein-Uhlenbeck process, a continuous-time model of an equilibrating stochastic system. Maximum likelihood and restricted maximum likelihood calculations for the Ornstein-Uhlenbeck state-space model involve only numerical maximization of an explicit multivariate normal likelihood, and so the extension allows for easy bootstrapping, yielding confidence intervals for model parameters, statistical hypothesis testing of density dependence, and selection among sub-models using information criteria. Ecologists and managers previously drawn to models lacking density dependence or observation error because such models accommodated unequal time intervals (for example, due to missing data) now have an alternative analysis framework incorporating density dependence, process noise, and observation error.