A state–space mixture approach for estimating catastrophic events in time series data

Abstract

Catastrophic events are considered a major contributor to extinction threats, yet are rarely explicitly estimated in population models. We extend the basic state–space population dynamics model to include a mixture distribution for the process error. The mixture distribution consists of a "normal" component, representing regular process error variability, and a "catastrophic" component, representing rare events that negatively affect the population. Direct estimation of parameters is rarely possible using a single time series; however, estimation is possible when time series are combined in hierarchical models. We apply the catastrophic state–space model to simulated time series of abundance from simple, nonlinear population dynamics models. Applications of the model to these simulated time series indicate that population parameters (such as the carrying capacity or growth rate) and observation and process errors are estimated robustly when appropriate time series are available. Our simulations indicate that the power to detect a catastrophe is also a function of the strength of catastrophes and the magnitude of observation and process errors. To illustrate one potential application of this model, we apply the state–space catastrophic model to four west coast populations of northern fur seals (Callorhinus ursinus).