Using time series to estimate rates of population change from abundance data

Assessing the dynamics of wild populations often involves an estimate of the finite rate of population increase (λ) or the instantaneous rate of increase (r). However, a pervasive problem in trend estimation is that many analytical techniques assume independent errors among the observations. To be valid, variance estimates around λ (or r) must account for serial correlation that exists in abundance data. Time series analysis provides a method for estimating population trends and associated variances when serial correlation of errors occurs. We offer an approach and present an example for estimating λ and its associated variance when observations are correlated over time. We present a simplified time series method and variance estimator to account for autocorrelation based on a moving average process. We illustrate the procedure using a spectacled eider (Somateria fischeri) data set of estimated annual abundances from aerial transect surveys conducted from 1957 to 1995. The analytic variance estimator provides away to plan future studies to reduce uncertainty and bias in estimates of population growth rates. Demographic studies with policy implications or those involving species of conservation concern should especially consider the correlated nature of population trend data.