Time series of population abundance estimates often are the only data available for evaluating the prospects for persistence of a species of concern. With such data, it is possible to perform a population viability analysis (PVA) with diffusion approximation methods using estimates of the mean population trend and the variance of the trend, the so-called process variation. Sampling error in the data, however, may bias estimators of process variation derived by simple methods. We develop a restricted maximum likelihood (REML)-based method for estimating trend, process variation, and sampling error from a single time series based on a discrete-time model of density-independent growth coupled with a model of the sampling process. Transformation of the data yields a conventional linear mixed model, in which the variance components are functions of the process variation and sampling error. Simulation results show essentially unbiased estimators of trend, process variation, and sampling error over a range of process variation/sampling error combinations. Example data analyses are provided for the Whooping Crane (Grus americana), grizzly bear (Ursus arctos horribilis), California Condor (Gymnogyps californianus), and Puerto Rican Parrot (Amazona vittata). This REML-based method is useful for PVA methods that depend on accurate estimation of process variation from time-series data.
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