Using uncertainty estimates in analyses of population time series

Recording and monitoring wildlife is crucial for the conservation of wild species and the protection of their environment. The most common type of information reported from a monitoring scheme is a time series of population abundance estimates, but the potential of such data for analyzing population dynamics is limited due to lack of information on sampling error. Recent work has shown that replicating the sampling process and analyzing replicates jointly in a dynamical model can considerably increase estimation efficiency compared to analyzing population estimates alone. This method requires that independent replicates are available, and model fitting can be complex in general. Often, however, population estimates are accompanied by standard errors, or standard errors may be estimated from raw data using a sampling model. We evaluate a method where standard errors are used in combination with population estimates to account for sampling variability in state-space models of population dynamics. The method is simple and lends itself readily to data derived from many sampling procedures but ignores uncertainty in the standard errors themselves. We simulate data from a Gaussian state-space model where several observations, which may come from different sites, are available for the population at each time. Fitting the simulated data, we show that the method yields similar or even better results than a method utilizing all observations, even when there are few observations at each time. This holds under a range of simulation settings involving heteroscedastic observation error, site effects, and correlation among observations. We illustrate the approach on real data from the North American Breeding Bird Survey and show that it performs well in comparison to a more difficult maximum-likelihood analysis of the full data under non-Gaussian sampling error.