Estimating environmental effects on population dynamics: consequences of observation error

Within the paradigm of population dynamics a central task is to identify environmental factors affecting population change and to estimate the strength of these effects. We here investigate the impact of observation errors in measurements of population densities on estimates of environmental effects. Adding observation errors may change the autocorrelation of a population time series with potential consequences for estimates of effects of autocorrelated environmental covariates. Using Monte Carlo simulations, we compare the performance of maximum likelihood estimates from three stochastic versions of the Gompertz model (log-linear first order autoregressive model), assuming 1) process error only, 2) observation error only, and 3) both process and observation error (the linear state-space model on log-scale). We also simulated population dynamics using the Ricker model, and evaluated the corresponding maximum likelihood estimates for process error models. When there is observation error in the data and the considered environmental variable is strongly autocorrelated, its estimated effect is likely to be biased when using process error models. The environmental effect is overestimated when the sign of the autocorrelations of the intrinsic dynamics and the environment are the same and underestimated when the signs differ. With non-autocorrelated environmental covariates, process error models produce fairly exact point estimates as well as reliable confidence intervals for environmental effects. In all scenarios, observation error models produce unbiased estimates with reasonable precision, but confidence intervals derived from the likelihood profiles are far too optimistic if there is process error present. The safest approach is to use state-space models in presence of observation error. These are factors worthwhile to consider when interpreting earlier empirical results on population time series, and in future studies, we recommend choosing carefully the modelling approach with respect to intrinsic population dynamics and covariate autocorrelation.