Estimating density dependence and latent population trajectories with unknown observation error

Abstract

Summary1. Observation error is the uncertainty in population size that results from not only sampling error but also migration, population heterogeneity, observer error, population interactions with weather and habitat, analysis of observational data, and other sources of error that may introduce Gaussian or non‐Gaussian noise between the observed population and its modelled dynamics.2. We investigate the use of the normal inverse Gaussian (NIG) distribution as a model of observation error that flexibly captures processes such as undercounting, overcounting and outlying observations. The NIG distribution captures asymmetry and heavy‐tailedness in an interpretable parametric model that includes the popular Gaussian observation model as a limiting case.3. The implications of using the NIG model are explored by fitting nonlinear density‐dependent population models with environmental stochasticity to animal census data. We pay particular attention to the estimated per capita growth rate, estimates of future population size and quasi‐extinction risk.4. We use Bayes factors to evaluate the support for hypotheses for non‐Gaussian observation error model, including priors that represent alternative hypotheses of asymmetry in the observation model. Support for these flexible observation models are contrasted with the special case of a Gaussian observation model.5. Flexible observation error may affect estimates of population per capita growth rates and predictions of extinction risk. The dependence of estimates, and predictions, on the choice of observation model may occur even if the data provide comparable support for both Gaussian and non‐Gaussian observation errors. Thus, for some populations with census data, the relative degree of prior belief in alternative hypotheses of process and observation model structure will significantly affect ecological predictions with management implications, such as quasi‐extinction risk.