Confronting preferential sampling when analysing population distributions: diagnosis and model‐based triage

Abstract

Summary Population surveys are often used to estimate the density, abundance, or distribution of natural populations. Recently, model‐based approaches to analyzing survey data have become popular because one can more readily accommodate departures from pre‐planned survey routes and construct more detailed maps than one can with design‐based procedures. Spatial models for population distributions (SMPDs) often make the implicit assumption that locations chosen for sampling and animal abundance at those locations are conditionally independent given modelled covariates. However, this assumption may be violated when survey effort is non‐randomized, leading to preferential sampling. We develop a hierarchical statistical modelling framework for detecting and alleviating the biasing effects of preferential sampling in spatial distribution models fitted to count data. The approach works by specifying a joint model for population density and the locations selected for sampling, and specifying a dependent correlation structure between the two processes. Using simulation, we show that moderate levels of preferential sampling can lead to large (e.g. 40%) bias in estimates of animal density and that our modelling approach can considerably reduce this bias. In contrast, preferential sampling did not appear to bias inferences about parameters informing species–habitat relationships (i.e. slope parameters). We apply our approach to aerial survey counts of bearded seals (Erignathus barbatus) in the eastern Bering Sea. As expected, models with a preferential sampling effect led to lower abundance than those without. However, several lines of reasoning (better predictive performance, higher biological realism) led us to prefer models without a preferential sampling effect for this dataset. When population surveys break from traditional scientific survey design principles, ecologists should recognize the potentially biasing effects of preferential sampling when estimating population density or occurrence. Joint models, such as those described in this paper, can be used to test and correct for such biases. However, such models can be unstable; ultimately the best way to avoid preferential sampling bias is to incorporate design‐based principles such as randomization and/or systematic sampling into survey design.