On the impact of preferential sampling on ecological status and trend assessment

Assessments of the status and trends of abiotic and biotic indicators are two central objectives in many ecological studies and monitoring programs. Given the impracticality of making measurements or observations at every point in geographic space, even within a limited domain, consideration of spatial sampling is crucial to ensure the reliability of statistical inference regarding such status or temporal trends.The sampling units in geographic space (e.g., sites, plots, quadrats) for field observations are often selected with a preference for those expected to be species-rich or those with the highest abundances or occupancy probabilities. This sampling approach, called preferential sampling, can be based on probability sampling theory, but in practice, it is usually a form of nonprobability sampling.Introducing a selection force that disproportionately includes units in the sample based on the expected values of the variables of interest can lead to (severely) biased inferences. This is because inclusion probabilities — referred to here as propensities for units to be part of the sample — cannot be accounted for in statistical estimators when they are unknown to the sampler.In this article, we model sampling processes (considered without replacement) for a finite spatial population of sampling units using probability sampling designs. We consider four designs: Bernoulli sampling, Poisson sampling, simple random sampling, and conditional Poisson sampling. We document the bias introduced by preferential sampling in the estimation of a mean, whether for a status assessment (e.g., mean species richness) or a trend assessment (e.g., trend in mean abundance). For this purpose, we use Monte Carlo simulations and an analytical expression for the bias of the sample mean.This analytical expression shows that the bias of the sample mean (1) increases with increasing covariance between the propensities and the values of the variable of interest and (2) decreases with increasing sampling effort (sampling fraction or expected sampling fraction). This fundamental statistical result is neither widely known nor appreciated by most ecologists, even though it has the potential to ruin status or trend assessments and to lead to erroneous conclusions.The findings on preferential sampling in ecology presented in this article are reviewed from a methodological perspective, mainly for an audience of quantitative ecologists, wildlife statisticians, and biometricians involved in the design or implementation of ecological studies and monitoring programs. To facilitate future exchange among researchers on this topic by clarifying the concepts, in the discussion we also examine the terminology found in the literature for the notions related to preferential sampling.