Failure to meet the exchangeability assumption in Bayesian multispecies occupancy models: Implications for study design

Abstract

Bayesian hierarchical models are ubiquitous in ecology. Random effect model structures are often employed that treat individual effects as deviations from larger population-level effects. In this way individuals are assumed to be "exchangeable" samples. Ecologists may address this exchangeability assumption intuitively, but might in certain modeling contexts ignore it altogether, including in situations where it may have large implications for study design. Multispecies occupancy models based on detection/non-detection data are an approach that can be utilized by those tasked with monitoring rare and endangered species because most literature suggests that, compared to single species occupancy models, improved parameter estimates are assured. Yet, we illustrate through a power analysis how sampling requirements to detect experimental treatment effects vary tremendously depending on whether the species exchangeability assumption is met. The degree to which species in a community respond similarly to covariates governs the ability to accurately estimate parameters using multispecies occupancy models. Detecting small or moderate changes in occupancy resulting from habitat restoration treatments may be impossible for small datasets (e.g., < 36 sampling locations, each surveyed < 8 times) even with a paired treatment-control design if the exchangeability assumption is violated. By contrast, when the assumption is met, small effects may be confidently estimated with as few as 12 sampling locations (6 pairs) and 6-8 survey events. Often, it may be impossible to know whether the exchangeability assumption is met. The statistical power needed to accurately estimate species-specific effects using detection/non-detection multispecies occupancy models depends on the unknown values of treatment effects and whether responses by species in the community diverge. When the species exchangeability assumption is violated, and at lower levels of sampling effort, multispecies occupancy models may provide worse inference than single species occupancy models.