Modeling the rarest of the rare: A comparison between joint species distribution models, ensembles of small models, and single-species models at extremely low sample sizes

Determining the distribution and environmental preferences of rare species threatened by global change has long been a focus of conservation. Typical minimum suggested number of occurrences ranges from [~]5 to 30, but many species are represented by even fewer occurrences. However, several newer methods may be able to accommodate such low samples sizes. These include Bayesian joint species distribution models (JSDMs) which allow rare species to statistically "borrow strength" from more common species with similar niches, and ensembles of small models (ESMs), which reduce the number of parameters by averaging smaller models. Here we explore how niche breadth and niche position relative to other species influence model performance at low sample sizes (N=2, 4, 8, 16, 32, 64) using virtual species within a community of real species. ESMs were better at discrimination tasks for most species, and yielded better-than-random accuracy even for N=2. In contrast, "traditional" single species or JSDMs were better able to estimate the underlying response curves of variables that influenced the niche, but at low sample sizes also were more likely to incorrectly identify unimportant factors as influential. Species with niches that were narrow and peripheral to the available environmental space yielded models with better discrimination capacity than species with broad niches or niches that were similar to those of other species, regardless of whether the modeling algorithm allowed for borrowing of strength. Our study suggests that some rare species may be able to be modeled reliably at very low sample sizes, although the best algorithm depends on number of occurrences and whether the niche or distribution is the focus.