Modeling the rarest of the rare: a comparison between multi‐species distribution models, ensembles of small models, and single‐species models at extremely low sample sizes

Abstract

Species distribution models are useful for estimating the distribution and environmental preferences of rare species, but these same species are challenging to model on account of sparse data. We contrast a traditional single‐species approach (generalized linear models, GLMs) with two promising frameworks for modeling rare species: ensembles of small models (ESMs), which average across simple models; and multi‐species distribution models (MSDMs), which allow rarer species to benefit from statistical ‘borrowing of strength' from more common species. Using a virtual species within a community of real species, we evaluated how model accuracy was influenced by the number of occurrences of the rare species (N = 2–64), niche breadth, and similarity to more numerous species' niches. For discriminating between presence and absence, ESMs with just linear terms (ESM‐L) performed best for N ≤ 4, whereas for GLMs and ESMs with polynomial terms (ESM‐P) were best for N ≥ 8. For calibrating the species' response to influential variables, the MSDM hierarchical modeling of species communities (HMSC) and ESM‐P were best for species with niches similar to those of other species. For species with dissimilar niches, ESM‐P did best for N ≥ 8, but no model was well calibrated for smaller sample sizes. For identifying uninfluential variables, ESM‐L and species archetype models (SAMs), a type of MSDM, did well for ≤ 4, and ESM‐L for N ≥ 8. Models of species with narrow niches dissimilar to others had the highest discrimination capacity compared to models for generalist species and/or species with niches similar to other species' niches. ‘Borrowing of strength' in MSDMs can assist with some inference tasks, but does not necessarily improve predictions for rare species; simpler, single‐species models may be better at a given task. The best algorithm depends on modeling goal (discrimination versus calibration), sample size, and niche breadth and similarity.Keywords: borrowing of strength, calibration, data‐deficient species, discrimination, presence–absence, rare species