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.

中文翻译：

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对稀有中的稀有建模：多物种分布模型、小模型集合和极低样本量下的单一物种模型之间的比较

物种分布模型可用于估计稀有物种的分布和环境偏好，但由于数据稀疏，这些相同的物种很难建模。我们将传统的单一物种方法（广义线性模型，GLM）与两个有前途的稀有物种建模框架进行对比：小型模型（ESM）的集合，其平均跨简单模型；和多物种分布模型 (MSDM)，它允许稀有物种从更常见物种的统计“借力”中受益。使用真实物种群落中的虚拟物种，我们评估了模型准确性如何受到稀有物种 (N = 2–64) 出现次数、生态位宽度以及与更多物种生态位的相似性的影响。为了区分存在与不存在，仅具有线性项的 ESM (ESM-L) 在 N ≤ 4 时表现最佳，而对于具有多项式项 (ESM-P) 的 GLM 和 ESM 在 N ≥ 8 时表现最佳。为了校准物种对有影响的变量的响应，MSDM 分层物种群落建模 (HMSC) 和 ESM-P 最适用于生态位与其他物种相似的物种。对于具有不同生态位的物种，ESM-P 在 N ≥ 8 时表现最佳，但没有模型针对较小的样本量进行了很好的校准。为了识别无影响的变量，ESM-L 和物种原型模型 (SAM)，一种 MSDM，在 ≤ 4 时表现良好，ESM-L 在 N ≥ 8 时表现良好。与其他物种不同的具有狭窄生态位的物种模型具有最高的辨别能力与通才物种和/或具有与其他物种生态位相似的生态位的物种的模型相比。“借用力量” 在 MSDM 中可以协助完成一些推理任务，但不一定会改善对稀有物种的预测；更简单的单一物种模型可能更适合给定的任务。最好的算法取决于建模目标（区分与校准）、样本大小以及利基广度和相似性。