1. In this study, we propose an extension of the N‐mixture family of models that targets an improvement of the statistical properties of rare species abundance estimators when sample sizes are low, yet typical for tropical studies. The proposed method harnesses information from other species in an ecological community to correct each species' estimator. We provide guidance to determine the sample size required to estimate accurately the abundance of rare tropical species when attempting to estimate the abundance of single species.
2. We evaluate the proposed methods using an assumption of 50 m radius plots and perform simulations comprising a broad range of sample sizes, true abundances and detectability values and a complex data‐generating process. The extension of the N‐mixture model is achieved by assuming that the detection probabilities are drawn at random from a beta distribution in a multi‐species fashion. This hierarchical model avoids having to specify a single detection probability parameter per species in the targeted community. Parameter estimation is done via maximum likelihood (ML).
3. We compared our multi‐species approach with previously proposed multi‐species N‐mixture models, which we show are biased when the true densities of species in the community are less than seven individuals per 100 ha. The beta N‐mixture model proposed here outperforms the traditional multi‐species N‐mixture model by allowing the estimation of organisms at lower densities and controlling the bias in the estimation.
4. We illustrate how our methodology can be used to suggest sample sizes required to estimate the abundance of organisms, when these are either rare, common or abundant. When the interest is full communities, we show how the multi‐species approaches, and in particular our beta model and estimation methodology, can be used as a practical solution to estimate organism densities from rapid inventory datasets. The statistical inferences done with our model via ML can also be used to group species in a community according to their detectabilities.

中文翻译：

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用于多物种丰度估计的 N 混合模型的有效扩展。

1. 
   在这项研究中，我们提出了 N 混合模型系列的扩展，其目标是在样本量较低但典型用于热带研究时改进稀有物种丰度估计器的统计特性。所提出的方法利用生态群落中其他物种的信息来纠正每个物种的估计量。在尝试估计单一物种的丰度时，我们提供指导来确定准确估计稀有热带物种丰度所需的样本量。
2. 
   我们使用 50 m 半径图的假设来评估所提出的方法，并进行模拟，包括广泛的样本大小、真实丰度和可检测性值以及复杂的数据生成过程。 N 混合模型的扩展是通过假设检测概率是从多物种方式的 beta 分布中随机抽取来实现的。这种分层模型避免了必须为目标群落中的每个物种指定单个检测概率参数。参数估计是通过最大似然 (ML) 完成的。
3. 
   我们将我们的多物种方法与之前提出的多物种 N 混合模型进行了比较，我们发现当群落中物种的真实密度低于每 100 公顷 7 个个体时，该模型就会出现偏差。这里提出的 beta N 混合模型优于传统的多物种 N 混合模型，允许以较低密度估计生物体并控制估计中的偏差。
4. 
   我们说明了如何使用我们的方法来建议估计生物体丰度所需的样本量（当这些生物体稀有、常见或丰富时）。当兴趣是完整的社区时，我们展示了如何使用多物种方法，特别是我们的 beta 模型和估计方法，作为从快速库存数据集估计生物体密度的实用解决方案。通过机器学习使用我们的模型进行的统计推断也可用于根据物种的可检测性对群落中的物种进行分组。