1. Most species in ecological communities are rare, whereas only a few are common. This distributional paradox has intrigued ecologists for decades but the interpretation of species abundance distributions remains elusive.
2. We present Fuzzy Quantification of Common and Rare Species in Ecological Communities (FuzzyQ) as an R package. FuzzyQ shifts the focus from the prevailing species-categorization approach to develop a quantitative framework that seeks to place each species along a rarity-commonness gradient. Given a community surveyed over a number of sites, quadrats, or any other convenient sampling unit, FuzzyQ uses a fuzzy clustering algorithm that estimates a probability for each species to be common or rare based on abundance–occupancy information. Such a probability can be interpreted as a commonness index ranging from 0 to 1. FuzzyQ also provides community-level metrics about the coherence of the allocation of species into the common and rare clusters that are informative of the nature of the community under study.
3. The functionality of FuzzyQ is shown with two real datasets. We demonstrate how FuzzyQ can effectively be used to monitor and model spatiotemporal changes in species commonness, and assess the impact of species introductions on ecological communities. We also show that the approach works satisfactorily with a wide range of communities varying in species richness, dispersion and abundance currencies.
4. FuzzyQ produces ecological indicators easy to measure and interpret that can give both clear, actionable insights into the nature of ecological communities and provides a powerful way to monitor environmental change on ecosystems. Comparison among communities is greatly facilitated by the fact that the method is relatively independent of the number of sites or sampling units considered. Thus, we consider FuzzyQ as a potentially valuable analytical tool in community ecology and conservation biology.

中文翻译：

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生态群落中常见和稀有物种的模糊量化（FuzzyQ）

1. 生态群落中的大多数物种是罕见的，而只有少数物种是常见的。几十年来，这种分布悖论一直吸引着生态学家，但对物种丰度分布的解释仍然难以捉摸。
2. 我们将生态社区中常见和稀有物种的模糊量化 (FuzzyQ) 作为 R 包提供。FuzzyQ 将重点从流行的物种分类方法转移到开发一个定量框架，该框架试图将每个物种置于稀有性-共同性梯度上。给定在多个地点、样方或任何其他方便的抽样单位上调查的社区，FuzzyQ 使用模糊聚类算法，该算法根据丰度 - 占用信息估计每个物种是常见或稀有的概率。这种概率可以解释为范围从 0 到 1 的共性指数。 FuzzyQ 还提供了关于物种分配到常见和稀有集群的一致性的社区级别指标，这些指标提供了所研究社区的性质信息。
3. FuzzyQ 的功能用两个真实数据集展示。我们展示了 FuzzyQ 如何有效地用于监测和模拟物种共性的时空变化，并评估物种引入对生态群落的影响。我们还表明，该方法在物种丰富度、分散度和丰度货币方面各不相同的各种群落中都能令人满意地工作。
4. FuzzyQ 产生易于测量和解释的生态指标，可以为生态群落的性质提供清晰、可操作的见解，并提供一种监测生态系统环境变化的有力方法。该方法相对独立于所考虑的地点或抽样单位的数量这一事实极大地促进了社区之间的比较。因此，我们认为 FuzzyQ 是社区生态学和保护生物学中潜在有价值的分析工具。