Based on the framework of attribute diversity (a generalization of Hill numbers of order q), we develop a class of functional diversity measures sensitive not only to species abundances but also to trait‐based species‐pairwise functional distances. The new method refines and improves on the conventional species‐equivalent approach in three areas: (1) the conventional method often gives similar values (close to unity) to assemblages with contrasting levels of functional diversity; (2) when a distance metric is unbounded, the conventional functional diversity depends on the presence/absence of other assemblages in the study; (3) in partitioning functional gamma diversity into alpha and beta components, the conventional gamma is sometimes less than alpha. To resolve these issues, we add to the attribute‐diversity framework a novel concept: τ, the threshold of functional distinctiveness between any two species; here, τ can be chosen to be any positive value. Any two species with functional distance ≥ τ are treated as functionally equally distinct. Our functional diversity quantifies the effective number of functionally equally distinct species (or “virtual functional groups”) with all pairwise distances at least τ for different species pairs. We advocate the use of two complementary diversity profiles (τ profile and q profile), which depict functional diversity with varying levels of τ and q, respectively. Both the conventional species‐equivalent method (i.e., τ is the maximum of species‐pairwise distances) and classic taxonomic diversity (i.e., τ is the minimum of non‐zero species‐pairwise distances) are incorporated into our proposed τ profile for an assemblage. For any type of species‐pairwise distance matrices, our attribute‐diversity approach allows proper diversity partitioning, with the desired property gamma ≥ alpha and thus avoids all the restrictions that apply to the conventional diversity decomposition. Our functional alpha and gamma are interpreted as the effective numbers of functionally equally distinct species, respectively, in an assemblage and in the pooled assemblage, while beta is the effective number of equally large assemblages with no shared species and all species in the assemblages being equally distinct. The resulting beta diversity can be transformed to obtain abundance‐sensitive Sørensen‐ and Jaccard‐type functional (dis)similarity profiles. Hypothetical and real examples are used to illustrate the framework. Online software and R codes are available to facilitate computations.

中文翻译：

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一种功能多样性，功能beta多样性和相关（不相似）度量的属性多样性方法

基于属性多样性的框架（阶q的希尔数的推广），我们开发了一类功能多样性测度，不仅对物种丰富度敏感，而且对基于特征的物种成对功能距离也很敏感。新方法在三个方面对常规物种等效方法进行了改进和改进：（1）常规方法通常在功能多样性相反的情况下为组合提供相似的值（接近统一）；（2）当距离度量不受限制时，常规功能的多样性取决于研究中是否存在其他组合；（3）在将功能性伽玛多样性划分为alpha和beta分量时，常规伽玛有时小于alpha。为了解决这些问题，我们在属性-多样性框架中添加了一个新颖的概念：τ，任意两个物种之间的功能独特性阈值；在这里，τ可以选择为任何正值。功能距离≥τ的任何两个物种在功能上均相同。我们的功能多样性以不同物种对的所有成对距离至少τ量化了功能上相同的不同物种（或“虚拟功能组”）的有效数量。我们提倡使用两个互补的多样性分布图（τ分布图和q分布图），它们描述了具有不同水平的τ和q的功能多样性， 分别。常规的物种等效方法（即，τ是物种成对距离的最大值）和经典的分类学多样性（即，τ是非零物种成对距离的最小值）都被纳入了我们提出的集合的τ谱中。对于任何类型的物种-成对距离矩阵，我们的属性-多样性方法都可以进行适当的多样性划分，并具有期望的特性gamma≥alpha，从而避免了适用于常规多样性分解的所有限制。我们的功能性alpha和gamma分别被解释为在组合和组合组合中功能上相同的不同物种的有效数量，而beta是在没有共享物种的情况下相等大型组合的有效数量，并且组合中的所有物种均相等清楚的。可以对由此产生的Beta多样性进行转换，以获得对丰度敏感的Sørensen和Jaccard型功能（非）相似性概况。假设和真实的例子用来说明该框架。可以使用在线软件和R代码来简化计算。