1. Functional beta redundancy has been recently defined as the fraction of species dissimilarity between two plots not expressed by functional dissimilarity. As such, it summarizes to what degree the compositional differences between two plots mirror their functional differences.
2. A fundamental condition to obtain an appropriate measure of functional beta redundancy is that the functional dissimilarity between the plots is always lower (or at least not higher) than the corresponding species dissimilarity. However, many of the extant measures of functional dissimilarity do not fulfil this requirement.
3. To overcome this problem, a class of tree-based indices of functional dissimilarity that conform to the above ‘redundancy property’ has been recently proposed. However, functional dissimilarity measures need not necessarily be based on a hierarchical representation of the species functional relationships.
4. In this paper, we introduce an algorithmic index of functional dissimilarity that conforms to the redundancy property. Since it does not rely on a hierarchical species organization, the proposed index allows to calculate functional beta redundancy in a more suitable way to the non-hierarchical structure of the species functional relationships. The behaviour of the proposed measure is illustrated with data on the species functional turnover along real and simulated ecological gradients.

中文翻译：

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功能生态的 Beta 冗余

1. 功能β冗余最近被定义为两个图之间的物种不相似性的分数，而不是由功能不相似性表达的。因此，它总结了两个图之间的组成差异在多大程度上反映了它们的功能差异。
2. 获得功能β冗余的适当度量的基本条件是，地块之间的功能差异始终低于（或至少不高于）相应的物种差异。然而，许多现存的功能差异性测量并不能满足这一要求。
3. 为了克服这个问题，最近提出了一类符合上述“冗余特性”的基于树的功能差异指数。然而，功能差异度量不一定基于物种功能关系的分层表示。
4. 在本文中，我们介绍了一种符合冗余特性的函数相异性算法指标。由于它不依赖于层级物种组织，所提出的指数允许以更适合物种功能关系的非层级结构的方式计算功能β冗余。所提出的措施的行为用沿真实和模拟生态梯度的物种功能周转数据进行了说明。