Beta redundancy for functional ecology

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. 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. 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. 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.