Why the standard method for partitioning functional and phylogenetic diversity is wrong, and what to do about it

Background/Question/Methods

Biological diversity can be measured for various characteristics of organisms, populations and species, including abundance, phylogenetic relationships, and ecological function. When individuals exist within a spatial hierarchy (e.g., communities within landscapes), we often want to partition that diversity within and among the subunits of that hierarchy. By convention, gamma diversity is that of the whole unit, alpha diversity is that of the subunits, and beta diversity is that among the subunits. When diversity is based on abundance and calculated as a Hill number, there is a well-defined method for doing this partitioning. Both gamma and alpha diversities are calculated from the data and beta diversity is calculated as: beta = gamma/alpha. This same method has been proposed for phylogenetic and functional diversities. However, applying that method to those types of data is incorrect.

Results/Conclusions

That method is incorrect because, unlike abundance data, phylogenetic and functional data are context dependent. Measurements within subunits are dependent on the identity and characteristics of individuals in other subunits. Because of this, the standard partition no longer holds. Instead of starting with measures of gamma and alpha diversity and deriving a measure of beta diversity, our method starts with measures of alpha and beta diversity and derives a measure of gamma diversity as: gamma = alpha x beta. We show, using artificial data, that the behavior of the diversity partition measured in this new way is more interpretable than that using the standard partition method. We also present two different methods for calculating beta diversity. In the first method, beta diversity is based on the average distance among subunits. In the second method, a kind of “diameter” of a set of n subunits is first calculated as a solution to the assignment problem for a matrix of pairwise distances between the subunits, and the estimation of beta diversity is based on that solution. Finally, we discuss how these measures can be used to inform us about the ecological processes responsible for patterns of ecological diversity.