Skip to main content

Supporting Information: Measuring Functional Redundancy Using Generalized Hill Numbers


Dick, Daniel (2023), Supporting Information: Measuring Functional Redundancy Using Generalized Hill Numbers, Dryad, Dataset,


A number of metrics for quantifying the amount of functional redundancy in a community have been proposed over the years. Two of the most popular metrics are based on comparing a taxonomic diversity measure with a generalized form of the same measure that accounts for functional dissimilarities between taxa. These two metrics express redundancy as either an absolute or relative difference between the taxonomic diversity measure and its generalized form. Because they express the amount of redundancy in a community in terms of raw diversity values, both redundancy metrics are susceptible to the same issues that complicate the interpretation of most commonly used diversity indices.

It is possible to overcome these issues by restating these two indices using a Hill numbers framework. As a growing number of authors have noted, these modified metrics provide a more intuitive quantitative definition of functional redundancy when used to rank communities. Beyond this intuitive definition, measuring redundancy in terms of Hill numbers allows researchers to control the influence of rare taxa on the output value, enabling ecologists to better predict how a community is expected to respond when exposed to an external perturbation that selectively eliminates rare or common taxa.

Here I show that, of the two possible Hill number-based redundancy metrics, the form based on a popular absolute redundancy metric is extremely sensitive to differences in taxonomic diversity and can provide a misleading picture of how much redundancy is present in a community. For this reason, I argue that Hill number-based functional redundancy should be quantified using a relative metric that explicitly accounts for differences in effective taxonomic diversity. The proposed Hill number-based relative redundancy measure is shown to provide a much more complete picture of the distribution of redundant taxa within a community, highlighting subtle patterns that are completely missed by the Hill number-based absolute redundancy metric.


Hypothetical datasets generated by the author, following the procedure described in the main text. Three hypothetical communities, each composed of equally abundant species, where five species are functionally identical, and the remaining species are functionally unique. X contains 10 species, Y contains 50 species, Z contains 100 species. Software (R code) created by Daniel G. Dick.

Usage notes

Hypothetical datasets can be opened using any text editor. R scripts can be opened using the most current version of R. Appendices can be opened in Microsoft Word or OpenOffice.