Summary of FEve issues
In constructing species networks, it is assumed that trait values are measured without error and that there is no variation within species, two assumptions that we know are false. This issue could be addressed by a procedure that would estimate the mean and variability of relevant estimates over all closely related networks. We do not know of any attempt to study that matter for any diversity metric. Nevertheless, this problem seems much more acute for FEve comparing with many other metrics because of the potential for non-unique MSTs in addition to errors in distance measures. Multiple estimates of a diversity metric obtained for different, closely-related networks are natural. However, it is conceptually incorrect to assume that functional evenness has multiple values for a community represented by a single network. Given the wide usage of FEve index over the last decade, the validity of the conclusions from those studies are now in question. Our examples show that a single dataset can result in considerable variability in FEve estimates, especially when the data include rare types. The combination of functional relationships and abundances (species distance divided by sum of their abundances) into a single assessment of evenness results in a metric that fails to distinguish between distance evenness and abundance evenness (Gregorius, 1990).
This entire paper has been about FEve, but we would be remiss if we do not mention PEve – phylogenetic evenness – which was defined by Dehling et al. (2014) to be identical to FEve, but substituting nearest-neighbor phylogenetic distances for distances in functional-trait space. We discussed the non-uniqueness problem with FEve that occurs when you have two species which have identical nearest-neighbor distances to a third, but differ in their abundances. This problem is most likely for categorical traits or those based on counts with just a few possible values and so many not occur that often. However, this problem is highly likely for phylogenetic data. It will occur any time you have a pair of sister species that are equally distant from a third and that differ in their abundances. PEve has been used much less frequently than FEve, but should also be abandoned. As with functional traits, there are alternative for phylogenetic evenness that can measure the same properties while avoiding the uniqueness problem (Tucker et al. 2017, Scheiner 2019).