Examples from data
Our constructed examples demonstrate the potential problems with the FEve metric. Here we show how the problem of multiple estimates from a single dataset emerges with actual data. Importantly, there is no way to know in advance the number or range of different FEve estimates for a given dataset. Our first example is the traditional type of data used for functional trait analyses: bats and feeding traits. The other three examples are from less commonly used data: genetic profiles where the traits are the presence and absence of different genes. These examples demonstrate the problem of multiple MSTs that arises with non-continuous traits. For the two examples that lack actual abundance data, we show how a single distance matrix can result in multiple, disparate FEve estimates with simulated abundances. For the other two examples, we show analyses with both actual abundances and two sets of simulated abundances to show how different types of abundance distributions can result in highly variable FEve estimates.
Bats and feeding traits .
The first example consists of a set of five bat species (Carollia manu , Chiroderma salvini , Dermanura glauca ,Enchisthenes hartii , and Micronycteris megalotis ) in the Manu Biosphere Reserve located on the eastern slopes of the Andes in southeastern Peru. Our analysis was based on species characterization with 16 binary categorical traits (Table S3 in Scheiner, Kosman, Presley, & Willig 2017) that were separated into three groups: diet (fruit, nectar, invertebrates, vertebrates, fish, blood), foraging location (open areas, over water, above canopy, canopy, subcanopy, understory), and foraging strategy (aerial, gleaning, hovering, other). To determine the functional distance between species, Jaccard dissimilarity was calculated for each group of binary traits, and then the combined distance between species was determined by an equal-weight averaging of the three group-specific dissimilarities (Table 1). Because the distance matrix contains many equal values, three different MSTs can be generated (Table 1). Because abundance data were not available, we provided two different sets of simulated values. For each set of simulated abudances, the multiple MSTs resulted in FEve estimates that varied 16% and 28%, respectively, between the smallest and largest values (0.374 to 0.480; and 0.676 to 0.785).
Bryozoan genotypes .
Cristatella mucedo is a diploid freshwater bryozoan. We used data on eight microsatellite loci (Table 2 in Kosman & Jokela, 2019) for ten genetically separate individuals from bryozoan colonies in Lake Aegery, Switzerland. The distance between the genotypes was calculated by assuming a stepwise mutation model of microsatellite evolution with variable rates of mutations at different loci (SMMv; Kosman & Jokela, 2019). The corresponding matrix of pairwise distances is presented in Table 2. Abundance data were not available, so we provided simulated values. Again, multiple MSTs can be generated based on the distance matrix that result in four different FEve estimates (Table 2) that ranged from 0.533 to 0.635.
Wheat fungal pathogen (Puccinia graminis f. sp. tritici)genotypes .
The data consisted of eleven virulence phenotypes of P. graminisisolates collected from bread wheat in the Novosibirsk region of Russia. The binary phenotypes (virulence/avirulence) were determined with a set of twenty North American wheat differential lines (Skolotneva et al., 2020). The distance between the phenotypes was calculated using simple mismatch dissimilarity; the corresponding matrix of pairwise distances are presented in Table 3. Twenty-four different MSTs can be generated (Table 3). For the actual abundances, ten different FEve estimates ranged from 0.659 to 0.737 (Fig. 4). Even minor changes in abundances resulted in substantial changes in number and values of different FEve estimates: for the Y-modification, twenty-four values ranged from 0.708 to 0.793; for the Z-modification, eighteen values ranged from 0.573 to 0.695 (Fig. 4).
Wheat fungal pathogen (Puccinia triticina Erikss) genotypes .
The data consist of eleven genotypes of single‐uredinial isolates ofP. triticina (a dikaryotic fungus) collected from durum wheat in Russia using eleven microsatellite markers (Table 3 in Kosman & Jokela, 2019; Gultyaeva et al., 2017). The distance between the microsatellite genotypes was calculated assuming an infinite alleles model (IAM; Kosman & Leonard, 2005), and the corresponding matrix of pairwise distances is presented in Table 4A. Three different MSTs can be generated based on the distance matrix (Table 4B). We compared the FEve estimates for the actual abundances with simulated values for three scenarios: (1) two dominant and nine rare types (simulation P), nine dominant and two rare types (simulation R), and all types equally abundant (simulation E). For the real abundances, FEve values ranged from 0.612 to 0.651 (about 7%). For simulation P, the values have a wider range (0.711 – 0.801, around 13%). For simulation R, the values have a very wide range, from 0.234 to 0.828 (about 354%), which shows the outsized influence of differences in MSTs when the node has a high abundance. For simulate E, as expected, equally abundant types resulted in the same value of 0.88 for all MSTs, despite their variation.