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.