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The impact of trait number and correlation on functional diversity metrics in real-world ecosystems
The impact of trait number and correlation on functional diversity metrics in real-world ecosystems
https://orcid.org/0000-0001-6976-5114
Ohlert Timothy Conceptualization Formal analysis Methodology Project administration Visualization Writing – original draft 1 *
Kimmel Kaitlin Conceptualization Data curation Formal analysis Investigation Methodology Project administration Visualization Writing – original draft Writing – review & editing 2
Avolio Meghan Supervision Writing – review & editing 3
Chang Cynthia Data curation Writing – review & editing 4
Forrestel Elisabeth Data curation 5
https://orcid.org/0000-0003-0884-6142
Gerstner Benjamin P. Data curation Writing – review & editing 6
Hobbie Sarah E. Data curation Funding acquisition Writing – review & editing 7
Reich Peter Data curation Funding acquisition Writing – review & editing 8 9 10
Whitney Kenneth D. Data curation Funding acquisition Writing – review & editing 6
Komatsu Kimberly Data curation Funding acquisition Supervision Writing – review & editing 11
1 Department of Biology, Colorado State University, Fort Collins, CO, United States of America
2 Global Water Security Center, University of Alabama, Tuscaloosa, AL, United States of America
3 Department of Earth & Planetary Sciences, Johns Hopkins University, Baltimore, MD, United States of America
4 Division of Biological Sciences, University of Washington, Bothell, WA, United States of America
5 Department of Viticulture and Enology, University of California, Davis, Davis, CA, United States of America
6 Department of Biology, University of New Mexico, Albuquerque, NM, United States of America
7 Ecology, Evolution and Behavior Department, University of Minnesota, St. Paul, MN, United States of America
8 Department of Forest Resources, University of Minnesota, Minneapolis, MN, United States of America
9 Institute for Global Change Biology and School for Environment and Sustainability, University of Michigan, Ann Arbor, MI, United States of America
10 Hawkesbury Institute for the Environment, Western Sydney University, Penrith South, NSW, Australia
11 Department of Biology, University of North Carolina at Greensboro, Greensboro, NC, United States of America
Boscutti Francesco Editor
University of Udine: Universita degli Studi di Udine, ITALY
Competing Interests: The authors have declared that no competing interests exist.

* E-mail: tohlert@colostate.edu
23 9 2024
2024
19 9 e030634226 1 2024
11 6 2024
© 2024 Ohlert et al
2024
Ohlert et al
https://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Exploring the impact of trait number and type on functional diversity metrics in real-world ecosystems The use of trait-based approaches to understand ecological communities has increased in the past two decades because of their promise to preserve more information about community structure than taxonomic methods and their potential to connect community responses to subsequent effects of ecosystem functioning. Though trait-based approaches are a powerful tool for describing ecological communities, many important properties of commonly-used trait metrics remain unexamined. Previous work with simulated communities and trait distributions shows sensitivity of functional diversity measures to the number and correlation of traits used to calculate them, but these relationships have yet to be studied in actual plant communities with a realistic distribution of trait values, ecologically meaningful covariation of traits, and a realistic number of traits available for analysis. To address this gap, we used data from six grassland plant communities in Minnesota and New Mexico, USA to test how the number of traits and the correlation between traits used in the calculation of eight functional diversity indices impact the magnitude of functional diversity metrics in real plant communities. We found that most metrics were sensitive to the number of traits used to calculate them, but functional dispersion (FDis), kernel density estimation dispersion (KDE dispersion), and Rao’s quadratic entropy (Rao’s Q) maintained consistent rankings of communities across the range of trait numbers. Despite sensitivity of metrics to trait correlation, there was no consistent pattern between communities as to how metrics were affected by the correlation of traits used to calculate them. We recommend that future use of evenness metrics include sensitivity analyses to ensure results are robust to the number of traits used to calculate them. In addition, we recommend use of FDis, KDE dispersion, and Rao’s Q when ecologically applicable due to their ability to produce consistent rankings among communities across a range of the numbers of traits used to calculate them.

http://dx.doi.org/10.13039/100000001 National Science Foundation DEB-1257965 Whitney Kenneth D. http://dx.doi.org/10.13039/100000001 National Science Foundation DBI- 1725683 Hobbie Sarah E. http://dx.doi.org/10.13039/100000001 National Science Foundation DEB-1753859 Hobbie Sarah E. http://dx.doi.org/10.13039/100000001 National Science Foundation DEB- 1831944 Hobbie Sarah E. http://dx.doi.org/10.13039/100000001 National Science Foundation DBI- 1725683 Reich Peter B. http://dx.doi.org/10.13039/100000001 National Science Foundation DEB-1753859 Reich Peter B. http://dx.doi.org/10.13039/100000001 National Science Foundation DBI-2021898 Reich Peter B. http://dx.doi.org/10.13039/100000001 National Science Foundation DEB-0841917 Forrestel Elisabeth NSF DEB-1257965 (Kenneth D. Whitney); NSF DBI- 1725683, NSF DEB-1753859, NSF DEB- 1831944 (Sarah E. Hobbie); NSF DBI- 1725683, NSF DEB-1753859, NSF-DBI-2021898 (Peter B. Reich), NSF DEB-0841917 (Elisabeth Forrestel). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Data AvailabilityAll data and scripts may be found at https://github.com/kaitkimmel/FDiv/tree/master/R.
Data Availability

All data and scripts may be found at https://github.com/kaitkimmel/FDiv/tree/master/R.
==== Body
pmcIntroduction

Trait-based diversity measures have advanced the field of community ecology by increasing our understanding of both community assembly and diversity impacts on ecosystem functions [1, 2]. Functional diversity metrics allow researchers to quantify multiple facets of diversity, place an emphasis on mechanisms of community assembly, and provide a ‘common currency’ by which communities can be compared across sites and ecosystems [3, 4].Traditional measures for characterizing communities, such as species richness and species ordinations, use species’ taxonomic classifications as discrete units, but functional diversity metrics can preserve more information about community assembly and function by including traits of species organized on continuous axes [5, 6].

Several aspects of functional and taxonomic diversity have been extensively studied. Scientists have probed functional diversity’s correlation with species richness [7, 8] and ecosystem functioning [4], the importance of intraspecific trait variation for diversity [4, 9, 10], and the ecological hypotheses that functional diversity metrics can test, such as optimal strategies or functional turnover [6, 11]. Many taxonomic measures of community diversity have been extensively studied for their mathematical properties to allow these metrics to be comparable across sites and ecosystems, such as Shannon’s diversity and Simpson’s evenness that have mathematical characteristics linked to species number [12, 13]. Similarly, functional diversity metrics have mathematical characteristics that may cause the number or type of traits used to calculate the metric to impact the measure. For example, multidimensional metrics are calculated with additional dimensions for each additional trait included, and the correlation between traits affects the importance of each dimension to the metric [14]. Therefore, functional diversity could differ among replicate plots or sites simply because of the number or types of traits used to calculate the metric without any underlying ecological basis. Though single-trait indices are an effective tool for linking trait diversity to specific ecosystem processes [15, 16], indices based on multiple traits may better match ecological theories of community assembly around multidimensional niche space [17–19]. As use of multi-trait functional diversity increases, it is important to determine the conditions under which they reflect ecological processes as opposed to mathematical patterns.

Studies using simulated communities have tested whether the number and correlation of traits used in functional diversity metrics can impact the magnitude of the metric [7, 20]. Using simulated data, Legras et al. [20] showed that functional richness and functional divergence metrics decreased with increased trait number, but functional evenness metrics were not responsive to increasing trait numbers. Also using simulated data, Cornwell et al. [7] showed that convex hull volume (commonly referred to as “functional richness”) tended to decrease with increasing correlation among traits included in the metric calculation, and that the decrease was greater in more species-rich communities. The limitations of functional diversity metrics described in these studies with simulated community data could be exacerbated when applied in natural communities. Calculating functional diversity measures in natural communities poses additional challenges both ecological and practical. Real plant communities are non-random assemblages of species which are influenced by competitive interactions, coexistence, mutualisms, niche partitioning, and environmental filtering among many other processes of community assembly [21–26]. Functional diversity metrics are likely to exhibit patterns due to ecologically meaningful correlation of traits in real communities, in particular, among suites of traits typically used in community ecology such as the leaf economic spectrum and root economic spectrum [27, 28]. Moreover, real data collection introduces constraints on trait data, such as realistic numbers of traits collected given limited resources and missing trait data, particularly for rare species. Functional diversity metrics, therefore, are most often calculated with fewer traits and fewer species than those in studies based on simulated communities.

The field lacks clear guidelines for researchers to follow when choosing the number and types of traits to include when calculating functional diversity metrics. Decisions are often based on researcher intuition and the practices of similar studies, but such intuition and interpretation of trait selection can be improved by rigorous exploration of the impact of trait selection on diversity metrics [4, 29, 30]. These decisions can fall along a spectrum of options ranging from selecting the minimum number of traits needed to calculate a metric to using every trait available. For example, some studies suggest that researchers use a small number of traits related to certain ecosystem properties or other topics of interest (e.g., [8]), regardless of how correlated they may be. Other studies use all available traits in order to maximize the dimensions of diversity being studied in an effort to comprehensively assess the niche space that species and communities occupy (e.g., [31]). Choosing traits that are highly correlated can result in an underrepresentation of the diversity of functions present by overemphasizing groups of traits which describe similar processes, such as traits involved in the leaf economics spectrum [32]. Further, functional diversity metric calculation in high dimensional space can require dimensionality reduction–another decision that can impact the metrics. However, few studies scrutinize how these decisions can impact conclusions when using functional diversity metrics to characterize communities.

Here, we aimed to understand how the number of traits and correlation between traits impact functional diversity values. We focused on eight measures of functional diversity that express principal facets of community trait composition (see Table 1 for more details on each metric): functional richness (FRich), functional evenness (FEve), functional divergence (FDiv), functional dispersion (FDis), Rao’s quadratic entropy (Rao’s Q), kernel density estimation (KDE) richness, KDE evenness, and KDE dispersion [33–35]. We used trait data from real (natural/intact and experimental) plant communities, which allowed us to understand how these metrics respond to a realistic spread of traits and species richness. In this study, we used trait data collected from six U.S. grassland communities at two sites to test impacts of trait number and identity in functional diversity metric values. Our dataset included plant traits collected on location at these sites that include both naturally assembled and planted communities.

10.1371/journal.pone.0306342.t001 Table 1 Description of tested trait metrics and examples of usage.

Functional diversity metric	Abbreviation	Ecological relevance	Examples of usage	Citations	
Functional richness	FRich	Functional space filled by the community	De Vries and Bardgett 2016 [54]
De la Riva et al. 2018 [55]
Lourenco Jr. et al. 2021 [56]	Cornwell et al. 2006 [7], Villéger et al. 2008 [8]	
Kernel density richness	KDE richness	Functional space filled by the community	Soares et al. 2022 [57]
Piano et al. 2020 [58]
Pavlek & Mammola 2021 [59]	Blonder 2018 [14], Mammola and Cardoso 2020 [35]	
Functional evenness	FEve	The similarity trait abundances within the community	Bello et al. 2013 [60]
Niu et al. 2016 [61]
Biswas et al. 2019 [62]	Villéger et al. 2008 [8]	
Kernel density evenness	KDE evenness	Similarity of trait abundances within the community	Soares et al. 2022 [57]
Piano et al. 2020 [58]	Mammola and Cardoso 2020 [35]	
Functional dispersion	FDis	Average trait difference between individuals within the community	Zuo et al. 2021 [63]
Shovon et al. 2020 [64]
Griffin-Nolan et al. 2019 [53]	Laliberte and Legendre 2010 [34]	
Functional divergence	FDiv	Average trait difference between individuals within the community	Jäschke et al. 2020 [65]
Ebeling et al. 2018 [66]
Thakur & Chawla 2019 [67]	Villéger et al. 2008 [8]	
Rao’s quadratic entropy	Rao’s Q	Average trait difference between individuals within the community	De Bello et al. 2009 [68]
Ebeling et al. 2014 [69]
Pillar et al. 2013 [70]
Wang et al. 2018 [71]	Rao 1982 [73], Botta-Dukát 2005 [47]	
Kernel density dispersion	KDE dispersion	Average trait difference between individuals within the community	Piano et al. 2020 [58]
Greenop et al. 2021 [72]	Mammola and Cardoso 2020 [35]	

Specifically, we asked:

(1) Do functional diversity metrics exhibit specific patterns with respect to the number and correlation of traits used? Based on findings from [20], we expect functional richness, KDE richness, functional dispersion, and functional divergence to decrease with increasing numbers of traits, but for Rao’s Q to increase [36] and functional evenness to be unresponsive to the number of traits. We do not have a priori hypotheses for KDE evenness and KDE dispersion since properties of these metrics have yet to be explicitly studied. Based on [7], we expect that functional richness will be greater when traits are less correlated. However, we do not have directional hypotheses with respect to effects of trait correlation on the rest of the metrics.

(2) Is metric sensitivity to trait number/type consistent across sites and experiments? If metric sensitivity is consistent across sites, it will be easier to standardize functional diversity metrics across different studies. If sensitivity is not consistent across sites, further caution will be needed in interpreting cross-site comparisons of functional diversity.

Methods

We performed methods as described in the Registered Report Protocol [37]. Alterations to the protocol are explained in Table 2 and the following methods represent only those methods performed for this study.

10.1371/journal.pone.0306342.t002 Table 2 Summary of methodological changes from registered report doi.org/10.1371/journal.pone.0272791.

Proposed method	Used method	Rationale for change	
Data sources from Cedar Creek, Konza Prairie, and Sevilleta	Data sources from only Cedar Creek and Sevilleta	Trait data from Konza Prairie did not meet our 80% threshold of coverage of the community as stated in the registered report and therefore was not used. Specifically, the annually burned community had a maximum trait coverage of 77%, the annually burned and grazed community has a maximum trait coverage of 56%, the community burned every 20 years had a maximum trait coverage of 33%, and the community burned every 20 years that was grazed had a maximum trait coverage of 34%.	
At Cedar Creek, trait data come from the monoculture plots of the BioCON experiment that correspond to the CO2 and N treatments to match with 16-species community plots	Trait values for select species were pulled from an adjacent experiment to ensure total trait coverage.	SLA was not available for two species (Poa pratensis and Bouteloua gracilis). Seed mass was not available for five species (Achillea millefolium, Amorpha canescens, Anemone cylindrica, Asclepias tuberosa, and Petalostemum villosum). These two traits were calculated from the Big Biodiversity experiment trait dataset and substituted for all CO2 and N communities.	
Root %C and %N was only available for Anemone cylindrica in one of the CO2 and N communities in monoculture. The other communities were filled in with this value.	
Use ten traits for Cedar Creek	Used nine traits for Cedar Creek	We miscounted the number of traits available. The registered report only named nine traits to be used.	
Compare linear, quadratic, cubic, and quartic models	Compare null, linear, and quadratic models	Many of the best-fitting linear models had a slope close to 0. We decided to add the intercept-only null model to be able to interpret between linear models that had a slope and those with slopes close to 0. The null model indicates that the independent variables did not describe the variation of the response variable.	
Cubic and quartic models were initially included to mimic the methods of Legras et al. (2020). We did not use cubic and quartic fits as we could not interpret the meaning of these higher-order model fits as it relates to the use of these indices.	
Perform correction for multiple comparisons	No correction for multiple comparisons	We are not focusing on the p-values of our best-fit lines, rather just comparing model fits. We only used p-values to determine the best fit of a line and not in the traditional sense of determining whether a certain variable was statistically significant. Therefore, there was no need to use multiple comparison corrections in our analysis.	
Sensitivity analysis of PCoa	No sensitivity analysis	We tried to run an initial sensitivity analysis calculating FRic with different m values—the parameter in the FDiv package that sets the number of dimensions. However, dimensions were automatically reduced to two since you cannot have more axes than species and our data have numerous plots with very few species. Therefore, we could not perform a full sensitivity analysis.	

Site descriptions

Here we used data from six communities in two United States grasslands that span a range of species diversity. Two communities were from a site with natural species assemblages and four communities were from a site with planted species assemblages in order to be representative of the state of grassland studies where some use naturally assembled communities while others use planted communities. Cedar Creek Ecosystem Science Reserve (CDR; East Bethel, Minnesota, USA; latitude = 45.4, longitude = -93.2) is in central Minnesota and classified as a tallgrass prairie. According to Koppen and Geiger classification, the climate is characterized as cold continental with hot summer, but without a dry season [38]. The mean growing season (May–August) precipitation is approximately 420 mm, mean minimum growing season temperature is 12°C, and mean maximum growing season temperature is 25°C (1982–2016 period; http://www.cedarcreek.umn.edu/research/data). Soils at Cedar Creek are characterized as nutrient-poor entisols derived from a glacial outwash sand plain [38]. The study from Cedar Creek consists of artificially planted communities. The Sevilleta National Wildlife Refuge (SEV) is in central New Mexico at the northern edge of the Chihuahuan Desert (latitude = 34.4, longitude = -106.7). The Sevilleta includes desert grasslands, and the climate is characterized as cold semi-arid according to the Koppen and Geiger classification [38]. The growing season is characterized by two rainy periods (March—May and July—September) split by a dry period. The mean monsoon growing season precipitation is approximately 150 mm and the mean monsoon growing season temperature is 22°C.

Community composition data

We used community composition data from two communities at the Sevilleta and four at Cedar Creek (n = 6 communities total) collected within a single year (2018 for Sevilleta, 2020 for Cedar Creek) to characterize the functional diversity of grassland plant communities.

At Cedar Creek, we used community composition data from all 16-species plots in a biodiversity, CO2, and nitrogen addition experiment (BioCON, n = 48; 12 plots for each CO2-N combination). All 16-species plots were originally planted with the same mixture of species (Achillea millefolium, Amorpha canescens, Andropogon gerardii, Anemone cylindrica, Asclepias tuberosa, Bouteloua gracilis, Bromus inermis, Elymus repens, Koeleria cristata, Lespedeza capitata, Lupinus perennis, Petalostemum villosum, Poa pratensis, Schizachyrium scoparium, Solidago rigida, and Sorghastrum nutans) such that all species were seeded at the same density in 1997. Plots were weeded every year to remove invading species. Through time, the plots can lose species (and regain those) but could never gain new species. Further, species abundances shifted from the equal proportion planted in the first year. Every August, species abundances were visually estimated in a 1 m2 permanent plot.

At Sevilleta, we used community composition data from two observational sites, one in a Great Plains grassland ecosystem and the other in a desert grassland ecosystem. The Great Plains grassland is dominated by Bouteloua gracilis (blue grama), a long-lived, caespitose, C4 perennial grass common throughout much of the United States and Canada. The desert grassland is dominated by B. eriopoda (black grama), a stoloniferous C4 perennial grass common in the southwestern United States and Mexico. These two dominant perennial grasses account for about 80% of vegetative cover in their respective ecosystems. Each site has 28 1 m2 quadrats which were sampled in September of 2018, at the peak of the post-monsoon growing season. In each quadrat, plants were identified to species and their percent ground cover was visually estimated.

Trait data

Trait data were collected on individuals found at each of the different sites. Thus, our trait data are representative of the traits actually found in the given community and not just an average independent of location. Traits include measurements from leaves (e.g. specific leaf area), stems (e.g. stem dry matter content), roots (e.g. root dry matter content), whole-plant (e.g. height), and ecological attributes (e.g. amount of nitrogen in monoculture). Including traits across these measurement categories provides a more-complete representation of community assemblages [39–42]. For detailed descriptions of trait collection protocols at each site, see the S1 and S2 Figs.

At Cedar Creek, we used trait data collected in the monoculture plots of the BioCON experiment that correspond to the CO2 and N treatments to match with 16-species community plots. Trait data were collected between 1998 and 2020. Some traits were collected over multiple years whereas others were only collected once. In total, there were 9 distinct traits: specific leaf area (SLA), I* (the amount of light at the soil surface in monoculture), R* (the amount of nitrogen in monoculture), root %C, root %N, total root biomass, shoot %N, shoot %C, and seed mass.

At Sevilleta, we used trait data collected from 2017–2021 on individuals growing under ambient conditions near permanent ambient plots used to monitor plant communities. The full suite of traits were often measured on the same individuals, up to 10 individuals per species. In total there were 10 distinct traits: maximum plant height, leaf dry matter content, specific leaf area, d15N, d13C, leaf %N, leaf %C, stem dry matter content, root dry matter content, and photosynthetic pathway.

For each trait at each site, we calculated an average trait value based on all the measurements for the given species and trait. We acknowledge that this obscures variation within a given trait (intraspecific variation) for a species; such variation can be quite important for some questions [43–46]. The impacts of intraspecific variation in this study are minimized by only using trait values collected at each site, but sufficient data were not collected for each trait of each species to include intraspecific variation into our analysis. Before analysis, we removed species that had less than 100% trait coverage. We made sure that the communities were still represented by at least 80% of species abundance–this approach de-emphasizes the importance of rare species, but is a logistical constraint faced by many researchers doing trait analyses. This ensured that we represented the community to the best of our ability with the given trait data.

Brief background on functional diversity metrics

We focused our analyses on eight common functional diversity metrics: functional richness (FRich) [8], functional evenness (FEve) [9], functional dispersion (FDis), functional divergence (FDiv), Rao’s quadratic entropy (Rao’s Q), kernel density estimation (KDE) richness, KDE evenness, and KDE dispersion [34]. FRich is the multidimensional equivalent of a range [8]. It is calculated as the convex hull volume that is made from all trait values for up to n traits in the community. The number of dimensions used to calculate the final volume can be reduced from the total trait number [45]. FEve is the minimum spanning tree to quantify the regularity of branch lengths and the evenness in trait relative abundances. For each branch, l, of the minimum spanning tree, the weighted evenness (EW) is calculated as EWl=dist(i,j)wi+wj where i and j are species, and wi is the relative abundance of species i. Then, the partial weighted evenness (PEW) is calculated for each branch as PEWl=EWl∑l=1S−1EWl, where S is the total number of species in the community. FEve is then defined as ∑l=1S−1min(PEWl,1S−1)−1S−11−1S−1 [8]. FDis is the weighted mean distance between species and a weighted-centroid. It is calculated as ∑ajzj∑aj where aj is the relative abundance of species j and zj is the distance species j is from the weighted centroid [34]. FDiv is a relative abundance-weighted spread of traits along a trait axis independent of functional richness and is calculated as Δd+dG¯Δ|d|+dG¯ where dG¯ is the mean distance of species to the weighted-centroid and Δd is the sum of relative abundance-weighted deviances from the weighted-centroid [9]. Rao’s Q measures the pairwise differences in traits between species in a community and is calculated as Σi−1s−1Σj=i+1S dijpi where S is the number of species in the community, dij is the functional difference between the i-th and j-th species, and p is a vector of relative abundance values [46]. These five functional diversity metrics commonly incorporate distance measures by reducing dimensionality using principal coordinates analysis (PCoA) to return PCoA axes which are used to calculate the functional diversity metrics. However, we will avoid this dimensionality reduction for all metrics except FRich, see discussion in Functional Diversity Calculations section. n-dimensional hypervolumes use Gaussian kernel density estimation (KDE) to create a relative abundance-weighted probability distribution of traits in multidimensional space [35]. KDE richness is the total volume of the n-dimensional hypervolume created from unweighted trait values present in the community. KDE evenness is the overlap between the abundance-weighted n-dimensional hypervolume and a similar hypervolume in which all traits and abundances are distributed evenly. KDE dispersion is the average distance between random points within the n-dimensional hypervolume and the hypervolume centroid.

Functional diversity calculations

For each site, we followed the same protocol for calculating functional diversity metrics. We calculated FRich, FEve, and FDis, FDiv, and Rao’s Q using the ‘FD’ package in R [46] using both Gower and Euclidean dissimilarity as the distance measure, along with using the hypervolume package in R to calculate KDE n-dimensional hypervolumes which are passed to the ‘bat’ package to create KDE richness, KDE evenness, and KDE dispersion [35, 48]. Functional diversity metrics from the ‘FD’ package and kernel density estimation are among the most-used metrics for quantifying trait-based diversity within communities due to both ease of use and ecological relevance [35, 45]. To understand the impact of trait number on functional diversity, each functional diversity metric was calculated using all possible combinations of two traits up to all possible combinations of the maximum number of traits at each site. For example, at Sevilleta there are 10 different traits so there are 45 2-trait calculations, 120 3-trait calculations, 210 4-trait calculations, and so forth up to 10 9-trait calculations and 1 10-trait calculation. This allows us to focus on the impact of trait number independent of the constituent set of traits used to calculate the metric.

To calculate the five metrics using the ‘FD’ package, we first calculated a species-trait distance matrix using both Gower (categorical and continuous traits) and Euclidean (continuous traits only) distances. These distance matrices were calculated with both scaled and centered and non-scaled trait data for each community. Centering was done by subtracting the trait mean from each observation and scaling was done by dividing the centered traits by their standard deviations (as in the ‘FD’ package). These distance matrices along with a species-abundance matrix are the input for the ‘FD’ package. The ‘FD’ package performs a principal components analysis on the full species-trait distance matrix. Dimensionality reduction only occurs for FRic and FDiv metric calculation. For all FRich and FDiv analyses, we hold the number of dimensions equal to 2, similar to Legras et al. [20]. Because some communities only had two species, we did not perform a sensitivity analysis to look at how increased dimensionality impacted our results since these species depauperate communities would be excluded. Further, when running the analyses for FRic, FEve, and FDiv, one plot from each Sevilleta community with only one species present was removed because FRic, FEve, and FDiv are undefined in monoculture communities. For calculation of KDE metrics, a species-abundance matrix and a species-trait matrix were loaded for each of the six communities while the distance matrix was set to either Gower or Euclidean depending on the calculation being performed. To measure the effects of trait correlation on functional diversity, we focused on metrics calculated with four traits only to standardize between sites. We calculated the minimum, maximum, and mean correlation between the traits at each community. Only combinations of four traits were used as a balance between reduction of noise in the evaluation of minimum and maximum correlation (calculated as the pairwise correlation of just two traits) and the lower end of the number of traits likely to be used to calculate these metrics in the literature.

Statistical analyses

For each community separately, we ran mixed effects models to test the dependence of the eight functional trait metrics on trait number and on trait correlation using the lme function from the ‘nlme’ package in R [48]. To examine how trait number impacts the values of a given functional trait metric, we ran the model Metric ~ trait number for 2–10 unique traits. To examine how trait-trait correlation impacts the values of a given functional diversity metric, calculated three metrics of trait correlation for each unique combination of four traits: 1) min trait correlation is the minimum two-trait correlation among the set of four traits, 2) max trait correlation is the maximum two-trait correlation among the set of four traits, and 3) mean trait correlation is the average of all trait-trait correlations among the set of four traits. Next, we ran three models for each community: Metric ~ min trait correlation, Metric ~ max trait correlation, Metric ~ mean trait correlation. We explored which functional form of the predictor variables best fit the spread of the functional metric data by fitting null (e.g., intercept only), linear, and quadratic fits. We selected models based on best fit using AIC values. We accounted for repeated samples within plots by fitting plot as a random effect and using an autoregressive correlation structure. Raw model outputs for the total 1,152 models are generated by scripts n_traitStats_simplified.R, n_traitStats_euc_simplified.R, max_corrStats_simplified.R, max_corrStats_euc_simplified.R,min_corrStats_simplified.R, min_corrStats_euc_simplified.R, mean_corrStats_simplified.R, mean_corrStats_euc_simplified.R’ in this GitHub repository <https://github.com/kaitkimmel/FDiv/tree/master/R>.

Results

Data processing summary

Cedar Creek and Sevilleta had adequate trait coverage to proceed with the analyses. At Cedar Creek, all plots from all communities had 100% trait coverage. Overall, we included data from four different communities (defined as different nitrogen fertilization and carbon dioxide enrichment treatments) each with 16 total plots. At Sevilleta, the minimum plot-level trait coverage from the ‘Blue grama’ communities was 79.96%. We included all the plots as 79.96% was close to the 80% trait-coverage threshold. Thus, we had 28 individual plots within this community. The minimum plot-level trait coverage from the ‘Black grama’ communities at Sevilleta was 77.72%. We removed this one plot and had a total of 27 plot from the ‘Black grama’ community.

Sensitivity of functional diversity metrics to trait number

FDis calculated with Gower dissimilarity was insensitive to the number of traits used to calculate it across all six communities (Fig 1I; Table 3). KDE richness, KDE dispersion, and Rao’s Q with Gower dissimilarity were negatively correlated with the number of traits (Fig 1B, 1J and 1M). However, the rankings of communities from low to high values remained consistent. That is, community order was maintained within these three metrics across the range of trait numbers. Similarly, FRich, KDE richness, FDis, KDE dispersion, and Rao’s Q calculated with Euclidean dissimilarity maintained rankings among communities throughout the range of trait numbers, though these metrics all increased with the number of traits (Fig 1C, 1D, 1K, 1L and 1O; Table 3). For both Gower and Euclidean dissimilarity, FEve, KDE evenness, and FDiv had different rankings among communities depending upon the number of traits used to calculate them.

10.1371/journal.pone.0306342.g001 Fig 1 The relationship between trait number and functional diversity metrics using both Gower (columns 1 & 2) and Euclidean (columns 3 & 4) dissimilarity matrices.

Each point represents the mean value for the given community for a certain number of traits used to calculate the metric. Solid lines are the predicted fits of the best model and shaded regions are +/- SE of the predicted fit. Different colors represent the six communities used in this study (four experimental communities at Cedar Creek Ecosystem Science Reserve, CDR, and two natural communities at Sevilleta National Wildlife Refuge, SEV). N = 6,024 observations for each Cedar Creek community (432 2-trait combinations, 1,008 3-trait combinations, 1,512 4-trait, 1,512 5 trait combinations, 1,008 6-trait combinations, 432 7-trait combinations, 108 8-trait combinations, 1 9-trait combination); n = 27,351 observations for SEV1; n = 28,364 observations for SEV2.

10.1371/journal.pone.0306342.t003 Table 3 Counts of the number of best fit models for different predictor variables and functional diversity metrics calculated using Gower and Euclidean distances.

For six communities, each of eight metrics was calculated across a range of the four predictor variables using both Gower and Euclidean dissimilarity matrices. Three functional forms of models were tested: intercept only, linear, and quadratic. In this table, counts underneath those functional form columns display the number of communities (out of six) for which that functional form was the best model. For example, FRich predicted by trait number and calculated with Gower dissimilarity was best predicted by a linear model for three communities and best predicted by a quadratic model for three communities. In total, this table summarizes the results of 384 models.

Predictor	Metric	Intercept Only	Linear	Quadratic	
Gow	Euc	Gow	Euc	Gow	Euc	
Trait Number	FRich	0	0	3	3	3	3	
KDE richness	0	0	2	1	4	5	
FEve	1	1	3	2	2	3	
KDE evenness	2	2	1	3	3	1	
FDis	6	0	0	0	0	6	
KDE dispersion	0	0	1	0	5	6	
FDiv	0	0	2	0	4	6	
Rao’s Q	0	0	0	6	6	0	
Maximum Correlation	FRich	0	1	2	1	4	4	
KDE richness	1	0	2	2	3	4	
FEve	4	1	1	2	1	3	
KDE evenness	2	2	1	3	3	1	
FDis	1	0	0	1	5	5	
KDE dispersion	1	1	2	1	3	4	
FDiv	1	2	3	2	2	2	
Rao’s Q	0	1	2	2	4	3	
Minimum Correlation	FRich	0	1	0	0	6	5	
KDE richness	1	0	0	1	5	5	
FEve	3	4	3	1	0	4	
KDE evenness	1	2	1	2	4	2	
FDis	0	1	1	0	5	5	
KDE dispersion	1	0	2	3	3	3	
FDiv	3	2	1	1	2	3	
Rao’s Q	0	0	1	2	5	4	
Mean Correlation	FRich	1	0	1	0	4	6	
KDE richness	1	1	1	0	4	5	
FEve	2	1	3	1	1	4	
KDE evenness	3	3	1	0	2	3	
FDis	1	0	2	1	3	5	
KDE dispersion	2	1	0	0	4	5	
FDiv	1	0	0	2	5	4	
Rao’s Q	0	0	4	2	2	4	

Sensitivity of functional diversity metrics to trait correlations

Trait correlations (mean, maximum, and minimum trait-trait correlation for combinations of four traits) had limited power to predict the calculated metrics for both dissimilarity matrices and the relationships between metrics and trait correlation varied widely among communities (Fig 2, S1 and S2 Figs). Consequently, we observed inconsistent rankings among communities with respect to trait correlation (Fig 2, S1 and S2 Figs). For example, for FRich calculated with an Euclidean matrix at maximum correlation of 0.40, FRich of the CDR2 community was greater than that of CDR1, whereas at maximum correlation of 0.75, the reverse was true, FRich of CDR1 was greater than that of CDR2 (Fig 2C). Such reorganizations of community rankings were common across functional diversity metrics, distance matrices, and correlation metrics (max, min, mean) (Fig 2). In some cases, metrics were not responsive to trait correlations (e.g., null models were the best fit for 19% of all max correlation models, 20% of min correlation models, 18% of mean correlation models).

10.1371/journal.pone.0306342.g002 Fig 2 The relationship between the maximum trait-trait correlation for each set of 4 traits and functional diversity metrics using both Gower (columns 1 & 2) and Euclidean (columns 3 & 4) dissimilarity matrices.

Each point represents the mean value for the given community at that correlation. Solid lines are the predicted fits of the best model and shaded regions are +/- SE of the predicted fit. Different colors represent the six communities used in this study (four experimental communities at Cedar Creek Ecosystem Science Reserve, CDR, and two natural communities at Sevilleta National Wildlife Refuge, SEV). N = 1,512 observations for each CDR community; n = 3,402 for SEV1; n = 3,528 for SEV2.

Distance matrices

Overall, metrics calculated with Gower and Euclidean distance matrices maintained consistent results with respect to the ranking of the six communities (four experimental planted communities from Cedar Creek and two natural communities at Sevilleta) for different metrics. The Euclidean distance matrix tended to amplify the differences among communities as the numbers of traits increased for KDE richness, FDis, Rao’s Q, and KDE dispersion. Certain functional diversity metrics were poor at maintaining the ranking of communities across ranges of the number and correlation of traits (e.g. FEve; Figs 1E, 1G, 2E and 2G). However, for instances in which the ranking of communities changed, neither Gower nor Euclidean distance improved the issues.

Discussion

Sensitivity to the number of traits

Our study aimed to understand the sensitivity of functional diversity metrics to trait inputs. Here, we found that FDis had consistent values when calculated with Gower dissimilarity such that, across all communities, there was no correlation with the number of traits used (e.g., it remained consistent regardless of trait number). This suggests that FDis provides reliable values across different communities and sets of traits, making it a potentially valuable tool for assessing patterns of functional diversity across communities and ecosystems. Similarly, Rao’s Q, KDE dispersion, and KDE richness maintained consistent ordered rankings of metrics among communities across the range of trait numbers for both Gower and Euclidean dissimilarity matrices along with FDis calculated with Euclidean dissimilarity. Other metrics (FEve, KDE evenness, FDiv) had less consistency across the range of traits used to calculate them as relative rankings of different communities changed with the number of traits used in constructing the metrics.

A previous simulation study found no sensitivity to the number of traits for FEve and FDiv and magnitude decreases with increasing trait number for FRich, KDE richness, FDis, and Rao’s Q calculated with Gower dissimilarity [20]. Our results were consistent with Legras et al. [20] for Rao’s Q and KDE richness, but we found FDis unresponsive to the number of traits and FDiv, FEve, and KDE evenness to have inconsistent slopes among communities. These differences in findings might be attributed to the inherent complexity and noise present in real-world data. Real communities often contain anomalous species with outlier trait values (e.g. a gymnosperm among angiosperms, a tree seedling among herbaceous plants, or other rare species outlier values), which can exert considerable influence on evenness indices.

We found further discrepancies with previous studies reporting results using Euclidean dissimilarity. Previous studies found no sensitivity of FEve and FDiv [20, 36], and increases with increasing trait number for KDE richness, Rao’s Q [35], and FRich [20] when calculated with Euclidean dissimilarity. Our results of increasing FDis with the number of traits matches Legras et al. [20] while Zhang et al. [36] reported no sensitivity. A potential explanation for this discrepancy is the difference in the number of traits considered. Our study and the simulated data in Legras et al. [20] were limited to a maximum of 10 traits while Zhang et al. [36] used a maximum of 34 traits. While there may indeed be no sensitivity of FDis calculated with Euclidean dissimilarity at numbers of traits as high as 34, studies employing these metrics more often use fewer than 10 traits, within the range in which we found sensitivity.

Some metrics may be unreliable measures for comparing functional diversity among communities since comparisons are dependent upon the number of traits used to calculate them. Specifically, FRich, FEve, and KDE evenness showed crossing slopes among communities (i.e. ranking of communities changed with the number of traits) for both Gower and Euclidean distance matrices. The inconsistency of communities’ relationships to one another across the range of the number of traits raises concerns. For example, community CDR4 had a greater FEve than community SEV1 when using four traits, but CDR4 had a smaller FEve than SEV1 when calculated with eight traits. Such discrepancies have the potential to introduce discordant results in the literature, even when otherwise identical studies have been conducted. This is particularly concerning given the often-arbitrary nature of selecting the number of traits used in a study. The number of traits is often dictated by the resources available to collect data or the completeness of publicly available data [49, 50]. Therefore, additional analyses are warranted when using these metrics to ensure that results are not merely an artifact of the number of traits used to calculate the metrics. Interestingly, the more consistent indices—such as KDE alpha, FDis, Rao’s Q, and KDE dispersion—measure similar ecological properties (e.g., the range of traits expressed in the community) as FRich [6, 33, 35] and therefore, these indices could be substituted for FRich in analyses. However, evenness metrics, both FEve and KDE evenness, quantify a different type of ecological property, the relative homogeneity of traits within a community [35]. These indices do not have obvious substitutes for measuring these ecological properties among the metrics studied here.

Trait correlation concerns in calculating metrics: Much ado about nothing?

We found inconsistent and null relationships between metrics and the correlation of traits used for their calculations. Despite suggestions in the literature that trait selection should minimize correlation [35], lower levels of trait-trait correlation did not result in more or less clear comparisons among communities. Though nonlinearity was prevalent in our analysis, most trait metrics demonstrated similarity across the entire range of maximum trait-trait correlation (i.e. the range of values was relatively small). Lefcheck et al. [29] utilized simulated data and reported insensitivity of Rao’s Q, FEve, and FDis to trait correlation except at very high levels of correlation (Pearson’s |R| > 0.95). However, they observed that FRich and FDiv decreased with trait correlation—a trend that was not evident in our study. Additionally, Lefcheck et al. [29] noted that sensitivity to trait correlation became most apparent for FDiv and FRich when larger numbers of traits were considered, whereas we only tested combinations of four traits. Notably, Mammola and Cardoso [35] recommended avoiding the use of highly correlated traits (Pearson |r| > = 0.8) when calculating KDE metrics. Though we did not find substantial support for such a cutoff, our set of collected traits also had very few combinations with correlation above 0.8. Overall, our results show no consistent link between trait correlation and the values of functional diversity metrics.

Gower and Euclidean dissimilarity

Both Gower and Euclidean distances performed similarly, though diversity metric values varied more with the number of traits under Euclidean distance. Metrics that preserved rankings among communities across the trait number and correlation gradients did so with both Gower and Euclidean matrices. The primary difference driving the use of these distance matrices in the literature is that unlike Euclidean distance, Gower distance can conveniently accommodate categorical data. Categorical traits, such as photosynthetic pathway, growth form, and nitrogen fixation capacity, are often easy to collect and more reliably scored than continuous traits. Moreover, trait databases typically have a great deal of missing data [50, 51] and categorical traits are more reliably gap-filled ad-hoc (e.g. growth form may be determined from a picture or nitrogen fixation capacity pulled from literature) than continuous traits. Given that both distance matrices performed similarly across our broad range of functional diversity indices, trait correlations, and trait numbers, there is no clear reason to favor use of a particular matrix other than the ability of Gower matrices to include categorical trait types.

Ecological significance of methodology and recommendations

Perhaps most important is to center ecological significance and interpretation when choosing traits and metrics. Though many metrics produced consistent results with respect to the rankings of communities from two to ten traits, there are many sensible reasons to include more than 2 traits in order to capture more dimensions of diversity [43, 52]. Similarly, though we found no obvious difference of results when including highly correlated traits, this may not be license to include the maximum number of traits available in all circumstances. One example of responsible use of traits is found in Griffin-Nolan et al. [53] in which traits were used to assess plant community responses to drought. In this case, the analyses focused solely on hydrological traits, ignoring many other traits commonly used in the literature (e.g. seed mass), but the authors correctly emphasized the importance of choosing only traits relevant to the particular treatments and plant functions of interest. While use of the maximum number of traits available may be justifiable when seeking to quantify diversity defined broadly, we discourage inclusion of traits without ecological rationale.

Based on our findings, we recommend use of FDis, KDE dispersion, and/or Rao’s Q in analyses of functional diversity as all of these measures provide consistent results among communities at all numbers of traits tested. Additionally, due to the inconsistency of evenness metrics with respect to community rankings, we strongly recommend that any use of FEve or KDE evenness metrics include supplemental analyses to test whether results are consistent with different numbers of traits used to calculate them. Surprisingly, we found no rationale to favor a particular distance matrix; we simply suggest that the number of traits used or correlation of traits need not be a consideration when choosing between Gower and Euclidean dissimilarity matrices. While functional diversity indices enrich the toolbox for exploring trait-based plant diversity, it remains important to ensure that our findings and inferences are rooted primarily in ecological principles rather than being solely reflective of the metrics employed in assessing functional diversity.

Supporting information

S1 Fig The relationship between mean trait-trait correlation for each set of 4 traits and functional diversity metrics using both Gower (columns 1 & 2) and Euclidean (columns 3 & 4) dissimilarity matrices.

Each point represents the mean value for the given community for a specific number of traits. Solid lines are the predicted fits of the best model and shaded regions are +/- SE of the predicted fit. Different colors represent the six communities used in this study (four experimental communities at Cedar Creek Ecosystem Science Reserve, CDR and two natural communities at Sevilleta National Wildlife Refuge, SEV). N = 1,512 observations for each CDR community; n = 3,402 for SEV1; n = 3,528 for SEV2.

(PDF)

S2 Fig The relationship between the minimum trait-trait correlation for each set of 4 traits and functional diversity metrics using both Gower (columns 1 & 2) and Euclidean (columns 3 & 4) dissimilarity matrices.

Each point represents the mean value for the given community at that correlation. Solid lines are the predicted fits of the best model and shaded regions are +/- SE of the predicted fit. Different colors represent the six communities used in this study (four experimental communities at Cedar Creek Ecosystem Science Reserve, CDR, and two natural communities at Sevilleta National Wildlife Refuge, SEV). N = 1,512 observations for each CDR community; n = 3,402 for SEV1; n = 3,528 for SEV2.

(PDF)

Thank you to two anonymous reviewers for providing feedback that improved the quality of this research.

10.1371/journal.pone.0306342.r001
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PONE-D-24-03515The impact of trait number and correlation on functional diversity metrics in real-world ecosystemsPLOS ONE

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Reviewer #1: ## Review PLOSONE: the impact of trait number and correlation on functional diversity metrics in real-world ecosystems

# General comments

I review the paper entitled "the impact of trait number and correlation on functional diversity metrics in real-world ecosystems" submitted to Plos ONE journal. In this paper, the authors deal with a timely question in functional ecology related to the choice of functional traits to calculate functional diversity indices. Indeed, given the development of trait measurements in ecology, trait-based approaches are more and more common to go behind taxonomic diversity. A key aspect of these approaches is the sensitivity of functional diversity indices to the choice of functional traits (e.g. number and correlation).

In this paper, the authors propose to test the sensitivity of 8 functional diversity indices on real community of plants. Thus, they test the behavior of functional diversity indices to the number of functional traits used to describe the community. In addition they also test how the traits correlation influence the FD indices. They found that some indices decrease when the number of traits increased, while other increase and some are not changing. They also found that the trait-trait correlation have no significant influence of the functional indices.

The more I read the paper the more I had some problems to understand the real aim of this paper. When the authors claim L. 75 "Therefore, functional diversity could differ among replicate plots or sites simply because of the number or types of traits used to calculate the metric without any underlying ecological basis." and L. 407: "Some metrics may be unreliable measures for comparing functional diversity among communities since comparisons are dependent upon the number of traits used to calculate them." OK, I agree, but does people really compared FD of communities calculated on different number of traits ? I would not do it in any case, whatever the metrics give similar or different values. It is just like comparing apple and pear.

As a general comment, I would say that the authors pointed out a real question in their introduction, but the analyses and interpretations are not sufficient to answer the question. The main problem here is the lack of analyses on the type of traits, only the number is taking into consideration. L.104 "The field lacks clear guidelines for researchers to follow when choosing the number and types of traits to include when calculating functional diversity metrics." Although this statement is not completely true, this study do not help to solve it. There is no conclusion on which traits and how many traits is required. So far, this study gives hint about sensitivity of indices on trait number. Moreover, there is no clear explanation about ecological processes behind, since analyses performed here pointed out mathematical properties of the different indices to trait number.

About the sensitivity of FD to trait number: This is a very exiting question ! However, I am not sure I found a satisfying answer in this paper, or at least given the analyses the authors performed here. The fact that FD indices varies with the number of traits is not surprising but more importantly, I do not know how to interpret it! The authors seem to interpret it as a weak point of the method since they focus on FDis (1st paragraph of discussion), which do not vary with the number of traits. They justify it by the fact that : "This suggests that FDis provides reliable values across different communities and sets of traits, making it a potentially valuable tool for assessing patterns of functional diversity across communities and ecosystems." This is not true. For me, what is important is the ranking of communities across trait number. The question of community ranking is the key aspect here. Indeed, more than the values itself, most of the study in community ecology are based of the relationship of FD indices between communities. I would like to see this part more developed.

Moreover, FD indices, at least some of them, are highly influenced by the species richness. Most of community ecologist working of FD used null models where they compared the observed values to expected values. This would be more interesting to analysis and interpret, because SES will be comparable between community irrespective of their species richness, but also between number of traits with clear null hypothesis that a useful SES values of a FD index should be stable.

From a methodological point of view, I am not sure whether the FD indices are calculated directly using traits or after PC(o)A. L. 280, the authors claim that they "used dimensionally reduction where necessary". but later in the paragraph, they said L.291 they "calculated each metric using all possible combination of two traits up to all possible combinations of the maximum number of traits". There is also no information on whether traits are center/scale before calculated FD indices. I got a bit lost here, or try to explain better what you want to do. This might have strong implications, since if not scaled, traits might have different weight.

If the authors used traits to calculate indices; I disagree with their discussion. L. 407, they said that some FD indices are not suitable because the ranking changes given the number of traits. and later, L.415: "This is particularly concerning given the often arbitrary nature of selecting the number of traits used in a study.". This is not surprising but instead, it can be useful, meaning that some traits (or combination) add some information. Otherwise why not using only body size... Moreover there is no explanation why such differences happened. Does some specific type of traits bring new information and change the patterns ? Here, and more generally in the discussion, there is a lack of ecological explanations of the results. A great advantage of working on real community would be to correlate outputs of indices (mathematics) to ecological process or at least to the different type of traits/species.

In addition, when we have several traits, a common strategy is to make a PCA/PCoA, then it would have been wise to test if the number of traits changes the results, not on the raw data but on the FD indices calculated after using a PCoA. FD indices would be calculated on a PCoA with same number of dimension. Such approach would be more relevant.

About the trait-trait analysis, the effect of traits correlation was calculated only with 4 traits (L.295), but I am a bit surprising of this choice. Please justify it. All this lack of details (including my previous remarks) make that the trait-trait analyses have weak support so far.

Finally, there is no mention of the trait selection. The choice of the traits and its selection seems to be randomized (e.g., L; 294: "10 different traits so there are 45 2-trait calculations, 120 3-trait calculations[...]). Do it mean that only the number but not the identity matter? And should we expect similar results if the type of traits is different ? For instance the authors L. 402 explain differences with other studies by the number of traits, but in any case we have information of the type of traits used.

# Minor comments

L. 46. Do you have example of such studies ? This is quite dangerous approach

L. 75. reference is needed

L. 75. "Therefore, functional diversity could differ among replicate plots or sites simply because of the number or types of traits used to calculate the metric without any underlying ecological basis." But if the trait differs, its means that the ecological processes also differ. here the problem is not about metrics, but more about what we mean by "functional diversity". In another way, it is NOT because we got similar result with different set of traits, that the metric is better (or true).

L. 81. "it is important to determine the conditions under which they reflect ecological processes as opposed to mathematical patterns." I agree, but this aspect is not solve in this paper. for that a analysis on the trait type and relevance with ecological processes is needed not on the metrics. Metrics is just a way to calculate but it will in any case represent ecological processes.

L. 80. "As use of multi-trait functional diversity increases, it is important to determine the conditions under which they reflect ecological processes as opposed to mathematical patterns." OK, but this is not what the authors are doing here.

L. 122. replace value by metrics

L. 137: To refine objective of the paper I suggest to clarify the objective 1 (L. 137) the term "vary" need to be better explained. Moreover, I do not understand well this objective since the expectations are mathematical properties of the indices. Maybe can be wise to adapt them to the specific trait/species of the grassland?

L. 228/ Are the traits scaled/centered?

L. 280/ What means "where necessary"?

L. 318: "Adequate" avoid such vague vocabulary.

L. 328: How many communities have only one species ?

L. 331: this sentence is not clear

L. 332: "some": which?

L. 336: "relationships of communities to each other" rephrase it

L. 332: The reference to null model is not clear here. Do you mean that the relationship is not significantly different that expected under null model?

L. 362: I did not understand the goal of this analysis here. it has not been mention in introduction, and barely in method.

L. 376. The authors focused on 1 index, but it is not explain why here.

L. 402. Here a discussion about the type of trait is also needed.

L. 407. I do not agree. Here some analyses of SES are required to conclude

L. 412. Can you provide some explanation why such discrepancies of FEve? Does it come from mathematical issues or ecological process?

L. 450: I do not agree about this distinction between continuous/categorical data. Continuous are more common and available on a larger range of species. Moreover filling gap procedure are also well-know and work quite well ! Instead I would expect a real discussion on why indices are working on both type of distance.

Fig: in some cases, not all communities are visible, maybe you can use thinner lines and/or transparency

Please check your references, some are in different style.

Sincerely,

Reviewer #2: I reviewed the manuscript ‘The impact of trait number and correlation on functional diversity metrics in real-world ecosystems’ submitted for publication in PLOS One. The authors use vegetation data from natural and experimental communities to explore how trait number and correlation impact on various functional diversity metrics. The Introduction is extremely well written and clearly explains the importance of this study. The Discussion is also great and provides useful guidelines for researchers analysing functional diversity. Since the paper is rather methodological I found that the Methods and Results part could benefit with some further explanations and clarifications to further enhance the clarity and readability of the study. Please see my suggestions below:

Methods:

Line 161 – it’s a little difficult to follow how many sites and grasslands there were (e.g. in line 163 could be understood that each grassland had a site with natural and a site with planted community), maybe start the site description with the fact that there were two sampling sites and then mention how many communities and whether natural or planted were sampled in each site

Lines 165, 173 – add approximate coordinates for the sites

Line 182 – add which year

Line 185 –unclear if the 48 plots were in total for four communities, or were there 48x4 plots? explain somewhere how the two communities were located and how they differed from each other

Line 205 – the text in line 202 gives impression that data was collected only in 2018, so it reads a little strange here that the 2018 was selected

Line 249 – remove one ‘then’ from the sentence

Line 258 – missing part of the formula

Line 266 – this is also mentioned in lines 276-277, maybe not needed here

Line 305 – unclear here how the models were run for each community if the min/max/mean trait correlations were also calculated for each community (so there’s a single value of explanatory variable)

Results

Lines 317-329 – this would fit better in the methods, some of this information is already mentioned earlier in the text

Line 332 – if i understand correctly then only null model shows no relationship? if that’s the case then use ‘i.e.’ instead of ‘e.g.’

Line 335 – are these results shown somewhere? add reference to figure

Line 336 – the part ‘relationships of communities to each other’ is unclear, maybe just use the phrasing that is currently in the parentheses (and maybe use ‘from low to high functional diversity metric values’ for clarity)

Line 344 – is this correct ‘depending upon the number of traits used to calculate them’? isn’t this the relationship that is being tested? maybe rephrase to clarify, consider also adding an explanation to the Methods what rankings were compared

Table 3

Unclear what is ‘functional form’.

Add some further explanations in the table header as to how to read the table, it’s not very intuitive that the models that are compared are per each metric, distance matrix and predictor combination (within a row, but considering the same distance matrix, right?), and not clear that the 6 (for each distance measure) models are for different communities.

Explain also what mean, maximum and minimum correlations mean, so the table would be understandable without necessarily reading the text.

Line 352 – add a reference to a table or figure

LIne 354 – use ‘an Euclidean’

Line 360 – unclear what is the percentage from, models?

Discussion:

Line 381 – the part ‘though their magnitude was affected by input trait number’ could be removed since this is said also at the end of the sentence and currently makes the sentence difficult to read

Line 412 – use ‘community CDR4’ to remind the reader again what these acronyms stand for

Line 428 – what is ‘and unresponsive relationship’, do you mean ‘or no relationships’

Line 444 – could this be better as ‘Gower or Euclidean dissimilarity’?

Fig. 1

Are some of the communities not shown, e.g. in J, or are they covered up by each other? Maybe with a bit thinner lines and smaller points they could be visible?

Supplementary materials

The data collection protocols include Konza, but since this data was not used in the current study, maybe not needed to include here to avoid confusion

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10.1371/journal.pone.0306342.r002
Author response to Decision Letter 0
Submission Version1
19 Apr 2024

We thank the two reviewers for their comments. Their reviews were most helpful for improving the clarity of the text and focusing the aims of our study. We have responded to each individual comment. In most cases, we agreed with the reviewers comments and either altered text or changed/added analyses as necessary. In a few instances for which additional analyses were proposed, we have provided justification for the methodology proposed in the Registered Report article and performed for this manuscript. For convenience, we have included in these responses quoted text from our most recent submission. Reviewers comments are shown in standard black text while our responses are in blue italicized text.

Reviewer #1: ## Review PLOSONE: the impact of trait number and correlation on functional diversity metrics in real-world ecosystems

# General comments

I review the paper entitled "the impact of trait number and correlation on functional diversity metrics in real-world ecosystems" submitted to Plos ONE journal. In this paper, the authors deal with a timely question in functional ecology related to the choice of functional traits to calculate functional diversity indices. Indeed, given the development of trait measurements in ecology, trait-based approaches are more and more common to go behind taxonomic diversity. A key aspect of these approaches is the sensitivity of functional diversity indices to the choice of functional traits (e.g. number and correlation).

In this paper, the authors propose to test the sensitivity of 8 functional diversity indices on real community of plants. Thus, they test the behavior of functional diversity indices to the number of functional traits used to describe the community. In addition they also test how the traits correlation influence the FD indices. They found that some indices decrease when the number of traits increased, while other increase and some are not changing. They also found that the trait-trait correlation have no significant influence of the functional indices.

The more I read the paper the more I had some problems to understand the real aim of this paper. When the authors claim L. 75 "Therefore, functional diversity could differ among replicate plots or sites simply because of the number or types of traits used to calculate the metric without any underlying ecological basis." and L. 407: "Some metrics may be unreliable measures for comparing functional diversity among communities since comparisons are dependent upon the number of traits used to calculate them." OK, I agree, but does people really compared FD of communities calculated on different number of traits ? I would not do it in any case, whatever the metrics give similar or different values. It is just like comparing apple and pear.

As a general comment, I would say that the authors pointed out a real question in their introduction, but the analyses and interpretations are not sufficient to answer the question. The main problem here is the lack of analyses on the type of traits, only the number is taking into consideration. L.104 "The field lacks clear guidelines for researchers to follow when choosing the number and types of traits to include when calculating functional diversity metrics." Although this statement is not completely true, this study do not help to solve it. There is no conclusion on which traits and how many traits is required. So far, this study gives hint about sensitivity of indices on trait number. Moreover, there is no clear explanation about ecological processes behind, since analyses performed here pointed out mathematical properties of the different indices to trait number.

Thank you for this comment as it has helped us clarify the aims of this study. Though we might have found a conclusive answer as to the specific number of traits required to generate a robust comparison of rankings among communities, our results generated no such obvious conclusion. We did report results and include recommendations for using certain metrics for which rankings among communities were inconsistent across the range of number of traits used to calculate them (such as FEve). We agree that the focus of this paper is primarily to test the mathematical properties of these metrics and we believe that our study represents meaningful progress in the field by, for the first time, using real grassland data in this investigation instead of simulated data.

About the sensitivity of FD to trait number: This is a very exiting question ! However, I am not sure I found a satisfying answer in this paper, or at least given the analyses the authors performed here. The fact that FD indices varies with the number of traits is not surprising but more importantly, I do not know how to interpret it! The authors seem to interpret it as a weak point of the method since they focus on FDis (1st paragraph of discussion), which do not vary with the number of traits. They justify it by the fact that : "This suggests that FDis provides reliable values across different communities and sets of traits, making it a potentially valuable tool for assessing patterns of functional diversity across communities and ecosystems." This is not true. For me, what is important is the ranking of communities across trait number. The question of community ranking is the key aspect here. Indeed, more than the values itself, most of the study in community ecology are based of the relationship of FD indices between communities. I would like to see this part more developed.

We agree that the relationships of FD indices among communities is the most important factor to consider. To that end, the first paragraph of the discussion section highlights the suite of metrics that maintain consistent relationships among communities across the range of trait numbers L 435-441: “Similarly, Rao's Q, KDE dispersion, and KDE richness maintained consistent ordered rankings of metrics among communities across the range of trait numbers for both Gower and Euclidean dissimilarity matrices, although differences between communities were magnified at higher numbers of traits when using Euclidean matrices. Other metrics (FEve, KDE evenness, FDiv) had less consistency across the range of traits used to calculate them as relative rankings of different communities changed with the number of traits used in constructing the metrics.“

L. 463-469: “Specifically, FRich, FEve, and KDE evenness showed crossing slopes among communities (i.e. ranking of communities changed with the number of traits) for both Gower and Euclidean distance matrices. The inconsistency of communities’ relationships to one another across the range of the number of traits raises concerns. For example, community CDR4 had a greater FEve than community SEV1 when using four traits, but CDR4 had a smaller FEve than SEV1 when calculated with eight traits. Such discrepancies have the potential to introduce discordant results in the literature, even when otherwise identical studies have been conducted.”

In addition, our recommendations support the use of metrics that maintain consistent rankings of communities and suggest supplementary analyses for studies using metrics for which rankings among communities are inconsistent L 528-533: “Based on our findings, we recommend use of FDis, KDE dispersion, and/or Rao’s Q in analyses of functional diversity as all of these measures provide consistent results among communities at all numbers of traits tested. Additionally, due to the inconsistency of evenness metrics with respect to community rankings, we strongly recommend that any use of FEve or KDE evenness metrics include supplemental analyses to test whether results are consistent with different numbers of traits used to calculate them.“

Moreover, FD indices, at least some of them, are highly influenced by the species richness. Most of community ecologist working of FD used null models where they compared the observed values to expected values. This would be more interesting to analysis and interpret, because SES will be comparable between community irrespective of their species richness, but also between number of traits with clear null hypothesis that a useful SES values of a FD index should be stable.

We recognize that use of richness-based null models is helpful in some contexts in order to isolate the effects of traits on FD separate from effects of species richness. In this study, we specifically chose an approach agnostic to species richness as the focal objective was to resolve the predictability and reliability of metrics across ranges of trait number and correlations as opposed to investigating which metrics were more or less informative than simple species richness. Consider, if a species-based null model was chosen as the best model through model selection in our paper, we could conclude that the FD metric is a worse predictor than species richness but would have learned nothing about reliability of FD metrics. To that end, we do include a null, intercept-only models which test whether or not any change in metrics occurs across the variables which we test (number of traits and correlation). Many papers in the literature take a similar, trait-agnostic approach when questions focus on comparing functional diversity among communities as opposed to comparing relative explanatory power of richness among communities (e.g. Zihao et al. 2021, Mao et al. 2022).

From a methodological point of view, I am not sure whether the FD indices are calculated directly using traits or after PC(o)A. L. 280, the authors claim that they "used dimensionally reduction where necessary". but later in the paragraph, they said L.291 they "calculated each metric using all possible combination of two traits up to all possible combinations of the maximum number of traits".There is also no information on whether traits are center/scale before calculated FD indices. I got a bit lost here, or try to explain better what you want to do. This might have strong implications, since if not scaled, traits might have different weight.

We have now added additional text to clarify our methodology. There seems to be confusion about dimensionality reduction and how we looked at the impact of trait number on the metrics. The text now reads:

L 281-287: “To understand the impact of trait number on functional diversity, each functional diversity metric was calculated using all possible combinations of two traits up to all possible combinations of the maximum number of traits at each site. For example, at Sevilleta there are 10 different traits so there are 45 2-trait calculations, 120 3-trait calculations, 210 4-trait calculations, and so forth up to 10 9-trait calculations and 1 10-trait calculation. This allows us to focus on the impact of trait number independent of the constituent set of traits used to calculate the metric.”

L288-297: “To calculate the five metrics using the FD package, we first calculated a species-trait distance matrix using both Gower (categorical and continuous traits) and Euclidean (continuous traits only) distances. These distance matrices were calculated with both scaled and centered and non-scaled trait data for each community. Centering was done by subtracting the trait mean from each observation and scaling was done by dividing the centered traits by their standard deviations (as in the FD package). These distance matrices along with a species-abundance matrix are the input for the FD package. The FD package performs a principal components analysis on the full species-trait distance matrix. Dimensionality reduction only occurs for FRic and FDiv metric calculation. For all FRich and FDiv analyses, we hold the number of dimensions equal to 2, similar to Legras et al. [20].”

We have added a table to the supplemental material which shows the model selection results when unscaled data are used (i.e. Table 3 in the main text but using unscaled data). The best fit functional forms changed for just a few of the metrics and overall the changes do not affect our interpretation of the results.

If the authors used traits to calculate indices; I disagree with their discussion. L. 407, they said that some FD indices are not suitable because the ranking changes given the number of traits. and later, L.415: "This is particularly concerning given the often arbitrary nature of selecting the number of traits used in a study.". This is not surprising but instead, it can be useful, meaning that some traits (or combination) add some information. Otherwise why not using only body size... Moreover there is no explanation why such differences happened. Does some specific type of traits bring new information and change the patterns ? Here, and more generally in the discussion, there is a lack of ecological explanations of the results. A great advantage of working on real community would be to correlate outputs of indices (mathematics) to ecological process or at least to the different type of traits/species.

Thank you for this comment. We agree that the primary results from this work represents mathematical properties of these indices and therefore we do not try to make unsupported ecological conclusions. In our analyses, every combination of traits exists at each of the values of number of traits on the x-axis. Therefore, since every trait is equally represented across the range of x-axis values, the fact that the values of metrics change across the range of values is not due to ecological processes of different traits being used to calculate the metrics. In other words, the trait-number analyses do not assess relative contribution of certain traits because it is agnostic of trait identity. Conveniently, the trait correlation analyses provide information as to how the types of traits used impact the metrics, albeit with a focus on trait correlation as opposed to trait identity per se. Though we can speculate as to how certain traits drive variability in certain metrics (e.g. line 446-450 which reads “These differences in findings might be attributed to the inherent complexity and noise present in real-world data. Real communities often contain anomalous species with outlier trait values (e.g. a gymnosperm among angiosperms, a tree seedling among herbaceous plants, or other rare species outlier values), which can exert considerable influence on evenness indices.“), conclusions about how these metrics relate to ecological properties or specific conclusions about certain traits or species are outside of the scope of this work and would require a wholly different study design. However, we agree on the importance of such work.

In addition, when we have several traits, a common strategy is to make a PCA/PCoA, then it would have been wise to test if the number of traits changes the results, not on the raw data but on the FD indices calculated after using a PCoA. FD indices would be calculated on a PCoA with same number of dimension. Such approach would be more relevant.

Though use of PCA/PCoA for dimensionality reduction is common in studies using functional diversity metrics, it is also common to not use dimensionality reduction (e.g. Thakur & Chawla 2019, Zuo et al. 2021, Biswas et al. 2019, Niu et al. 2015). In particular, KDE metrics do not use dimensionality reduction in their calculation and in order to make metrics most comparable to each other, we also did not use dimensionality reduction in the FD metrics except for those metrics that require it. Moreover, Legras et al. 2020 showed in their supplemental material that metrics are very similar regardless of the extent of dimensionality reduction.

About the trait-trait analysis, the effect of traits correlation was calculated only with 4 traits (L.295), but I am a bit surprising of this choice. Please justify it. All this lack of details (including my previous remarks) make that the trait-trait analyses have weak support so far.

Four traits was chosen as a compromise between the minimum number of traits likely to be used to calculate these indices and an effort to reduce noise in the evaluation of minimum and maximum trait correlation. Max and min include all possible combinations of four traits and therefore all possible pairwise combinations of two traits to generate max and min. Including greater numbers of traits in these a

Attachment Submitted filename: Response to reviewers.docx

10.1371/journal.pone.0306342.r003
Decision Letter 1
Boscutti Francesco Academic Editor
© 2024 Francesco Boscutti
2024
Francesco Boscutti
https://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Submission Version1
23 May 2024

PONE-D-24-03515R1The impact of trait number and correlation on functional diversity metrics in real-world ecosystemsPLOS ONE

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Reviewers' comments:

Reviewer #2:

 The authors have done a great job in revising the paper and addressing reviewers' comments. I only have a few minor suggestions to improve the clarity of the text in a few places:

Line 50 – the acronyms are not defined in the abstract, better to write out or define in lines 44-45

Table 3

Line 375 – in the table header the example for Frich, Trait number and Gower (first line in the table) doesn’t fit with the results in the table (text says 2 for linear and 4 for quadratic, but table has 3 and 3 – i think the text hasn’t been updated for the new version of the table)

In the table use ‘FRich’, ‘FDis’, ‘FEve’ and ‘FDiv’ like in the rest of the manuscript

KDE diversity measures are not capitalised in the the text (e.g. ‘evenness’), but are here and on the figures – better to use the same spelling everywhere

Line 385 – this is the first time CDR is used, but it’s not defined anywhere

Fig. 1 and Fig. 2 have different legends, but I guess these should be the same?

Fig. 2, Fig S1, Fig S2

Lines 399, 407, 415 – CDR and SEV are not defined

Line 527 – perhaps this section could be combined with the previous one (e.g. using heading ‘The ecological significance of methodology and recommendations’ or something similar) since some recommendations are already given in lines 519-526

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10.1371/journal.pone.0306342.r004
Author response to Decision Letter 1
Submission Version2
3 Jun 2024

Reviewers' comments:

Reviewer #2:

The authors have done a great job in revising the paper and addressing reviewers' comments. I only have a few minor suggestions to improve the clarity of the text in a few places:

Line 50 – the acronyms are not defined in the abstract, better to write out or define in lines 44-45

We agree and have made this change.

“We found that most metrics were sensitive to the number of traits used to calculate them, but functional dispersion (FDis), kernel density estimation dispersion (KDE dispersion), and Rao’s quadratic entropy (Rao’s Q) maintained consistent rankings of communities across the range of trait numbers” lines 43-46

Table 3

Line 375 – in the table header the example for Frich, Trait number and Gower (first line in the table) doesn’t fit with the results in the table (text says 2 for linear and 4 for quadratic, but table has 3 and 3 – i think the text hasn’t been updated for the new version of the table)

In the table use ‘FRich’, ‘FDis’, ‘FEve’ and ‘FDiv’ like in the rest of the manuscript

KDE diversity measures are not capitalised in the the text (e.g. ‘evenness’), but are here and on the figures – better to use the same spelling everywhere

We agree and have made these consistent.

Line 385 – this is the first time CDR is used, but it’s not defined anywhere

We have now defined CDR and SEV in lines 170 and 178, respectively.

Fig. 1 and Fig. 2 have different legends, but I guess these should be the same?

These are now consistent.

Fig. 2, Fig S1, Fig S2

Lines 399, 407, 415 – CDR and SEV are not defined

We have now defined these in lines 170 and 178.

Line 527 – perhaps this section could be combined with the previous one (e.g. using heading ‘The ecological significance of methodology and recommendations’ or something similar) since some recommendations are already given in lines 519-526

We like this idea and have edited it accordingly. Line 515

Attachment Submitted filename: Reviewer comments Round 2.docx

10.1371/journal.pone.0306342.r005
Decision Letter 2
Boscutti Francesco Academic Editor
© 2024 Francesco Boscutti
2024
Francesco Boscutti
https://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Submission Version2
11 Jun 2024

The impact of trait number and correlation on functional diversity metrics in real-world ecosystems

PONE-D-24-03515R2

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10.1371/journal.pone.0306342.r006
Acceptance letter
Boscutti Francesco Academic Editor
© 2024 Francesco Boscutti
2024
Francesco Boscutti
https://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
20 Jun 2024

PONE-D-24-03515R2

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==== Refs
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