Overview

Motivated by the original application of consensus clustering [49], our methodology comprises a multi-step clustering approach that addresses the challenge of uncertainty and correlation between traits (Fig 1). In summary, we resample our dataset S times, generating a clustering ensemble, where, for each resample, we fit a GMM with the total number of components (functional groups) that minimizes BIC (Clustering ensemble), hence, so that every species is assigned to a group which can very within iterations. This generates a clustering ensemble that is synthesized using consensus clustering, hence, computing how often each pair of species was linked together (Consensus clustering). These proportions are then treated as a distance metric between species, making it suitable for the use of hierarchical clustering. This allows for a flexible clustering scheme, where the number of groups can be decided based on the particular application.

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Fig 1. Conceptual diagram for consensus clustering with data uncertainty.

a) The input of the model is the data and prediction error to account for data uncertainty. These data and prediction error are used to perform resamples that are clustered using GMM by optimizing the number of groups with BIC. b) These resamples yield a clustering ensemble, where for each pair of species it is possible to compute the proportion of times they were linked together. This builds a consensus matrix. c) This consensus matrix is used as a distance matrix to perform hierarchical clustering to optimize the silhouette score (due to the absence of a likelihood for BIC-based selection) and obtain the final group assignations.

https://doi.org/10.1371/journal.pcbi.1014278.g001

Throughout, we denote matrices with bold and capital letters (e.g., A), vectors with bold and lowercase letters (e.g., a), and scalars and indices with non-bold letters (e.g., a, i, j). The cardinality of a set , representing the number of elements in the set, is denoted by . We otherwise define any notation that is specific to this methodology.

Clustering ensemble

The first step in this method addresses the fact that trait data are noisy, whether due to intraspecific or ontogenetic variation, or to measurement error or imputation noise. We address this uncertainty by adopting an ensemble approach to clustering, where we resample the data in the presence of uncertainty, and fit a Gaussian mixture model to each resample.

Specifically, let X denote a matrix in which each row corresponds to a species, and each column represents a trait. Formally, X has N rows (species) and M columns (traits). Let us consider as the set containing all species, and as the set containing all traits. We are not considering the case where some traits could be categorical, as this further complicates the clustering problem [50].

The clustering problem itself consists of finding a partition of , denoted as , hence a collection of sets that do not share any element with each other and that would jointly account for every species in . We denote G as the number of sets from the partition, which is equivalent to the number of groups. Also, denote as the set g in the partition. The first challenge of this problem is that we do not know the value of G, as this is part of what we are trying to answer.

The second challenge of our clustering problem is that our matrix of observations X comes with uncertainty. This happens because some entries of the matrix were imputed using predictive methods. To address this uncertainty, we are going to consider the input of the clustering problem to be a random variable W, which we can resample S times. Then, let W^(s) represent the s-th instance for clustering, where these instances are independently and identically distributed. Each resampling iteration yields a distinct partition , which may come with a different total number of groups G^(s).

In this section, we will first detail how to model the random variable W, then detail how to fit a GMM for each resample of this variable, and finally how to choose the best value of G for each resample.

Resampling from error distribution.

To account for trait variation and prediction errors in our data, we use a resampling approach that is repeated in order to obtain a robust cluster. Think of W_ij as a random variable for the value of trait j for species i, with the following distribution:

(1)

Here, E_ij denotes the error distribution for species i and trait j. For example, this can be specified non-parametrically by sampling from empirical prediction errors, or parametrically using a normal distribution centered at zero with the observed standard deviation. The matrix W is then a random matrix, where each entry represents a random variable reflecting uncertainty in trait values.

Fitting a Gaussian mixture model

We adopt to use Gaussian Mixture Models for each resample because of the intrinsic ability of a GMM to account for correlation between traits, and its ability to allow for different correlation structures for each group [51]. Moreover, GMMs provide a flexible probabilistic framework for clustering that can capture a wide range of cluster shapes through mixtures of Gaussian components. Compared to methods such as k-means or PAM, which rely on distance-based partitioning, GMMs allow clusters to differ in covariance structure and orientation. This flexibility is particularly useful for ecological trait data. In particular, the data used in our experiments exhibit a clear correlation structure, and the traits are approximately normally distributed (S1 and S2 Figs), making GMM a well-suited choice in this case. Nevertheless, depending on the ecological application and the expected importance of trait covariation, alternative clustering methods may be more appropriate.

For the effects of this section, consider to be any realization of the random variable that serves as input for the clustering algorithm. Note that in cases with uncertainty in the data, fitting a GMM without resampling likely leads to overfitting (S10 Fig).

In a GMM, each group g would be defined by a Multivariate Normal distribution with mean , covariance matrix , and weight , that determines the probability of a species belonging to group g. We will refer to the complete set of parameters as: . These parameters are latent variables of the model (unobserved) that we are trying to recover by maximizing log-likelihood.

To estimate the parameters , we maximize the log-likelihood using the EM-algorithm [52], which involves two steps:

E-step: Calculate the posterior probabilities that i belongs to g, given the current parameter estimates. Using Bayes and the law of total probability:

(2)

where is the Multivariate Normal density function.

M-step: Update the parameters , , and by maximizing the expected log-likelihood (3) using the posterior probabilities from the E-step (2).

(3)

The algorithm alternates between these steps until the parameter estimates converge. After fitting the model, group membership for each species can be interpreted either as a probability distribution, where , or by assigning each species to the group with the highest posterior probability, .

Choosing the optimal number of groups G is challenging since increasing G naturally improves the log-likelihood by adding more parameters. Thus, the goal is to find the smallest G that still adequately fits the data.

An approach to choose the value of G comes by using the Bayesian Information Criterion (BIC), as we are working directly with a probability distribution. This metric balances the trade-off between the log-likelihood and the number of parameters. This metric has been shown to estimate the correct true number of groups in multiple situations under certain simulated conditions and is usually recommended against other metrics like the Aikake Information Criterion [53]. Note that the number of parameters increases linearly as we fit more groups. Defining as the number of parameters for a GMM with G groups (without considering repeated parameters), the BIC value for a GMM with G components is:

(4)

(5)

Using this metric, we can try different values of G and choose the GMM that maximizes the BIC score. Then, we can define . Note that other metrics used for choosing the number of clusters, such as the silhouette-score or the elbow method, do not penalize model complexity, can be affected by correlation, and ignore the probabilistic nature of the model [53–55].

Consensus clustering

Through resampling, we obtained a collection of partitions , each of which is the best clustering result for a particular resample of our data. This is useful, as we generated a distribution of clusters that accounts for uncertainty. However, this process introduces a new challenge: determining a singular assignment for each species from the multitude of individual clusterings. To address this issue, we need to decide a singular assignment for species i based on how often it was linked to the other species .

The idea of consensus clustering was first introduced for visualizing gene expression [49]. The main purpose of this algorithm is to find consensus between multiple cluster algorithms or multiple realizations of the same algorithm. While the original framework proposes bootstrapping as a resampling method, we saw the potential to incorporate prediction error as a resampling mechanism to address uncertainty. Then, we construct a consensus matrix C that summarizes the clustering ensemble previously obtained. In this matrix, component shows how often species i was linked to species throughout the S iterations of resampling.

(6)

Note that the clustering ensemble and the construction of the consensus matrix could be done simultaneously in an efficient way as described in Algorithm 1.

In this section, we will go through how to build a clustering structure with the consensus matrix, and how to ultimately choose the number of groups with this structure.

Algorithm 1 Consensus Clustering with Trait Resampling and GMM random assignations

1:  Input: Original matrix , error distributions E, number of samples S, number of random assignations A

2:  Output: Final matrix C containing average cluster co-occurrences

3:  Initialize C as an N × N zero matrix

4:  for s = 1 to S do

5:   Sample W^(s) as described in 1

6:   Fit GMM to W^(s) to obtain probability matrix as described in 2

7:   for a = 1 to A do

8:    Sample partition from

9:    Initialize as an N × N zero matrix

10:    for each pair do

11:      if , otherwise 0

12:    end for

13:    

14:   end for

15:  end for

16:  

Hierarchical clustering

Hierarchical clustering, particularly linkage-based methods, is well-suited for our clustering framework because it requires only a distance metric rather than specific observations. This is ideal for our case, as the consensus matrix C can be interpreted as a distance matrix. By defining , we treat species with high consensus as closer to each other for clustering purposes, making hierarchical clustering a natural choice for this step.

For our application, we employ the Ward linkage method due to its ability to create compact, homogeneous clusters while minimizing variance [40], making it widely adopted in ecological studies for phylogenetics and species distribution [49,56,57]. It forms clusters by merging pairs that result in the smallest increase in within-cluster variance at each step using an agglomerative approach. In doing so, it implicitly results in clusters that are compact and approximately spherical in multivariate trait space, which is consistent with ecological niche theory, which holds that species occupy bounded, unimodal regions in multidimensional niche and trait space [58,33]. Nevertheless, although we adopt Ward’s method due to its simplicity and ecological relevance, we stress that any hierarchical clustering linkage method could be used in place, depending on the desired application and resolution of small vs. large clusters, and the expected shape of the ecologically relevant clusters in multivariate trait space.

Choosing the number of groups for hierarchical clustering.

As with the GMM procedure, we once again face the challenge of choosing the number of groups to obtain a single consensus cluster. We address this using a dendrogram generated by the Ward linkage, which is a tree-like diagram that illustrates the arrangement of clusters formed at various levels. We denote the number of groups as K to distinguish it from those in the GMM. Unlike GMM, which is a flat clustering algorithm, hierarchical clustering allows flexibility to adjust K by cutting the dendrogram at different levels [59].

To choose the best value for K, we use the silhouette score, which measures how well a species aligns with its cluster versus other clusters. This score is effective in identifying the true number of clusters across various applications [54]. In contrast to the previous resampling step, which used a likelihood-based criterion such as BIC, this approach relies on a distance matrix and therefore does not permit the use of likelihood-based methods. The silhouette score s_K(i) for species i in a clustering with K groups is defined as:

(7)

Where intuitively: a_K(i) is the average distance from the species i to all other species in the same cluster, and b_K(i) is the average distance from species i to all the species in the nearest next cluster. Then K^* is the value that maximizes .

By maximizing the silhouette score, we obtain a final partition of , denoted as , which serves as the outcome of the clustering framework. Note again that this partition is hierarchical, not flat like the one used for GMM, allowing flexibility to adjust the number of groups ( or ) within the same clustering structure.

It is important to note that the optimum in terms of silhouette-score comes from a hierarchical clustering perspective that is different to the resampling approach. The optimal number of clusters chosen at the last step does not need to match the mean of optimums obtained during the resampling step.

Case study: Functional groups of trees

Traits are particularly important for trees, as they govern water, nutrient, and light economies within individuals [1,60], which underpin key life-history trade-offs that lead to trait selection across different environments [61]. Trees have unique traits related to woody structure, size, and longevity [62,63], which sets them apart from herbaceous, non-dendritic plant species, whose analysis is often restricted to leaf-related traits [64,65]. The unique traits of trees can provide insight into broader ecological functions of trees, such as a forest’s carbon storage capacity [66,67] and its resilience to climate change [15,68,69]. Such analyses are indispensable for predicting the impacts of environmental shifts and planning effective conservation strategies.

In this case study, we apply our consensus clustering approach in the presence of trait uncertainty, as some of the trait measurements have been imputed using machine learning methods [70]. We address 2 main questions: (1) how many groups there are, and (2) what these groups are. Question (1) is addressed from an optimization perspective, where maximize metrics that are related to how good a clustering result is. Question (2) is addressed from a perspective of trait uncertainty, where each resample of the data yields a different possibility of how the clustering could look.

Data.

The dataset for this case study is based on observed species-level values and imputed values from a study analyzing global tree trait relationships [70]. Imputed values were generated using machine learning methods based on the phylogenetic distances between species, which introduces the uncertainty we will address in the clustering problem. The data consists of N = 47,828 species of trees and M = 18 traits (for details see Table 1, S1 and S2 Figs). This data accounts for around 70% of all tree species, across different taxa and geographic regions [71].

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Table 1. Trait statistics. Each trait specifies the unit of measurement, the mean and standard deviation for natural-log transformed values, the mean, standard deviation, minimum, and maximum values for the original scale, the number of error samples, and the Mean Absolute Error (MAE) on the standardised log scale.

https://doi.org/10.1371/journal.pcbi.1014278.t001

Prior to clustering, all traits were log-transformed, as is typical for functional trait analysis in plants [72]. This is for two reasons: first, ecologically meaningful differences in traits are typically proportional rather than absolute, as strategies are differentiated by orders of magnitude rather than additive differences. In addition, because most ecological traits are strongly right-skewed, the log transformation stabilizes the variance and ensures approximate normality, which satisfies the assumptions of Gaussian processes.

Error data.

In the case of trees, the error distribution for trait j was computed by collecting all empirical errors available for that trait (S3 Fig). Maynard et al. produced species-level mean estimates of 18 traits, along with the corresponding error (observed - predicted) for each species that had one or more observed trait values. By collecting these trait-specific errors, we obtain an empirical posterior error distribution for each trait, nested within taxonomic groups (i.e., one set of angiosperms, one set for gymnosperms).

Specifically, let and be the sets of observed and predicted values for trait j, respectively. We also differentiate between a set of angiosperms and a set of gymnosperms , as these taxonomic groups are significantly different and some methodologies to measure their traits could vary [73]. We specifically have angiosperms species and gymnosperm species. Then for traits that we know some observed values, we can sample errors using the following error sets:

(8)

Note that for some traits we do not have error samples (marked empty in Table 1). This happens because these traits were predicted using quantile random forest [70], therefore the observed and predicted values are not comparable for these traits. For this case, we assume that the error distribution comes from the union of all sets of errors that we do have.

(9)

This configuration of errors is well-suited for this particular case study, but it is recommended to adopt an error distribution that suits the particular application. In our case study, for example, we do not consider correlations between errors, in part because the sparsity of the original data set means that the covariance matrix cannot be robustly calculated apart from a subset of species [70]. We thus assume uncorrelated errors in our approach, with the prediction errors being sampled directly from the posterior empirical error distribution for each trait. In other settings, however, more complex error distributions could be incorporates, such as with Bayesian extension of probabilistic matrix factorization (BHPMF), which has been used to impute missing data in other plant datasets [43]. Such decisions should be based on the data availability and the question of interest.

Visualization

To visualize the clustering results, we use the following dimensionality reduction methods:

PCA [74]: Linear dimensionality reduction by creating new, uncorrelated variables ordered by variance.

t-SNE [74]: Uses a probabilistic approach to match a lower-dimensional distribution to the original.

UMAP [75]: Matches graph structures between high and low dimensions capturing non-linear relations.

It is important to acknowledge that dimensionality reduction methods may result in the loss of some information; however, they are useful to allow human interpretability of the data patterns.

Statistics

For each cluster , we computed aggregate statistics, such as the mean and standard deviation of each trait across species . Additionally, we analyzed the cluster sizes and examine the dendrogram that produces the partition.

For species level stability we explored how similar a species is to other species in its own cluster, and how similar it is to all species overall. This is expressed as:

We evaluated clustering robustness by comparing our consensus-based approach to repeated Gaussian Mixture Model (GMM) fits under resampling. On a reduced dataset, we generated multiple resampled subsets and computed pairwise Adjusted Rand Index (ARI) scores between resulting clusterings. We then applied our consensus procedure to groups of resampled runs and compared the stability of the resulting consensus clusterings.

When comparing group-based functional diversity metrics to traditional metrics, we use generalized additive models (GAMs) to account for spatial autocorrelation. Specifically, using the mgcv package in R, we fit GAMs using a B-spline basis for each predictor (k = 7, second-order penalty with first-order derivative), with a spherical smooth of geographic coordinates to account for spatial autocorrelation. Models were estimated using restricted maximum likelihood (REML) with an elevated smoothing parameter ( = 1.4) to guard against overfitting (e.g., gam(y ∼ s(x, bs = ‘bs’, k = 7, m = c(2, 1)) + s(Longitude, Latitude, bs = “sos”)). To estimate residual correlation after accounting for spatial autocorrelations, we fit separate GAMs for the predictor and outcome variables, retaining only the geographic spline term. We then calculated the Pearson correlation between the residuals of both models, providing a measure of association between x and y after removing spatially structured variation in both variables.

Software and hardware

The analysis was primarily done in Python 3.12.4, using scikit-learn for Gaussian Mixture Models [76], SciPy for hierarchical clustering [77], pandas for data manipulation [78], matplotlib [79], and seaborn [80] for visualizations. Computational experiments were conducted on a compute node equipped with 2× Intel Xeon Gold 6426Y (Sapphire Rapids) CPUs (32 physical cores total) and 512 GB of RAM; and initial model testing and downstream analyses were conducted on an AMD Ryzen Threadripper PRO 5995WX workstation (64 physical cores) with 1028 GB DDR4 RAM. The primary experiment (the most computationally demanding and corresponding to Fig 2) required approximately 7.5 hours using the described hardware configuration.

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Fig 2. Optimization for number of groups.

All resulting BIC curves and resulting curve as averaging all curves across G, shown for scaled a) and unscaled b) data. c): Silhouette score for different aggregations of the consensus matrix. A higher value of K means going lower in the dendogram, hence splitting one group. Note that BIC is optimized independently for each resample in (a) and (b), and therefore partitions with the same number of clusters may differ substantially. In contrast, the Silhouette score is optimized at the aggregated level across all resamples. As a result, the optimal number of clusters identified by these two criteria will not necessarily coincide.

https://doi.org/10.1371/journal.pcbi.1014278.g002

Code is available at https://github.com/pabloubilla/tree_clustering/ and is archived via Zenodo with corresponding DOI:10.5281/zenodo.19222113. The data have been archived via Figshare with corresponding DOI:10.5522/04/31833526.

Group selection through consensus clustering

For each individual data resampling, we obtain a corresponding BIC curve that identifies the optimal number of groups (G^*) at different values (Fig 2). The mean BIC curves exhibit similar patterns for both scaled and non-scaled resamples, although the BIC values are generally lower for the non-scaled resamples. However, since the BIC values come from different distributions, this does not imply that not scaling yields a better fit.

When comparing the four combinations of scaled or not scaled, and argmax or random assignment, we find they display similar patterns by quickly increasing the score until around 30 groups, then reaching a plateau with slow decreases after reaching their respective optima (Fig 2). The highest silhouette score is achieved with 42 groups for the scaled data at 0.20 using the argmax assignment, which was subsequently used for the final group assignment through hierarchical clustering.

Note that a value of 0.20 represents the optimal result given the level of uncertainty in the data; lower uncertainty would be expected to yield higher consensus and correspondingly higher silhouette scores. If all traits had zero error, the consensus would necessarily be 1.0, and if trait noise was substantially greater, the silhouette score would necessarily be lower. Thus, the silhouette score can also be used to indicate the extent to which trait error (or noise) weakens cohesion across the groups.

Using a reduced dataset of 1,365 species, we find that the stability of the clustering results is markedly improved following the consensus step (S4 Fig).

Functional groups results and visualization

When grouping species using hierarchical clustering into 42 groups, we observe a wide range of group sizes and varying levels of consensus within the groups (Fig 3). The consensus values are approximately normally distributed, with a mean of 0.39 with a standard deviation of 0.17. Ideally, average consensus values should be near 1, with dissimilarities (off-diagonal values) close to 0, forming a distinct red diagonal in the consensus matrix. We observe a similar result when looking at the species-level stability (S14 Fig) Our results show most clusters tend not to pair with others, except the last six clusters which show uncertain assignments and have average consensus below 0.2 (S1 Table).

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Fig 3. Summary of functional groups results.

(a) The consensus matrix displays the average consensus for all species pairs within clusters along the diagonal, while off-diagonal values represent the average consensus between species from different clusters (row vs. column). Square sizes are proportional to their respective cluster size. (b) Distribution of average consensus for the 42 observed groups, ranging from 0 (no consensus) to 1 (maximum consensus), divided into bins of width 0.1. (c) Size distribution of the 42 groups, where cluster size refers to the number of species per group, with bins of width 100.

https://doi.org/10.1371/journal.pcbi.1014278.g003

The cluster size distribution is left-skewed, with a mean size of 1,139 species and a standard deviation of 790. The majority of clusters contain close to 1,000 species, while a few larger clusters deviate significantly from this norm (Fig 3 and S1 Table). The size distribution is somewhat inconsistent, displaying gaps, which might be due to the relatively low number of clusters and the large range of potential cluster sizes. Notably, there is no cluster smaller than 300 species, with the minimum size being 324 species.

We are able to visualize the functional groups using t-SNE (Fig 4, interactive version in S1 Appendix), where we generally observe a clear separation between groups. Group 2 (blue square), being the largest, shows compactness at the centre of the distribution, whereas group 39 (red x), being the second largest, is spread across the entire distribution. Group 23 (black square) stands out by being tightly clustered, fully corresponding to all Pinales species (S8 and S9 Figs). Group 3 (teal cross) and 4 (magenta x) are also clearly distinct, both encompassing mostly Myrtales species. Other dimensionality reductions do not show as clear separation between clusters, but some are reasonably identified regardless of the reduction methodology (S5 and S6 Figs). Note that this visualization is only intended as a qualitative representation of cluster structure.

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Fig 4. t-SNE visualization of clustering results.

Species are visualized in a two-dimensional functional space using t-Distributed Stochastic Neighbor Embedding (t-SNE), a probabilistic technique that reduces high-dimensional data (originally 18 dimensions) to two dimensions while preserving the local structure and similarity relationships of the data points. Different colors and markers represent distinct groups, chosen to maximize visual distinction among clusters based on their distribution. The distances in this 2D space are probabilistic, reflecting the likelihood of similarity between species, and approximate the original high-dimensional probability distribution. Note that t-SNE is intended for visualisation of the shape and location of clusters, but it does not have the same interpretation as other dimensionality reduction techniques such as PCA (see S5 and S6 Figs for alternate visualisations). Please also see the interactive version of this figure in S1 Appendix, or available from the GitHub repository.

https://doi.org/10.1371/journal.pcbi.1014278.g004

The majority of the clusters are comprised of species that exhibit functionally unique combinations of traits, often aligning with well known taxonomic structures (e.g., within genus or family). However, we confidently identified one large, taxonomically broad group consisting of 4,291 species with non-distinct or ‘average’ traits, comprising taxa from across many families and orders (Fig 4; see interactive version in S1 Appendix). Other taxonomically dispersed groups, regardless of their size, show low consensus values (S1 Table). Whether this large dispersed group represents ecological generalists, reflects convergent evolution of common trait combinations, or captures species not readily assigned to distinct clusters is a compelling question for future work [81–84].

Group trait patterns

When exploring the trait patterns underpinning the groups, we see that they are not determined from just one or two traits, but rather all traits appear to be relevant in the identification of different functional groups (Fig 5, S2 Table). The lowest standard deviation across groups is for stem diameter at 70% of the original variation, while the highest is for leaf density at 99%. If a trait was not relevant, we would expect that there is no pattern to the assignment across that particular trait, meaning the standard deviation across groups would be much closer to 0. We reinforce the idea of group 2 being generalist, showing average values across all traits, while groups 38–42 also show average values across all traits they have higher variation for traits across species (S7 Fig).

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Fig 5. Centroids of 42 functional groups.

Mean values were calculated for each group across their species after normalizing the original dataset for each trait. The colour gradient represents these normalized values and is consistent across all traits, with values clipped at 3 standard deviations from the mean to enhance visualization contrast. A dendrogram, constructed using the Ward-linkage method, is included to illustrate the relative consensus distances among the groups.

https://doi.org/10.1371/journal.pcbi.1014278.g005

Functional groups to quantify functional diversity

The value of a functional group approach lies in the fact that functional groups provide a natural analogue of species, allowing the entire suite of species-based diversity metrics to be applied to functional groups. At the simplest level, functional group richness (the number of unique groups in a community) provides an intuitive metric for quantifying functional diversity that doesn’t require complex metrics or calculations. On the other hand, Simpson’s Index—a widely used measure of species-based diversity—can likewise be applied to functional groups, in which case it provides a direct measure of ‘functional redundancy’, i.e., the probability that any two randomly selected species in a community comprise the same functional group. Indeed, any species-based metric can be applied directly to functional group richness, providing relatively simple and intuitive measures of richness, redundancy, divergence, and evenness.

To illustrate how such metrics can be applied to functional groups, we use a recent global dataset of tree community composition [12], which contains presence-absence of around 37,000 tree species at 200-km resolution across the globe. We used our tree-species functional group classification to assign each tree species to a functional group. We then calculated functional redundancy (‘FRedund’, Simpson’s Index) and functional group richness (‘FGR’, number of groups) across all species contained within each pixel. We then compared these group-derived metrics with three traditional diversity metrics reported in Paz et al.: species richness (number of unique species), mean pairwise distance (Rao’s quadratic entropy, a measure of functional clustering), and functional richness (convex hull volume across all traits) (see Fig 6).

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Fig 6. Functional group diversity metrics compared to tradition measure of species richness and functional diversity, calculated for each of n = 16048 forested pixels across the global (with more than 3 clusters), as reported in Paz et al. [12].

The points show the raw observations, with the lines denoting the fitted trends from generalised additive models, adjusted for spatial autocorrelation (see Methods), along with 95% confidence intervals. (a-c) Functional group richness (the number of unique groups) is highly correlated with species richness at low levels, but saturates after approximately 500 species in the system. Functional redundancy is likely weakly correlated with Rao’s Q, which reflects spatial clustering in trait space, but, compared to functional redundancy exhibits a stronger (albeit still relatively weak) correlation with functional richness. (d-f) Functional redundancy (Simpson’s Index applied to groups) is inversely correlated with species richness, revealing significant variation in redundancy at high levels of richness, but is only weakly correlated with Rao’s Q and Functional richness, capturing complementary aspects of both. These results illustrate how traditional diversity metrics can be applied to functional groups, yielding intuitive and simple metrics for quantifying functional composition.

https://doi.org/10.1371/journal.pcbi.1014278.g006

These results demonstrate how functional group diversity complements and reflects key elements of traditional metrics, while also providing novel insight into the functional structure of natural communities. After accounting for spatial autocorrelation, Functional Group Richness (FGR) exhibits a saturating positive relationship with traditional species richness (Pearson r = 0.58, p < 0.001; Fig 6a), which flattens after ∼500 species, and likewise shows a strong linear correlation with functional richness (r = 0.74, p < 0.001). Conversely, FGR has negligible residual correlation with Rao’s Q (r = 0.15, p < 0.001; Fig 6b), highlighting that this metric is largely independent of distance-based similarity. Functional Redundancy, on the other hand, aims to capture overlap between species, and accordingly exhibits a moderate negative correlation with Rao’s Q (r = -0.40, p < 0.001; Fig 6e), along with a negligible correlation with species richness (r = -0.04 p < 0.001) and a slight negative relationship with functional richness (r = -0.21 p < 0.001; Fig 6f). Collectively, these results illustrate how group-based diversity metrics can provide complementary insight into functional structure by integrating different aspects of species richness, functional clustering, and functional breadth (also see S15 Fig for spatial projections). Moreover, the simplicity of group-based calculations helps to overcome some of the computational limitations of existing functional diversity metrics (e.g., the inability to calculate convex hull volume in communities where there are fewer species than traits) while also being based on well-known, interpretable species-diversity metrics.