Type of data

We use two classes of data to address the question of whether choosing sets of species according to PD captures the underlying trait diversity (as measured with FD) well. First, we used taxonomic groups (clades) of species as our unit of analysis (“species pool” hereafter) and, second, we investigated broad assemblages found across the globe. The former is more explicitly evolutionary, ensuring that our results are not driven by well-established relationships across large taxonomic groups (e.g., monotremes are distinct from placental mammals) and the latter is likely more relevant to actual conservation practice. We use distribution data to delineate geographical assemblage species pool and taxonomy to delineate clade-based species pools (namely families and orders).

Distribution data

For mammals, we used the distribution maps provided by the Mammal Red List Assessment (http://www.iucnredlist.org/) for 4616 species. For birds, full (breeding and wintering) and breeding ranges distribution maps were extracted from BirdLife (http://www.birdlife.org/) for 9993 species. The best resolution at which these maps should be used is still under discussion in the literature, so we decided to use the 40,000 km2 resolution (200 × 200 km gird cell at the equator) that is commonly used at global scale44,45. The total number of grid cells was 3646. Domestic and aquatic mammals were excluded from the analysis. In order to make sure our results were not driven by the important trait difference between volant and nonvolant mammals, we repeated our results excluding bats. For birds, we repeated our analysis using the full ranges. Finally, we evaluated the robustness of our result to the spatial resolution considered by repeating our analysis at a resolution of 100 × 100 km (number of cells was 13,330) for birds and mammals; we present these results in the supplementary materials, as they are qualitatively identical to those conducted at 200 × 200 km (Supplementary Figure 1). For fishes, we used a database of 1536 species, for which we had distribution data, phylogenetic and functional data. Distribution data were extracted from a global-scale distribution database46. Species composition was then extracted from grid cells of 5°x5°, corresponding to approximately 555 × 555 km at the equator47. This grain size of the grid was chosen because it represents a good compromise between the desired resolution and the geographical density of information. Fish distribution data are available upon request to DM and FL. Maps were handled and plotted in R using the packages rasterVis48 and latticeExtra49.

Phylogenetic data

In order to prioritize species to maximize PD, phylogenies of each species pool are needed. We used the first 100 published calibrated ultrametric trees of Jetz et al.39 for birds and of Faurby and Svenning38 for mammals. By repeating our analyses across a posterior distribution of phylogenetic hypotheses, we control and account for phylogenetic uncertainty. For tropical reef fishes, we built a phylogeny for 18 families (i.e., Labridae, Scaridae, Pomacentridae, Chaetodontidae, Acanthuridae, Haemulidae, Balistidae, Carangidae, Serranidae, Lutjanidae, Sparidae, Caesionidae, Holocentridae, Mullidae, Muraenidae, Tetraodontidae, Lethrinidae, and Siganidae) by pruning a dated molecular phylogenetic tree for 7822 extant fish species47. These families were selected as the most representative tropical reef fish families, that is, they are abundant and speciose on tropical reefs. We grafted missing species on the pruned phylogenetic tree (circa 50% among the 1536 studied species) based on published phylogenies for these families, supplemented by taxonomic information from fish identification guides and FishBase47,50. The corresponding tree is available on figshare (https://doi.org/10.6084/m9.figshare.6430982.v1). We recorded, for each of these trees, a measure of imbalance (as measured by beta51) and “tipiness” (as measured by gamma52). For both mammals and birds, we chose to group species in families and orders. We used these groupings when calculating the purely phylogenetic, clade-based analyses, but not within the spatial, assemblage-based analyses. For the taxonomic analysis of mammal families, we removed two families (Dipodidae and Echimyidae) because of their very poor phylogenetic resolution (i.e., polytomies for an important number of species).

Trait data

For birds and mammals, four traits (diet, (log-transformed) body mass, activity cycle, and foraging height) were extracted from Elton Traits1.042. These traits are generally assumed to appropriately represent Eltonian niche dimensions within an assemblage or clade of mammals or birds53,54. For fishes, we used a previously published database12. We used 6 categorical traits: size, mobility, period of activity, schooling, vertical position in the water column, and diet (for a full description of the dataset, see Mouillot et al.12). These traits have already been used to investigate community assembly rules55 and to seek vulnerable fish functions11. Fish trait data is available upon request to DM and FL. For each clade and assemblage, we used the raw trait (only body mass was log-transformed and rescaled by the clade/assemblage range of body masses) values to compute distances between species using Gower distance and use PCoA to summarize the trait space in few dimensions. We retained the numbers of PCoA axes necessary to represent 70% of the total initial variability (using a 80% threshold did not quantitatively change our conclusions, see Supplementary Figure 10). We also recorded phylogenetic signal for each PCoA axis using Blomberg’s K56.

General approach

Our aim was to evaluate, across a wide range of clades and regions, the ability of PD-informed prioritization scheme to capture FD in comparison with two other prioritization schemes: selecting species to directly maximize FD (“maxFD” hereafter) and selecting species randomly (Fig. 1). Our premise was that we often do not know or have not measured the traits that are most relevant for ecosystem function and services such that maximizing FD is not generally feasible. By focusing on a subset of traits and assuming that they are representative of ecologically relevant traits, we were able to get an estimate of how well PD does compared to the best we could possibly do. We used performance relative to choosing on the basis of FD as an upper-limit to the performance of PD as a surrogate for FD and used random species selection as a lower benchmark.

Random prioritization scheme

For each pool (i.e., each clade and each geographical assemblage) and each number of selected species (10, 20, 30, 40, 50, 60, 70, 80, 90, and 100% of the total pool), 1000 random sets of species were produced, from which the average FD was recorded.

Prioritization scheme maximizing PD (maxPD)

While there are many, overlapping metrics for measuring the evolutionary history encompassed by a set of species15,57, the most common is the sum of all branch lengths (often in units of time) connecting a set of species to a common root14, called phylogenetic diversity (PD). This is the metric whose maximization has most commonly been proposed as a conservation prioritization metric14,33,58, and as a measure of phylogenetic “richness” it most naturally maps onto our chosen FD metric57. We used the greedy algorithm proposed by Bordewich et al.59 to find our maxPD set of species S. For a given tree there are likely multiple, and possibly very many, sets of species with the same PD as S. As a consequence, we produced, for each pool, each number of selected species, and each alternative phylogenetic trees, 10 maxPD sets of species. We then averaged the FD of these sets across our 100 phylogenetic trees, so that each value is an average of 1000 sets (10 sets for each of the 100 trees).

Prioritization scheme maximizing FD (maxFD)

Functional diversity was estimated using a functional richness index (FRic)60,61,62. The FRic index relies on a multidimensional Euclidean space, where the axes are traits (or factorial axes from a principal coordinates analysis (PCoA) computed using these traits) along which species are placed according to their trait values. This index measures the volume of trait space occupied by a given species assemblage by calculating the convex hull volume62, defined by the species at the vertices of the functional space, that encompasses the entire trait space filled by all species in this assemblage. In a single dimension, this simply equals the range of values62. This broadly used metric in ecology is set monotonic with species richness, a property generally assumed desirable in conservation whereby the addition of a new species can never decrease the metric’s value63. FD measures the total amount of variation in trait values, making it conceptually comparable to PD57. We used the FRic index instead of the FD index based on a functional dendrogram since recent studies showed that the FD index may lead to biased assessments of functional diversity and inaccurate ecological conclusions64. The most straightforward way to obtain the maximal FD for n species is to compute FD for all possible combinations of n species and simply record the greatest value (the brute force approach). However, this is not feasible in practice as the numbers of combinations of selected species was too high (e.g., 1071 possible sets for all mammal assemblages). To rapidly and efficiently find the set of species that aim to maximize FD, we developed a novel (at least in ecology) greedy algorithm. In brief, our approach iteratively (starting with two species) select the species that is the furthest from the centroid of the already selected set. To avoid selecting two species that are far from the centroid but close to each other, we penalized the distance to the centroid by the distance to the closest neighbor in the already selected set. Here we present in details the greedy algorithm we used to find the set of species that maximize FD:

Step 1. Select the two species with the highest trait distance.

Step 2. Compute the centroid of these two selected species.

Step 3. Compute distances between species not in the set and this “set centroid”.

Step 4. Penalize these distances by adding the following factor f (Eq. 1)

$${f = K}\,\times\,{\mathrm{e}}^{{ {L}}\,\times\,{\mathrm{minD}}}$$ (1)

with K and L being penalizing factors and minD the distance between a given candidate species and the nearest species already in the selected set.

Step 5. Select the species that maximized the penalized distance.

Step 6. Go back to step one with this new set of species until the desired number of species is reached.

To avoid arbitrarily setting the penalizing parameters, we tested 1000 pairs of parameters drawn from a truncated normal distribution (mean = 1, SD = 0.5) and retained the parameter pairs that yielded the maximal FD.

In tests of subsets of the data for which finding the true maxFD was feasible, we found our approach to adequately approximate the true maxFD and to produce a very good approximation of the true degree of PD’s surrogacy for FD (Supplementary Figure 11).

Surrogacy estimates

We use a common approach27,28 to quantify the extent to which a given surrogate (here, the maxPD choice) reaches a certain objective (here, maximize FD). Species from a given pool (i.e., for each dataset (clade and assemblages) independently,) were prioritized and selected according to (1) the objective, i.e., maximize FD, producing the “optimal curve” (maxFD curve in Fig. 1) the surrogate, i.e., maximize PD, producing the “surrogate curve” (maxPD curve in Figs. 1 and 3) at random (random curve in Fig. 1), i.e., producing the “random curve” (Fig. 1). To compute a “surrogacy” estimate of PD (S PD–FD ), we compare the position of the surrogate curve (1) to the random curve (2) relative to the optimal curve (2) (Fig. 1 and Eq. 2) across the deciles of species richness of the pool (given as an interval 0–1):

$$S_{\mathrm {PD - FD}} = {\int

olimits_0^1} \frac{{{\mathrm {FD}}_{\mathrm {maxPD}} - {\mathrm {FD}}_{\mathrm {random}}}}{{{\mathrm {FD}}_{\mathrm {maxFD}} - {\mathrm {FD}}_{\mathrm {random}}}}$$ (2)

This surrogacy metric is at 100% when the surrogate perfectly meets the objective (i.e., the maxFD and maxPD curves are identical and the max PD set is the maxFD set), 0% when the surrogate is not better than randomly chosen sets of species (i.e., the random and maxPD curves are identical) and is negative if the surrogate choice is worse than random (i.e., the maxPD curve is below the random curve). Correlates of S PD–FD were evaluated using Spearman correlations.

Apart from focusing on average tendencies, we quantified the variability of the FD yielded by the PD—maximized selection strategy and the random selection strategy within each species pools. To do so, we compute, for each species pool and for each % of selected species independently, the number of cases where FD random > FD maxPD across the 1000 random *1000 maxPD sets combinations (i.e., 106 comparisons). We then averaged theses number across % of selected species and report statistics across datasets (Supplementary Table 1, Supplementary Figs. 3 and 4).

Code availability

R functions developed in this paper are available at https://github.com/FloMazel/FD_PD_Max

Data availability

Mammal and bird datasets are publicly available (see methods). The Fish phylogeny is available on figshare (https://doi.org/10.6084/m9.figshare.6430982.v1). The distribution and trait fish datasets are available upon request to D.M. and F.L.