Summary

In brief, using five traits, we built an ecological strategy surface (2-D), via a PCA, and ecological strategy spaces (5-D), via hypervolume estimation. All analyses were carried out using R version 3.5.1 (ref.62).

Traits

We used five traits: body mass, litter/clutch size, habitat breadth (number of IUCN habitats listed as suitable), generation length and diet (the dominant diet gradient across ten diet categories for all species, see below; Supplementary Fig. 4) for 5232 mammal and 10,252 bird species. These traits reflect the resource acquisition, utilization and release by species and thus summarize a species’ ecological strategy28,63,64. We extracted trait data for body mass, litter/clutch size and habitat breadth from our recently compiled—from four main sources14,65,66,67—database for mammals and birds28. For full details on the compilation of these three traits see Cooke et al.28. Generation length for birds was supplied by BirdLife. For mammals we obtained generation length values for mammals from a published dataset66, although we corrected three mammal generation length observations that have since been found to be anomalous:68 Cephalophus adersi, Cephalophus leucogaster, and Cephalophus spadix.

We removed four species from the trait dataset that have been confirmed as globally extinct since the trait data were compiled in 2016: Guam Reed-warbler Acrocephalus luscinius (last seen 1969), Bramble Cay melomys Melomys rubicola (last seen 2009), Christmas Island pipistrelle Pipistrellus murrayi (last seen 2009) and Bridled White-eye Zosterops conspicillatus (last seen 1983).

For diet, we calculated a continuous measure of a species’ diet. Raw diet information was available as semi-quantitative records (percentage use of ten different dietary categories)14. To convert this information into a continuous measure, we first calculated Gower distances between species based on the diet data, gowdis() function in the FD package69. We then performed a principal coordinates analysis (PCoA) on the Gower distances, dudi.pco() function (ade4 package70). PCoA rotates the matrix of Gower distances to summarize inter-species (dis)similarity in a low-dimensional, Euclidean space71. Thus, PCoA does not change the positions of the species relative to each other but changes the coordinate system. Trait space and hypervolume analyses assume that all axes contribute equally to distances and volumes31. Thus, only the first principal component from the diet PCoA was used in the trait space and hypervolume analyses, so that each trait dimension had equal weight (although see the Supplementary Methods and Supplementary Fig. 11, where both the first and second principal components were used). The values yielded by the first principal component of the PCoA serve as synthetic trait values (i.e., new trait values based on the relative importance of diet categories in the initial dataset) and are referred to as ‘diet’. Diet explained 36.2% of the variation across the diet categories and was predominantly loaded positively on invertebrates (PCoA loading = 3.69) and negatively on plant material (−1.66), fruit (−1.18), and seed (−0.80) (Supplementary Fig. 4); thus representing a gradient from invertivore to herbivore, reflecting previous diet ordination for mammals only72.

Trait data were transformed where it improved normality: log 10 for body mass, generation length and litter/clutch size; square root for habitat breadth; and all traits were standardized to zero mean and unit variance (z-transformation). Transformation and standardization to unitless coordinates is recommended for trait analyses46,73 and hypervolume calculations74.

Trait imputation

Trait data were not available for all species. Overall 12% of trait values were missing. The common practice of using only species with complete data (data-deletion approach) not only reduces sample size and consequently the statistical power of any analysis, but may also introduce bias75,76. Moreover, missing data would restrict the dimensionality of our analysis, as any species with at least one missing trait value cannot be used for hypervolume estimation, because an n-dimensional object is not well defined in fewer than n dimensions74. Instead, to achieve complete species-trait coverage we imputed missing data for litter/clutch size (42% imputed), habitat breadth (10%), diet (8%), and generation length (0.2%). Body mass data had complete species coverage. We used Multivariate Imputation with Chained Equations (MICE), based on the ecological (the transformed traits) and phylogenetic (the first ten phylogenetic eigenvectors extracted from trees for birds77 and mammals78) relationships between species28. MICE has been shown to have greater accuracy, improved sample size and smaller error and bias than single imputation methods and the data deletion approach75,76. The data deletion approach was performed for comparative purposes (8294 species; Supplementary Fig. 8). To generate imputed values, we used the mice() function from the mice package79.

To capture the uncertainty in the imputation process we imputed 25 trait datasets (Supplementary Fig. 2). These imputed datasets are based on the same input trait data, but differ in their estimations for the missing-data. Where possible we performed our analyses across the 25 imputed datasets (Fig. 1). However, utilizing the multiple datasets was not possible for the hypervolume analyses, due to the computational cost of the analyses (each hypervolume analysis took upto a day to run on a computer with an Intel Xeon CPU E5-2407 0 @ 2.2 GHz processor and 96GB of RAM, thus running multiple analyses 25 times each was unfeasible). Instead, for the hypervolume analyses, we used a single, randomly selected, imputation dataset.

Ecological strategy surface

We built an ecological strategy surface (2-D) from the transformed and standardized traits via a PCA, using the princomp() function in the vegan package80 (Fig. 1). The ordination of species across this surface represents a two-dimensional continuum, integrating ecological strategies within each of the five trait dimensions (i.e., creating an ecological strategy surface).

We used multivariate kernel density estimation to calculate the occurrence probability of given combinations of trait values (probability contours) across the ecological strategy surface29, via the kde() function (ks package81). We extracted contours at the 0.5, 0.95, and 0.99 quantiles of the probability distribution (Fig. 1). Because results depend on the choice of the bandwidth used for the smoothing kernel, we used unconstrained bandwidth selectors82. Specifically, we used the sum of asymptotic mean squared error pilot bandwidth selector83, through the Hpi() function in the ks package81.

Ecological strategy space

To evaluate the ecological strategy spaces of mammals and bird combined, and separately, we constructed trait hypervolumes. One of the major advantages of the hypervolume approach is that it can accurately measure the volume of a high-dimensional shape that may include holes, disjunctions or other complex geometrical features31,74, and thus hypervolumes model multidimensional spaces better than linear and continuous dimensions, such as convex hulls84. Moreover, hypervolumes are not as sensitive to outliers as convex hulls74,84 and do not assume any parametric probability distribution31,74. To build our hypervolumes we used the one-class support vector machine (SVM) estimation method31. SVM provides a smooth fit around data that is insensitive to outliers, yields a binary boundary classification (‘in’ or ‘out’), is invariant to rotational transformation (i.e., correlations between axes), and is computationally viable in large datasets and high-dimensional hyperspaces31. SVM is the most appropriate hypervolume method when extreme values in the observed data are thought to represent the true boundaries of the data31, as is the case here. However, the principal disadvantage is that the boundaries of the hyperspace (and therefore volume) can change non-monotonically when species are removed (see Extinction scenarios), due to the stochastic nature of the SVM algorithm32. In other words, the volume can increase when species are removed, due to the stochastic re-drawing of the hyperspace boundaries. We calculated the observed hypervolume based on the transformed and standardized traits using the hypervolume_svm() function in the hypervolume package32. Conversion to unitless coordinates (here z-transformation) is required so that volumes or overlaps can be defined31,74. The units of the hypervolumes are reported as the standard deviations of centered and scaled transformed trait values, raised to the power of the number of dimensions (SDnumber of dimensions).

The observed hypervolumes were compared to four alternative null models of multivariate variation of the transformed traits (see29 for full null model specifications). To compare the hypervolumes, we calculated the occupation by the observed ecological strategy space of the mean of 999 strategy spaces generated from the assumptions of each null model (Monte-Carlo permutations), with the as.randtest() function (ade4 package70).

Null model 1: Species traits vary independently and each of them comes from a uniform distribution29. This null model assumes that each of the traits represents an independent axis of specialization and that the occurrence of extreme and central values is equally probable29.

Null model 2: Species traits vary independently and each of them comes from a normal distribution29. This null model assumes that all traits evolve independently, as in null model 1, but extreme trait values are selected against during evolution29.

Null model 3: Species traits vary independently but—unlike in the previous null models—there is no assumption about the distribution of trait variation; each trait varies according to the observed univariate distributions29.

Null model 4: Species traits are normally distributed and follow the estimated correlation structure of the observed dataset29. This null model assumes that there are less than six independent axes of specialization and that extreme values are selected against29.

Extinction scenarios

To test the impact of future projected extinctions over the next 100 years, we assigned extinction probabilities to the IUCN Red List categories:33 0.999 for Critically Endangered (CR), 0.667 for Endangered (EN), 0.1 for Vulnerable (VU), 0.01 for Near Threatened (NT) and 0.0001 for Least Concern (LC) species. In addition, 13% of mammals (665 species) and 1% of birds (59 species) are categorized as Data Deficient (DD). DD species were, for simplicity, treated as LC (i.e., assigned them an extinction probability of 0.0001)34,85. For our dataset this results in the loss of 380 CR species (99.9%), 576 EN (66.7%), 125 VU (10%), 13 NT (1%), and 1 LC/DD species (0.01%) (total = 1095 species). Although we also provide alternative analyses where we (i) removed DD species and (ii) assigned DD species an average predicted extinction probability of 0.277 (Supplementary Methods). We also show the distribution of the IUCN Red List categories across the ecological strategy surface (Supplementary Fig. 5f).

We compared these projected extinctions to a null model based on randomized species extinctions, where an equivalent number of species go extinct over the next 100 years (1095 species) but randomly with respect to species identity and traits. We replicated both the projected and randomized scenarios 999 times. To evaluate the difference between the projected and randomized extinction scenarios we used a Kolmorgorov–Smirnov test with the ks.test() function (stats package62). We also calculated absolute effect sizes as observed volume—randomized volume and observed volume—projected volume, with 95% confidence intervals of the differences. To assess shifts in the trait distributions we used permutation tests, via the as.randtest() function (ade4 package70) (Supplementary Fig. 7).

Sensitivity

Overall our results and conclusions were qualitatively similar (i) with and without imputed trait data (Supplementary Figs. 2, 8, 9 and 10), (ii) when including the first or the first and second principal components from the diet PCoA (Supplementary Figs. 4 and 11), (iii) with and without DD species (Supplementary Figs. 12 and 13), and (iv) when assigning DD species an extinction probability of 0.0001 or 0.277 (Supplementary Figs. 14 and 15). Further information on these analyses is provided in the Supplementary Methods.

Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.