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Mapping local and global variability in plant trait distributions
Edited by William H. Schlesinger, Cary Institute of Ecosystem Studies, Millbrook, NY, and approved October 18, 2017 (received for review May 31, 2017)

Significance
Currently, Earth system models (ESMs) represent variation in plant life through the presence of a small set of plant functional types (PFTs), each of which accounts for hundreds or thousands of species across thousands of vegetated grid cells on land. By expanding plant traits from a single mean value per PFT to a full distribution per PFT that varies among grid cells, the trait variation present in nature is restored and may be propagated to estimates of ecosystem processes. Indeed, critical ecosystem processes tend to depend on the full trait distribution, which therefore needs to be represented accurately. These maps reintroduce substantial local variation and will allow for a more accurate representation of the land surface in ESMs.
Abstract
Our ability to understand and predict the response of ecosystems to a changing environment depends on quantifying vegetation functional diversity. However, representing this diversity at the global scale is challenging. Typically, in Earth system models, characterization of plant diversity has been limited to grouping related species into plant functional types (PFTs), with all trait variation in a PFT collapsed into a single mean value that is applied globally. Using the largest global plant trait database and state of the art Bayesian modeling, we created fine-grained global maps of plant trait distributions that can be applied to Earth system models. Focusing on a set of plant traits closely coupled to photosynthesis and foliar respiration—specific leaf area (SLA) and dry mass-based concentrations of leaf nitrogen (
Modeling global climate and the carbon cycle with Earth system models (ESMs) requires maps of plant traits that play key roles in leaf- and ecosystem-level metabolic processes (1⇓⇓–4). Multiple traits are critical to both photosynthesis and respiration, foremost leaf nitrogen concentration (
Previous work has extrapolated trait measurements across continental or larger regions through three methodologies: (i) grouping measurements of individuals into larger categories that share a set of properties [a working definition of plant functional types (PFTs)] (4, 15), (ii) exploiting trait–environment relationships (e.g., leaf
Information is lost when the range of measured trait values is compressed into a single PFT (Fig. 1). We observe that the global range of site-level SLA values for a single PFT such as broadleaf evergreen tropical trees (Fig. 1 A and C) is quite large (2.7–65.2 m2⋅kg−1). Even after limiting the scope to a single well-measured 0.5° × 0.5° pixel within Panama (Fig. 1 B and C), there is still a wide range of SLA values (4.7–37.7 m2⋅kg−1) with a local mean of 15.7 m2⋅kg−1 and a local standard deviation of 5.4 m2⋅kg−1—over one-third of the local mean. By contrast, the mean SLA value of all species associated with broadleaf evergreen tropical trees is 13.9 m2⋅kg−1, over 10% lower than the local average (Fig. 1C). Thus, single trait values per PFT fail to capture variability in trait values within or among grid cells, i.e., over a wide range of spatial scales.
Trait data. (A) Global locations and values of specific leaf area measurements for the PFT tropical broadleaf evergreen trees. (B) Locations and values of specific leaf area measurements for the tropical broadleaf evergreen trees in Panama. The square in the center indicates a
Transitioning from a single trait value per PFT (within or among grid cells) to a distribution may lead to significantly different modeling results (20) as critical plant processes, such as photosynthesis, are nonlinear with respect to these traits (28). This is reinforced by recent modeling studies that have begun to incorporate distributions of traits at regional (29, 30) and global (31) scales. It has been shown that using trait distributions leads to different estimates of carbon dynamics (32) and that higher-order moments of trait distributions contribute to sustaining multiple ecosystem functions (33). While species-level mapping (21, 23, 24) does capture trait distributions, it has been limited geographically and restricted to subsets of functional groups.
Even the largest plant trait database offers only partial coverage across the globe in terms of site-level measurements. Hence, gap-filling approaches need to be adopted to extrapolate trait values at regions with no data coverage. Here, we overcome data limitations through PFT classification, trait–environment relationships, and additional location information to develop a suite of models capable of estimating trait distributions across the entire vegetated globe. The simplest one is a categorical model, which assigns traits to maps of remotely sensed PFTs. Every species, with its corresponding trait values, is associated with a PFT and these trait distributions are extrapolated to the satellite-estimated range of the PFT (SI Appendix, Figs. S1 and S2). The second one is a Bayesian linear model that complements the PFT information with trait–environment relationships. The third one is a Bayesian spatial model that, in addition to PFTs and the trait–environment relationships, leverages additional location information via Gaussian processes (Materials and Methods). The use of a spatial Gaussian process in this context is unique and model evaluation reveals the superior predictive performance of this model.
Each of these methods interpolates (and extrapolates) both mean trait values and entire trait distributions across space (i.e., across grid cells on a global map). These models are further stratified by three different levels of PFT categorization: (i) PFT-free, all plants in a single group (i.e., no PFTs); (ii) broad, 4 groups based on growth form and leaf type; and (iii) narrow, 14 groups based on further environmental, phenological, and photosynthetic categories (Materials and Methods). The PFT-free categorization groups all plants into a single class, while the broad grouping (4-PFT) is similar to the vegetation classification used in the Joint UK Land Environment Simulator land surface (34), and the narrow (14-PFT) category is equivalent to the classification used in the Community Land Model (CLM) (4, 15, 35).
The abovementioned methods allow for a representation of global vegetation that enables a more accurate formulation of functional diversity than the single-trait value per PFT paradigm that is widely used (4). The traits studied here—SLA,
Results and Discussion
Model Evaluation.
Given the full suite of nine models proposed, we conducted extensive model evaluation (Table 1) to determine the trade-offs associated with each methodology and resolution of PFT. We assessed the predictive capability of the models, using the root-mean-square predictive error (RMSPE) based on out-of-sample data (SI Appendix, section S6). Among the nine models, the spatial narrow 14-PFT model emerged as the best predictor of mean trait values for SLA and
Model evaluation
The improvement in prediction afforded by the inclusion of (i) a spatial term and (ii) PFT information (Table 1) invites further examination. First, the spatial term in our model likely incorporates some of the finer-scale variation that is unavailable given the relatively large grid cell size of the environmental covariates used in global studies. Thus, the spatial term allows for adjustment of trait values among neighboring or regional grid cells that the relatively coarse environmental metrics are not able to capture. Finer-scale studies that can evaluate local variations in climate, soil, or other relevant abiotic or biotic covariates may see less improvement from the inclusion of a spatial term, as they may directly measure local sources of variation. Second, the use of PFTs greatly improves the models, perhaps for similar reasons involving the degree of variation the raw data fail to incorporate. The greatest decrease in RMSPE occurs between the PFT-free grouping (a single category for all plants) and the broad (4-PFT) grouping across each of the models tested. If our trait data were perfectly predicted by environment, there would be no usefulness to including PFTs in mapping traits. That this is not so implies that the broad PFTs, based primarily on growth form and leaf type, offer superior predictive skill than environmental covariates on their own (19). However, the extra information in the narrow (14-PFT) grouping does further improve the fit and produces the most accurate predicted trait surface.
Global Maps.
We selected two sets of maps to describe, in broad strokes, how trait distributions vary across the land surface: the narrow 14-PFT spatial model and its categorical counterpart. The narrow 14-PFT spatial model is the best predictor of mean trait values and provided adequate coverage probability (Figs. 2 A and B, 3 A and B, and 4 A and B). For comparison, we also include the 14-PFT categorical model, which is most similar to maps currently used in ESMs (Figs. 2 C and D, 3 C and D, and 4 C and D). Maps for the other models can be found in SI Appendix, Figs. S8–S16. The mean and SD are presented as a summary of the full log-normal distribution within each pixel, but there are full distributions estimated in each pixel (Case Studies).
SLA maps. (A and B) Narrow (14-PFT) Bayesian spatial model pixel mean and SD estimates, respectively. (C and D) Narrow (14-PFT) categorical model pixel mean estimates and SD estimates, respectively. For clarity, the color bars have been truncated at the compound 5th and 95th percentiles of both models. Latitude tick marks indicate the equator, tropics, and Arctic Circle and longitude is marked at 100°W, 0°, and 100°E.
Nitrogen (mass) maps. (A and B) Narrow (14-PFT) Bayesian spatial model pixel mean and SD estimates, respectively. (C and D) Narrow (14-PFT) categorical model pixel mean estimates and SD estimates, respectively. For clarity, the color bars have been truncated at the compound 5th and 95th percentiles of both models. Latitude tick marks indicate the equator, tropics, and Arctic Circle and longitude is marked at 100°W, 0°, and 100°E.
Phosphorus (mass) maps. (A and B) Narrow (14-PFT) Bayesian spatial model pixel mean and SD estimates, respectively. (C and D) Narrow (14-PFT) categorical model pixel mean estimates and SD estimates, respectively. For clarity, the color bars have been truncated at the compound 5th and 95th percentiles of both models. Latitude tick marks indicate the equator, tropics, and Arctic Circle and longitude is marked at 100°W, 0°, and 100°E.
The SD maps (Figs. 2 B and D, 3 B and D, and 4 B and D) compared with the mean maps (Figs. 2 A and C, 3 A and C, and 4 A and C) highlight one of the central results of this analysis—the local SDs of trait values are of similar magnitudes to their respective means. Generally, we observed that the local SD is close to half the local mean value but can approach the global range of the trait mean values; e.g.,
For each of the three traits, the broad features of both the categorical and spatial models are similar, but there are numerous marked differences across regional and fine spatial scales (Figs. 2–4). The shared broad features of the maps from both models include SLA (Fig. 2) and
The most consistent estimates between the categorical and spatial models are in the boreal regions dominated by needle-leaved trees; the measurements in this region are relatively sparse, which may have limited the ability of the spatial model to capture differences. On the other hand, broad-leaved trees span a wide range of environments, but a large portion of the measurements come from the tropics (66%), where there is a limited range of values among the climate covariates and therefore little variation with which to estimate a correlation. The grasses and shrubs have the largest SDs of the four broad PFTs (SI Appendix, Table S4) and dominate wide swaths of the land surface, but have fewer measurements—shrubs are the least measured of the broad PFTs in the database, and this appears to reduce the accuracy of the categorical model more than that of the spatial model (Table 1). The fact that shrubs are assumed to dominate in arid and boreal environments, which also tend to be undersampled, also likely contributes to these differences.
Our results also suggest that the breadth of functional niche space is reduced in both boreal and tropical biogeographic regions. The low variation across all three traits within the boreal forest implies that there is strong filtering and smaller niche space available in this relatively harsh environment. Surprisingly, despite the high species diversity in tropical forests, we also find that SLA and
Case Studies.
We conducted two regional case studies to provide a more in-depth analysis of the true and predicted shapes of trait distributions than can be provided by the SD maps and coverage probability. In these case studies trait data were pooled over an area to construct full trait distributions and then formally compared with the model predicted distributions.
We considered two areas with substantially different environmental conditions to evaluate the trait distributions obtained from the spatial and categorical models. We chose a single pixel that contained a highly studied site with numerous measurements of tropical trees, Barro Colorado Island (BCI), Panama; and a collection of pixels in an arid environment in which the mean estimates for SLA of the spatial and categorical models substantially disagreed, the southwestern United States. These areas were in the training data, and this analysis constituted a more detailed analysis of the models’ fit to the observed distribution of these locations. Here, the focus was on the structure of the full distribution of traits predicted at these sites; SI Appendix, Fig. S17 is a map of the measurements that comprised these locations and other sites included in this analysis. Both areas offer further insight into the structure of the distributions estimated by the categorical and spatial models.
In the pixel containing BCI, the categorical and spatial models broadly agreed for all three traits (Fig. 5 A, C, and E), although the spatial model means were only half as distant from the observed means for SLA and
Empirical trait distributions. Barro Colorado Island (A, C, and E) and the US Southwest (B, D, and F). A and B show SLA, C and D show leaf nitrogen, and E and F show leaf phosphorus. Each panel depicts the distribution of the data in solid black, the categorical model in blue, and the Bayesian spatial model in red. The dashed vertical lines indicate mean values.
The differences between the trait distributions of the categorical and Bayesian spatial models were stark in the southwestern United States, although the mean estimates for
Environmental Covariates and the Spatial Term.
The improvement in prediction from the linear model to the spatial model is partially explained by weak trait–environment relationships (SI Appendix, Tables S1–S3). The magnitude of spatial variation explained by the Gaussian process model is comparable to that of the unexplained trait variation. For most of the spatial models, the estimated spatial range was around 300 km; this suggests a strong spatial effect and implies that the spatial model can provide more precise information about the trait distribution near the locations where we have data. This was largely borne out in the case studies and is illustrated more explicitly in Fig. 6 where the predicted trait SD for the spatial model was up to 50% lower than for the linear nonspatial model near locations with trait measurements. The spatial model leverages local information to reduce the uncertainty of trait estimation near data locations and may provide guidance for future data collection by identifying high-uncertainty regions.
Spatial learning. (A) The spatial model SD of
Applications for Trait Distributions.
Plant traits vary across a range of spatial scales, and the spatial model best captures changes across large spatial gradients (such as in Amazonia and Australia) as well as the subtleties within pixels. Maps for all of the models highlight how much information about local variability is lost when representing plant traits with a single value and suggest that a first application of these maps will be for ESMs to incorporate these scales of variability. For process-based ESMs, the simplest model to incorporate will likely be the categorical model as it is closest to the current PFT approach, but this model is also the least flexible. The more sophisticated models developed here provide more accurate large-scale variation and may be used to infer new trait values in a novel climate by perturbing the climatic covariates (37). However, given the likelihood of nonlinear trait–environment relationships, the spatial sparsity of the data, and the possibility of alternate strategies within a PFT that may alter the trait–environment relationship in a future climate some caution is called for when using these models for extrapolation. Future ecosystem models could also integrate the leaf-level variation in these maps with canopy-scale changes in leaf display traits—leaf angle, azimuth, and total area.
We have emphasized the quality of the Bayesian spatial model with narrow PFTs, but there is an intriguing possibility opened by the PFT-free model (SI Appendix, Figs. S8, S11, and S14)—that being the representation of vegetation without reference to PFTs (1). In this case the representation of vegetation would rely entirely on the structure of trait distributions at various landscape scales (1). Such a representation eliminates the need to separately model the future locations of PFTs (or species) when inferring the future distribution of traits; hence, the output of a model like that developed here could be updated with future environmental covariates, with the caveats that “out of sample prediction” may entail. At the same time, this method would allow for greater functional diversity than multiple PFTs with single-trait values, as is currently used in most ESMs. Adopting this approach does, however, raise the issue of how to deal with the paucity of surface observations in some regions, as evidenced by the greater errors associated with estimating out of sample values with this model (Table 1). Complementary work has retrieved leaf trait maps from a global carbon cycle model fused with Earth observations (38), providing another method that could be used for direct comparison against the trait maps produced here. While the methodology outlined in our analysis brings the possibility of a PFT-free land surface closer, we remain several steps away from being able to make such maps as accurately as we do using PFT characterizations for trait prediction. Several actions can bring us closer to that goal. First, incorporation of additional information (such as phylogenetic relatedness and trait–trait covariance) will likely improve trait maps, even using existing observations. Second, as the current level of observations is extremely sparse in some regions and sparse in most regions, expanded trait databases will also aid in development of PFT-free trait maps.
Conclusions
SLA and
The global land surface is perhaps the most heterogeneous component of the Earth system. Reducing vegetation to a collection of PFTs with fixed trait values has been the preferred method to constrain this heterogeneity and group similar biochemical and biophysical properties; however, this has been at the expense of functional diversity. This analysis quantifies the substantial magnitude of this ignored trait variation. The approach and methods presented here retain the simplicity of the PFT representation, but capture a wider range of functional diversity.
Materials and Methods
Data.
The TRY database (www.try-db.org) (14) provided all data for leaf traits and the categorical traits to aggregate PFTs (TRY–Categorical Traits Dataset, https://www.try-db.org/TryWeb/Data.php#3, January 2016) used in the analysis. The TRY data may be requested from the TRY database custodians. See SI Appendix, section S10 for a complete list of the original publications associated with this subset of TRY. The extract from TRY used here has just under 45,000 measurements of individuals from 3,680 species with measurements of at least one of SLA, leaf nitrogen per dry leaf mass (
Classification of PFTs and Categorical Model.
We used three nested levels of PFT classification. In the first level, all plants are categorized into a single group (“PFT-free”). In the second level (“broad”), all plants are categorized into PFTs based on categorical traits associated with growth form (grass, shrub, tree) and leaf type (broad and needle-leaved), leading to the following four PFTs: grasses, shrubs, broad-leaved trees, and needle-leaved trees (SI Appendix, Fig. S1). In the third level (“narrow”), the broad PFTs are further refined by their climatic region—tropical, temperate, boreal—as well as leaf phenology and, for the grasses, photosynthetic pathway (
The categorical model uses the PFT categories and averages trait values for each species across individual measurements at each measured location. This defines the PFT as the interspecies range of trait values and ignores all local environmental factors. The results of the categorical model are summarized by the mean and SD of each PFT’s trait values (SI Appendix, Table S4) for all three resolutions of the model. Note that in the PFT-free case where no PFT information is used, the categorical model produces a constant trait distribution across the entire vegetated world. The categorical model and the Bayesian models described in the following section all use location-specific species mean values to estimate trait distributions. We assume no intraspecific variation in trait values. However, in regions dominated by a small number of species this may lead to biased predictions. The hyperdominance of a small group of species in the Amazon has recently been demonstrated (51) and thus serves as a case study to evaluate our assumption of equal species weighting (SI Appendix, section S8, Fig. S23). We found that equal weights (species means) produced trait distribution estimates closest to those of the hyperdominant trait abundances and this reinforces the use of this assumption globally. Further, as noted above, the omission of herbaceous species from tropical regions in this analysis (and ref. 51) may unduly limit trait diversity and calls for further research.
Bayesian Models.
A more fine-tuned depiction of geographical or spatial variation of plant trait values within each PFT can be achieved by leveraging environmental and location information, which allows trait values to adjust based on local conditions. Data for 17 climate- (45, 46) and soil-based (47) environmental predictors were available at the
We used environment–trait relationships to obtain predictions of trait values (1, 16⇓–18, 37, 43) in a linear regression setup. The formal details of the initial model are as follows. We denote log-transformed trait values at a geographical location s as
We then generalized the above model into a Bayesian spatial linear regression model that borrows information from geographically proximal regions to capture residual spatial patterns beyond what is explained by environmental predictors. A customary specification of a spatial regression model is obtained by splitting up the error term
The linear regression models used in previous studies (1, 16⇓–18) and both the spatial and nonspatial Bayesian models described above assume a global relationship between the traits and environment. Given the goal of predicting trait values for the entire land surface, the assumption of a universal trait–environment relationship may be an oversimplification (54). Moreover, if there is significant variation in plant trait values among different PFTs, the estimated parameters will be skewed toward values from abundantly sampled PFTs, such as broad-leaved trees. Additional information about plant characteristics at a specific location, if available, can potentially be used to improve predictions. As mentioned earlier, we have PFT classifications for each observation of the dataset used here and satellite estimates of PFT abundance at all pixels. The global regression approaches described above ignore this information and can yield biased predictions at locations dominated by PFTs poorly represented in the data, such as shrubs. Hence, we also incorporate the PFT information in these regression models by allowing the trait–environment relationship to vary between different PFTs. Finally, the PFT-specific distributions from the Bayesian models were weighted by the satellite-based PFT abundances to create a landscape-scale trait distribution, thereby enabling straightforward comparison between all three categorizations of PFT. Details of the PFT-based Bayesian models are provided in SI Appendix, section S2. The use of a GP-based spatial model as well as the Bayesian implementation of the regression models was unique to this application of plant trait mapping and, as results indicated, were critical to improving model predictions as well as properly quantifying trait distributions.
Acknowledgments
The authors appreciate the improvements suggested by two anonymous referees, which improved the clarity and depth of the manuscript. This research was supported as part of the Energy Exascale Earth System Model (E3SM) project, funded by the US Department of Energy, Office of Science, Office of Biological and Environmental Research (Grant DE-SC0012677 to E.E.B, H.F.M., M.C., K.R.W., A.B., and P.B.R.). O.K.A. acknowledges the support of the Australian Research Council (CE140100008). This research was also funded by programs from the NSF Long-Term Ecological Research (Grant DEB-1234162) and Long-Term Research in Environmental Biology (Grant DEB-1242531). A.B., F.F., and P.B.R. acknowledge funding from NSF Grant IIS-1563950. P.B.R. also acknowledges support from two University of Minnesota Institute on the Environment discovery grants. This study has been supported by the TRY initiative on plant traits (www.try-db.org). The TRY database is hosted at the Max Planck Institute for Biogeochemistry (Jena, Germany) and supported by DIVERSITAS/Future Earth, the German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig, and BACI (Towards a Biosphere Atmosphere Change Index) (Grant 640176). B.B. acknowledges a Natural Environment Research Council (NERC) independent research fellowship NE/M019160/1. J.P. acknowledges the financial support from the European Research Council Synergy Grant ERC-SyG-2013-610028 IMBALANCE-P, the Spanish Government Grant CGL2013-48074-P, and the Catalan Government Grant SGR 2014-274. B.B.-L. was supported by the Earth System Modeling program of the US Department of Energy, Office of Science, Office of Biological and Environmental Research. K.K. acknowledges the contribution of the Wageningen University and Research Investment theme Resilience for the project Resilient Forest (KB-29-009-003). P.M. acknowledges support from ARC Grant FT110100457 and NERC Grant NE/F002149/1. W.H. acknowledges support from the National Natural Science Foundation of China (Grant 41473068) and the “Light of West China” Program of the Chinese Academy of Sciences.
Footnotes
↵1E.E.B. and A.D. contributed equally to this work.
- ↵2To whom correspondence may be addressed. Email: eebutler{at}umn.edu or abhidatta{at}jhu.edu.
Author contributions: E.E.B., A.D., H.F.-M., M.C., K.R.W., F.F., A.B., O.K.A., J.K., and P.B.R. designed research; E.E.B. and A.D. performed research; E.E.B., A.D., H.F.-M., and J.K. analyzed data; and E.E.B., A.D., H.F.-M., M.C., K.R.W., A.B., O.K.A., J.K., B.A., B.B., G.B., B.B.-L., K.A.B., C.B., G.C., B.E.L.C., J.H.C.C., J.M.C., D.C., F.T.d.V., S.D., T.F.D., E.F., A.G.-M., N.G., W.H., W.N.H., T.H., S.J., K.K., N.J.B.K., H.K., D.C.L., P.M., V.M., Ü.N., Y.O., J.P., Q.R., L.S., B.S., N.A.S., M.J.S., E.S., P.E.T., F.V., P.M.v.B., M.W., C.W., and P.B.R. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
Data deposition: The code and data necessary to run the models are available at https://github.com/abhirupdatta/global_maps_of_plant_traits.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1708984114/-/DCSupplemental.
Published under the PNAS license.
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