Climatic constraints on trait-based forest assembly

Authors


Correspondence author. E-mail: d.laughlin@waikato.ac.nz

Summary

1. Climatic constraints on plant distributions are well known, but predicting community composition through knowledge of trait-based environmental filtering remains an important empirical challenge. Here, we evaluate the maximum entropy (MaxEnt) model of trait-based community assembly using forest communities occurring along a 12 °C gradient of mean annual temperature (MAT).We use independent cross-validation to evaluate model predictions from sites where trait constraints are predicted from environmental conditions. We also test whether orthogonal axes of trait variation can be used as predictors to improve model parsimony and explore MaxEnt forecasts of species distributions in a warmer climate.

2. Environmental factors explained between 31% and 74% of the community-weighted mean trait values, indicating moderate-to-strong selection of traits along the environmental gradients. A model with 10 traits explained 54% of the variation in observed relative abundances, which approached the upper limit of 57% given the available environmental information. Three orthogonal axes accounted for 81% of the trait variation among species, and environmental factors explained between 47% and 67% of the variation in these axes. However, the axes only explained 18% of the variation in relative abundances, suggesting that minor axes of functional variation may be important or that models with many traits may achieve good predictive capacity through over-fitting.

3. Trait–environment relationships formed the basis for predicting vegetation change in a future scenario where MAT was increased by 2.5 °C. The results suggested that up to 78% of Pinus ponderosa forest in Arizona may transition to dominance by Juniperus monosperma, but this forecast likely overestimates the rates of species migration.

4.Synthesis. MaxEnt is a mathematical translation of trait-based environmental filtering of the species pool and performs moderately well in predicting forest community structure using empirical trait–environment relationships. MaxEnt required many traits to achieve good fits, and three orthogonal axes of trait variation performed poorly as predictors of community structure. To be useful predictors, traits must vary strongly among species and community-weighted mean traits must vary predictably along environmental gradients.

Introduction

Climate exerts strong control over the distribution of vegetation, and climate change will likely alter these distributions (Lenoir et al. 2008). Species ranges are geographically constrained in large part because phenotypic properties (i.e. functional traits) of plants limit the range of environments in which they can sequester resources for growth and survival (Violle et al. 2007). For example, trees with high wood density have a greater resistance to drought-induced cavitation (Hacke et al. 2001) and will therefore have a higher fitness (or performance) in hot, dry environments than trees with low wood density. Many species distribution models primarily use bioclimatic envelopes (Pearson & Dawson 2003) and other environmental factors (Guisan & Zimmermann 2000) as direct predictors of species occurrences (Fig. 1) and do not attempt to explain distributions based on a physiological mechanism, such as the wood density–climate relationship (Hacke et al. 2001).

Figure 1.

 A trait-based approach to predicting species abundances explicitly incorporates a physiology-based link between the local environment and species abundances. The classic approach to species distribution modelling lacks a physiological linkage.

A trait-based approach may simultaneously provide predictive and explanatory ability because it specifies how performance filters alter trait distributions (Fig. 1; Keddy 1992; Webb et al. 2010). This approach assumes that individuals with traits that confer high performance in a given environment will be able to sequester a greater proportion of limited resources for growth and reproduction. From these first principles, a predictive model of community assembly can be built by developing equations where species relative abundances (pi) are the unknowns for which we will have to solve. Shipley, Vile & Garnier (2006) proposed that the vector of pi’s can be estimated by developing a system of linear constraint equations of the general form inline image. This equation states that the linear combination of species traits (ti) and unknown species relative abundances (pi) is equal to the constraint inline image, where inline image is the trait value of an average unit of biomass (or individual, depending on how relative abundance is quantified) in a community. It is biased towards trait values conferring better performance in a given environment because individuals possessing such traits are more abundant. inline image can vary predictably along environmental gradients (e.g. Cingolani et al. 2007) because traits have been selected along environmental gradients over evolutionary history (Ackerly et al. 2000). Webb et al. (2010) referred to this step in trait-based modelling as the ‘performance filter’, because local environments eliminate traits with inadequate local fitness (Fig. 1).

Most previous evaluations of the maximum entropy (MaxEnt) model have used ‘observed constraints’ by calculatinginline image from observed relative abundances (Shipley, Vile & Garnier 2006; Sonnier, Shipley & Navas 2010). These studies showed that the model can make good predictions, but a more general and desirable application of the model is to predict vegetation structure in communities where mean trait values are predicted from environmental conditions (Shipley, Vile & Garnier 2006). In this study, we use ‘predicted constraints’, such that inline image, thus providing a strong empirical test of the model. This also eliminates any apparent circularity in the model (Marks & Muller-Landau 2007; Roxburgh & Mokany 2007; Haegeman & Loreau 2008). This approach is also more general than classic species distribution modelling (Guisan & Zimmermann 2000) because it considers simultaneously the probability of occurrence of every species in the regional pool, not just the distribution of species that actually occur at a site (Shipley 2010b).

The MaxEnt model states that the relative abundance of every species in a given environment is a function of their trait values [i.e. log(pi) = f (traits)]. However, many traits are highly correlated with each other (Wright et al. 2004), and collinear predictors in any model have undesirable properties (Webb et al. 2010). Variation among leaf traits is largely orthogonal to variation in stem traits (Baraloto et al. 2010), suggesting that a few parsimonious and independent axes of functional trait variation may be useful predictors of community structure. Here, we provide the first test of whether orthogonal trait axes are useful predictors of community composition.

We tested the MaxEnt model of trait-based community assembly (Shipley, Vile & Garnier 2006) along a broad climatic gradient in upland forest communities of the south-western USA. We asked (i) how do traits and orthogonal trait axes vary along climatic gradients? and (ii) How well does MaxEnt utilize these empirical trait–environment relationships to predict forest community structure? We also explored the use of MaxEnt for forecasting shifts in species distributions in a warmer climate.

Materials and methods

Study System

We measured tree species abundances on 1046 plots at 19 sites in Arizona and New Mexico, USA. These sites spanned upland vegetation between 1900 and 3600 m altitude, corresponding to a 12 °C range in mean annual temperature (MAT). These sites spanned the range of high-elevation upland south-western USA forest types including conifer woodlands, montane conifer forests and subalpine forests (Brown 2004). We encountered 15 tree species in these upland communities (Table 1). We calculated relative abundances of each of the 15 species as the proportional basal area (at breast height, 1.37 m) of each of the species divided by the total basal area of the plot. See Appendix S1 in Supporting Information for more details about the forest vegetation samples.

Table 1.   Tree species (and associated four-letter codes) and their mean trait values used in the analysis. Traits are listed in order from most to least predictable from left to right (according to the generalized additive model inline image)
 Bark thicknessFlowering dateMax heightWood densityTwig dry matter contentSpecific root lengthSpecific leaf areaLeaf [P]Leaf [N]Leaf [C]
Trait abbreviationsBarkFlowerHeightWoodTDMCSRLSLA[P][N][C]
Abies concolor (ABCO)0.03616631.00.3990.49332.13.790.13431.2648.28
Abies lasiocarpa (ABLA)0.01517123.50.3270.46540.34.050.13591.5450.82
Juniperus deppeana (JUDE)0.0297215.00.4890.47951.23.580.08001.0549.72
Juniperus monosperma (JUMO)0.040908.40.5760.53528.92.720.09691.2250.45
Juniperus osteosperma (JUOS)0.028909.60.4860.48123.72.500.09561.0949.39
Juniperus scopulorum (JUSC)0.02213610.30.4360.49544.74.020.11371.3151.77
Pinus aristata (PIAR)0.01818617.00.5190.49841.74.420.08521.1749.82
Pinus edulis (PIED)0.03112011.20.5620.55118.04.320.14311.2250.52
Picea engelmannii (PIEN)0.00815128.10.3290.49160.03.240.10431.2048.68
Pinus ponderosa (PIPO)0.04116631.80.4480.49132.83.810.10421.2951.75
Pinus strobiformis (PIST)0.01416625.00.4070.45738.35.550.11231.2950.30
Populus tremuloides (POTR)0.02015125.70.4040.430114.115.320.33242.8950.16
Pseudotsuga menziesii (PSME)0.03012028.00.4480.49732.04.620.13751.0948.16
Quercus gambelii (QUGA)0.03913013.80.6340.54973.113.240.19412.5248.00
Robinia neomexicana (RONE)0.04315111.50.5940.53362.423.000.32334.5747.65
UnitsOuter bark: d.b.h. ratioJulian daymmg mm−3g g−1m g−1mm2 mg−1%%%
Variance explained by climate variables (inline image)0.740.640.570.550.540.540.470.420.380.31

Functional Traits and Trait Axes

We measured functional traits thought to influence plant performance along climatic gradients on all 15 species following standardized protocols (see Appendix S1 for full details).We measured stem traits, such as wood density and twig dry matter content (TDMC), because of their known relationships with water transport and effects on plant survival along moisture gradients (Hacke et al. 2001; Cornwell & Ackerly 2010). Maximum plant height is also related to climatic gradients because shorter trees are often associated with more stressful environments (King 1990).We measured bark thickness because it is known to influence tree survival following low-intensity surface fires (Vines 1968) and because fire regimes vary predictably along the climatic gradient in this study (Agee 1993).We measured leaf traits that influence resource acquisition, such as specific leaf area (SLA) and leaf nutrient concentrations, because they have been shown to vary along global climate gradients (Wright et al. 2004). We measured specific root length (SRL) because it may influence below-ground resource acquisition (Cornelissen et al. 2003). Finally, we obtained information on flowering dates of species because the timing of flowering is constrained by growing season length (Rathcke & Lacey 1985). We also measured seed mass and leaf dry matter content of each species, but these traits were excluded from the analysis because they were only weakly related to climate.

The trait values used in the analysis are species-specific means that are assumed to be constant over plots. This is a reasonable assumption because interspecific trait variation is generally stronger than intraspecific variation (see Appendix S1). For example, species identity explains 94% of the variation in leaf nitrogen concentration and 50% of the variation in bark thickness.

We used principal components analysis (PCA) to extract orthogonal axes of trait variation for use in the MaxEnt model. After computing the initial eigenvectors, we rotated the axes to maximize trait loadings on each axis via ‘varimax’ rotation to increase interpretability of the axes (see Appendix S1). A constant was added to the rotated axis scores so that scores were non-negative, as this is a requirement of the Improved Iterative Scaling algorithm (Della Pietra, Della Pietra & Lafferty 1997).

Climate and Soils

Given the complex topography of the study region, we included variables that relate to macroclimate, mesoclimate and soil resource availability as predictors of trait distributions. To quantify macroclimate, we used the 1-km resolution WorldClim climate grids (Hijmans et al. 2005) to obtain estimates of current MAT. Given this rather coarse resolution for a mountainous landscape, use of these modelled estimates of MAT introduces a source of uncertainty into the model. We did not include mean annual precipitation (MAP) as a predictor because it was strongly negatively correlated with temperature (= −0.78), and because changes in precipitation under climate change are far less certain (IPCC 2007).To quantify the influence of topography on mesoclimate, we used equations for estimating solar radiation from topographical slope, aspect and latitude (McCune & Keon 2002). To capture the influence of soil type on soil moisture and nutrient availability, we used a binary variable to differentiate plots on coarse-textured sedimentary-derived soils from fine-textured igneous-derived soils. The highest elevation site (i.e. San Francisco Peaks) consists of only igneous-derived soil because it is a stratovolcano.

Performance Filter

We used independent cross-validation to provide a strong test of the MaxEnt model. We split the data set in half by stratifying by forest type and randomly dividing within each stratum. Strata were used to ensure that enough plots from less-common forest types (e.g. subalpine forests) were included in the model building process. We used 512 plots (the ‘training data set’) to develop relationships between environmental predictors and traits, and used 534 plots (the ‘validation data set’) to evaluate model predictions. This approach addresses previous criticisms of the model, because model constraints are derived independently through knowledge of environmental conditions and are therefore not dependent on observed vegetation structure (Roxburgh & Mokany 2007).

We calculated community-weighted mean traits as inline image, where ti is the mean trait value and pi are the observed relative abundances for species i from 1, …, S. We used generalized additive models [GAMs; using the ‘gam’ function in the ‘mgcv’ library in r (Wood 2006; R Development Core Team 2010)] on the training data set to develop predictive models of community-weighted mean traits as nonlinear functions of MAT, solar radiation and soil type. We ranked models for each trait from high-to-low predictive capacity assessed by the model inline image and used this order for entering traits into the MaxEnt model.

Evaluating the MaxEnt Model

Using the GAMs developed from the training data set, we predicted the community-weighted mean trait values (inline image) in the validation data set. These predicted community-weighted mean traits were then used as constraints in the MaxEnt model. If the species pool has been identified and if the traits of every species are known, then one can solve for the unknown species abundances. In practice, there are typically far fewer constraint equations than unknown species abundances, which results in a system with many possible solutions. Shipley, Vile & Garnier (2006) proposed to select the solution with MaxEnt, i.e. the distribution that maximizes the entropy function, inline image. Entropy maximization is justified because the MaxEnt solution (i) is the distribution of pi that can be realized in nature the most ways; therefore, it is the most probable distribution and (ii) is the only distribution of pi that is determined entirely from the specified constraints, without implying additional constraints (Jaynes 2003).

We first obtained the MaxEnt predictions using the one trait that was best predicted by the GAMs. We subsequently tested other models where the two most predictable traits were used, then the four most predictable traits, etc., up until all 10 traits were used as constraints in the model. We evaluated the impact of this order on model performance by running another analysis in reverse order, i.e. the least predictable trait was entered first. We obtained the MaxEnt predictions using the ‘maxent’ function in the ‘FD’ library of r (Laliberté & Legendre 2010; Laliberté & Shipley 2010) with a tolerance level of 1 × 10−8. Uniform prior distributions were used in all instances. Model predictions were compared with observed relative abundances using two measures of fit: R2 (using untransformed relative abundances) and the Root Mean Square Error (RMSEsqrt) using square-root transformed relative abundances (Roxburgh & Mokany 2010). We evaluated the statistical significance of model predictions by comparing measures of fit obtained from predicted constraints against a null distribution of 999 measures of fit obtained by permuting observed relative abundances (see Appendix S2 for r code). We evaluated the statistical significance of model predictions obtained from ‘observed constraints’ with a permutation procedure (Shipley 2010a) that is implemented in the ‘maxent.test’ function in the ‘FD’ library of r (Laliberté & Shipley 2010).

We also used observed and predicted coenoclines to evaluate model performance. We compared nonlinear regression models (i.e. GAMs) of species response curves fit to observed relative abundances with those fit to MaxEnt-predicted relative abundances. This approach permitted us to compare how the mean predictions of relative abundances compare with mean observed relative abundances along the temperature gradient.

To estimate the maximum amount of variation in the species relative abundances that was explainable by climate directly, we fit a separate GAM relating the observed relative abundance for each of the 15 species as a function of MAT, solar radiation and soil type using training data, and obtained regression predictions on the validation data set. Because these form-free statistical fits imposed minimal assumptions on the relationships between relative abundances and climate, and because each model was fit separately for each species, the R2 between regression model-fitted and observed relative abundances represents an approximate upper bound on the predictive ability of any model whose empirical information is derived from environmental variables alone.

Climate Change Scenario

Mean annual temperature in the south-western USA is predicted to rise over the next century. Given that MaxEnt has been proposed as a pragmatic tool for providing predictions of relative abundances of real species in different environmental contexts (Shipley 2010b), we explore the use of this trait-based model in forecasting shifts in species distributions in a warmer climate using empirical trait–climate relationships. Given the variety of global circulation models and emission scenarios, we focused on the median-predicted temperature change across 21 global models for the A1B scenario, which is an increase of 2.5 °C by the year 2060 (IPCC 2007). Solar radiation and soil type were unchanged from current conditions in this scenario. We predicted a new set of community-weighted mean trait values (inline image) at each plot with the new set of predictors, and these new constraints were used to obtain the MaxEnt predictions of species relative abundances in the year 2060. For comparison, we also used the classic species distribution modelling approach to forecast future species distributions by regressing individual species abundances directly on the three predictor variables and used these models to project species responses to an increase of 2.5 °C. We acknowledge that this approach does not incorporate an exhaustive set of factors that are known to affect species distributions. For example, changes in precipitation will certainly affect species distributions, but future changes in precipitation are far less certain than changes in temperature. We discuss our results in the light of the limitations of this approach.

Results

Trait–Climate Relationships

Environmental conditions explained between 31% and 74% of the variance of the ten community-weighted mean functional traits (Table 1). MAT was a significant factor for all traits, solar radiation was a significant factor for all traits except bark thickness, and geological substrate was a significant factor for all traits except leaf [P] (Table S1). MAT explained most of the trait variation and often exhibited the strongest bivariate relationship with the traits. Significant nonlinear relationships were prevalent between traits and MAT (Fig. 2). Bark thickness increased with increasing MAT. Flowering date was earlier with increasing MAT. Wood density and TDMC tended to increase with MAT, although they both increased slightly at the coldest MAT. Maximum height peaked at intermediate MAT. SLA, leaf [P] and leaf [N] were lowest at the extremes of MAT and peaked at c. 4 °C MAT.

Figure 2.

 Regression models (generalized additive models) illustrating the nonlinear relationships between mean annual temperature and community-weighted mean functional traits (top three rows) and principal components analysis trait axes (bottom row). All models were significant (< 0.001). Black dots, sedimentary soils; grey dots, igneous soils.

The first three PCA axes accounted for 81% of the species–trait correlation matrix (Fig. 3). The first axis represented variation in leaf and root traits (SLA, leaf [P], leaf [N] and SRL). The second axis represented variation in stem traits (TDMC, bark thickness and wood density). The third axis represented variation in flowering date and maximum height. Environmental conditions explained 47%, 60% and 67% of the variation in the community-weighted mean PCA axis 1, 2 and 3 scores, respectively. Axes varied nonlinearly with MAT, but, in general, the first and third axes were negatively related to MAT, and the second axis was positively related to MAT (Fig. 2).

Figure 3.

 Distribution of the 15 tree species in reduced three-dimensional trait space. Three principal components analysis axes accounted for 81% of the variance in the species–trait correlation matrix. See Table 1 for four-letter species codes.

MaxEnt Predictions

The MaxEnt predictions of relative abundances in the validation data set were significant with only one trait, and predictive ability increased asymptotically with the number of traits used in the model (Fig. 4a). The model with one trait explained 8% of the variance in the relative abundances of all 15 species (R2 = 0.08, = 0.001; RMSEsqrt = 0.271, = 0.001). The model with 10 traits explained 54% of the variance (R2 = 0.54, = 0.001; RMSEsqrt = 0.192, = 0.001). The RMSEsqrt fit statistics were never lower than 0.1, but they were always significantly smaller than those obtained through permutation. The order of trait entry into the model influenced model performance because explained variance was reduced in models where the least predictable traits (i.e. leaf traits) were entered before the most predictable traits (Fig. 4).

Figure 4.

 Relationship between the amount of explained variance of the maximum entropy model and (a) the number of traits and (b) the number of principal components analysis (PCA) trait axes used in the model. Filled symbols represent models that used predicted community-weighted mean traits as constraints, whereas open symbols represent models that used observed community-weighted mean traits as constraints. Filled circles represent models in which traits were entered into the model in the order at which they are listed from left to right, based on how well they could be predicted from the environment. For example, bark thickness was the first trait entered in (a) as the generalized additive models explained 74% of its variance (see Table 1 for predictive ability and trait abbreviations), and the ‘two trait model’ included both bark thickness and flowering date as predictors. In contrast, filled triangles represent models in which the order of trait entry into models was reversed from the order that is shown (i.e. leaf traits were entered first). The only non-significant model tested was the two PCA axis model with observed constraints (indicated by the asterisk).

The MaxEnt model we tested proposes that climate constrains trait distributions, which in turn influence community composition (Fig. 1). How much variance in observed relative abundances can be explained by climate directly? We found that 57% of the variation of observed relative abundances in the validation data set could be explained by the climate variables using 15 separate species-specific regression models. Thus, the limit of explained variance as the number of traits approaches − 1 cannot be >57% in this case (this limit is illustrated by the horizontal dotted line in Fig. 4). The predictive ability of the MaxEnt model with 10 predicted constraints approached that which was possibly given the climate variables (Fig. 4a), i.e. the MaxEnt model was 95% efficient (54/57 = 0.95) in explaining observed relative abundances because of trait-based environmental filtering. Models that used the observed community-weighted mean traits as constraints obtained near perfect predictive ability (R2 = 0.94) using the first four traits (Fig. 4a), suggesting that if these traits could be perfectly predicted from environmental conditions, then very accurate predictions of species relative abundances could be achieved with only a restricted number of traits.

MaxEnt models that used PCA trait axes in lieu of individual traits did not perform well (Fig. 4b). When all three predicted community-weighted mean PCA axes were used as constraints, the predictions of species abundances were significant, yet only explained 18% of the variance (R2 = 0.18, = 0.001; RMSEsqrt = 0.257, = 0.001). Models that used three observed community-weighted mean PCA axis scores accounted for 71% of the variation in observed relative abundances.

Fitted response curves (i.e. coenocline) of all 15 species along the elevation gradient were nearly identical between observed and MaxEnt-predicted relative abundances (Fig. 5a,b). Response curves fit through relative abundances predicted from a classic regression model approach were also very similar to response curves fit through observed relative abundances (data not shown). Given that only 54% of the variance of relative abundances could be explained using the 10 predicted constraints, it is somewhat surprising that the MaxEnt model gives reasonably good predictions of how the mean relative abundance of individual species changes along the climatic gradient (Fig. 5b).

Figure 5.

 Species response curves (i.e. coenoclines) for all 15 tree species along the elevation gradient in the contemporary time period [top panels (a) and (b)] and under a future climate change scenario of a 2.5 °C increase in mean annual temperature (MAT) [bottom panels (c) and (d)]. Panel (a) illustrates nonlinear regression models (generalized additive models, GAMs) fit through recently observed species relative abundances. Panel (b) illustrates nonlinear regression models (GAMs) fit through maximum entropy (MaxEnt)-predicted relative abundances that were obtained from independent cross-validation using the model with the 10 predicted community-weighted mean traits. It should be noted that the high correspondence between models fit through (a) observed and (b) MaxEnt-predicted relative abundances. Panel (c) illustrates models of future species distributions using classic regression modelling where species abundances were directly modelled as functions of climate. Panel (d) illustrates models of future species distributions using MaxEnt-predicted relative abundances under a 2.5 °C increase in MAT. It should be noted that we restricted elevations to be >2000 m in panels (c) and (d) because the future temperature scenarios at elevations <2000 m were well-above the range of those used in model development.

Climate Change Scenario

We obtained the MaxEnt predictions of species relative abundances using the projected increase in MAT of 2.5 °C by the year 2060. Because factors other than MAT were included in the models used to predict the community-weighted mean traits, the change in predicted mean trait values and consequent changes in species response curves was not a simple shift of each curve along the elevation gradient: each species responded individualistically to increased temperatures (Fig. 5c,d). According to the model, the forest surrounding Flagstaff, Arizona, is forecast to shift from a Pinus ponderosa-dominated forest to one that is dominated by Juniperus monosperma and J. osteosperma. The elevation optimum of P. ponderosa is forecast to shift upward ∼500 m and attain dominance in the current sites that support mixed-conifer and subalpine forest. The subalpine species (Pinus aristata, Picea engelmannii and Abies lasiocarpa) were forecast to decline considerably in relative abundance at the highest elevations. The MaxEnt forecast is similar, though not identical, to those obtained from a classic regression approach to forecasting future species distributions where climate variables were direct predictors of species abundances (Fig. 5c). Differences between the two forecasting approaches are apparent in the coenoclines (Fig. 5c,d), but the MaxEnt forecast was significantly correlated with the regression approach (= 0.56, = 0.001).

Discussion

Ecologists have long suspected that functional traits play an important role in community assembly (Schimper 1903), but the lack of an analytical framework for predicting species relative abundances from their traits has hindered progress in identifying trait-based assembly rules (Keddy 1992). Shipley, Vile & Garnier (2006) translation of trait-based environmental filtering into a mathematical model has given ecologists a new tool for testing the importance of traits in the assembly process. Given the many factors that control the assembly process (i.e. population demography, species interactions, etc.), it seems a tall order for a model based only on mean trait values to be able to accurately predict the relative abundances of every species in the species pool. Our analysis suggests that trait-based environmental filtering of the regional species pool explains half of the variation in tree community composition across uplands in the south-western USA. This is likely a minimum estimate of the relative importance of trait-based species sorting, because we may have excluded important traits, we may have excluded important environmental variables, and we did not explicitly account for measurement error in either traits or environmental variables.

Not all traits were equally useful for predicting species abundances. If the constraints in the MaxEnt model are predicted from environmental gradients, the traits that are strongly selected along the gradients will likely be the most useful for predicting species abundances. Figure 4 illustrates that if the first four traits in the model could be perfectly predicted from climate (i.e. the predicted values of inline image the observed values of inline image), then the model would achieve near perfect predictions of species abundances. However, this was not the case. Leaf traits accounted for a significant amount of functional variation among the tree species in this study, but they were not well predicted from climatic conditions (Table 1, Fig. 2). The performance of the model declined when leaf traits were entered into the model first because they did not vary predictably along the climatic gradient (Fig. 4). Shipley et al. (2011) also found that leaf traits, such as SLA and leaf [N], were poorly predicted from environmental conditions, even though SLA and leaf [N] exhibited considerable variation among the species in that study (Laughlin et al. 2010).

This raises a critical issue with respect to trait-based models of community assembly: traits can only be good predictors of abundance if they vary among species, but traits that vary strongly among species are not necessarily the best predictors of relative abundance. Shipley (2010b) described how the Lagrangian multipliers (λ) found in the objective function of the model provide information about the relative strength and sign of the selection of a trait along a gradient. Theoretically, Lagrangian multipliers with large absolute values are the most important (if traits are scaled to unit variance) for determining relative abundances in the context of the MaxEnt model. However, this is only true when model predictions closely match observations, which is often not the case when ‘predicted constraints’ are used in the model. From a prediction-oriented perspective, we conclude that when ‘predicted constraints’ are used in the MaxEnt model, the best traits for predicting species abundances must both (i) vary strongly among species and (ii) vary predictably along environmental gradients.

Stem traits met both of these conditions. Bark thickness, for example, varied strongly among species, and it was the most predictable community-weighted mean trait (Table 1, Fig. 2). Bark thickness is indirectly related to climate through the mediating effects of fire regimes. Climate influences fire regimes by controlling fuel loadings, fuel moisture and weather conditions (Westerling et al. 2006). Fires are most frequent in the pine–oak and lower mixed-conifer forest types (Agee 1993). Species with thick outer bark (e.g. P. ponderosa and Pseudotsuga menziesii) have greater protection from heat-induced cambial death (Vines 1968) and will have a higher probability of growing, reproducing and surviving in a regime of frequent fires than species with thin outer bark. In contrast, thin bark is prevalent among species that occur in cold subalpine forests (e.g. A. lasiocarpa) that burn very infrequently.

Wood density is another stem trait that was predictable along the climatic gradient. Following expectations (Hacke et al. 2001), mean wood density was highest in the hot and dry pinyon–juniper woodlands and lowest in the more mesic upper mixed-conifer forests. However, mean wood density increased towards tree line because the dominant species, P. aristata, produce very dense wood. Dense wood is likely an advantageous trait at tree line where physiological drought is caused by desiccating winds and cold temperatures. The identification of traits that reflect climatic conditions is a crucial step towards understanding how vegetation will respond to climate change. Although no single trait has been identified to capture a species temperature optimum, traits such as wood density and flowering date do reflect a species’ ability to tolerate certain climatic conditions.

Flowering date was another predictable trait in this study. Tree species in warm climates flower early in the season, whereas species in cold climates must wait until much later in the season to flower owing to constraints on growing season length (Table 1, Fig. 2). Phenological events, such as flowering and leaf out, are changing in response to warming (Ibáñez et al. 2010), suggesting that the plasticity of flowering time may render a model based on species-specific means of questionable value. However, there is a tremendous range in flowering dates among tree species in this study (range = 114 days). Shifts in flowering date are most often unidirectional (i.e. earlier), suggesting that flowering dates of species relative to each other may remain intact if they change in response to warming. Nevertheless, the assumption of a constant mean trait for each species in any model seems overly simplistic, and the sensitivity of this assumption needs further testing with a data set that includes adequate information on intraspecific variation in trait distributions.

Orthogonal spectra of coordinated traits were not good predictors of species abundances. This was surprising given that 81% of the variation in the trait data was captured by the first three principal components. Apparently, enough variation in the trait values among species was lost in the data reduction to render the MaxEnt solutions poor fits to observed abundances compared with predictions obtained using individual traits. Other studies have clearly shown that wood and leaf traits are important to community assembly (Cornwell and Ackerly 2010), but in this study the wood and leaf trait axes did not provide enough information by themselves to make good predictions of community structure. This suggests that the MaxEnt model requires many traits to achieve excellent fits, which can easily lead to statistical over-fitting. Over-fitting can be partially avoided through the judicious selection of traits and through statistical significance testing (Shipley 2010a; see approach in Appendix S2). This also implies that climatic constraints on functional traits are not the only factors that determine species distributions, especially in the light of the fact that environment could only explain a maximum of 57% of the variance in relative abundances.

Trait–environment relationships formed the basis for predicting shifts in species distributions in a warmer world. In theory, changes in climate at a given site will shift the average trait in a community towards values that confer high performance in that new climate. For example, if warming causes an increase in drought-induced cavitation, thereby giving an advantage to species with higher wood density (Hacke et al. 2001), then the average wood density of the community should increase at that site. The MaxEnt model allows us to estimate how such a fundamental physiological mechanism will lead to changes in community composition. The MaxEnt model forecasted an upward shift of c. 500 m in tree species elevation optimums (Lenoir et al. 2008) that would dramatically alter the character of northern Arizona landscapes. These shifts are within the range of vegetation change that has been observed in the palaeoecological record in the south-western USA (Cole 1990), suggesting that these are possible given adequate dispersal and recruitment. Tree species range shifts could already be underway given that tree mortality rates have recently increased across the western USA, possibly because of climate stressors (van Mantgem et al. 2009).

According to the model results, the transition between J. monosperma woodland and P. ponderosa forest will shift upward from ∼2000 m to ∼2350 m (Fig. 5a,d). P. ponderosa forest currently occupies 1 857 200 ha in Arizona, of which 1 440 700 ha occurs below 2350 m. This implies that up to 78% of P. ponderosa forest in Arizona may transition to dominance by J. monosperma by 2060. These results are useful for informing management strategies to passively assist the migration of species into climatically suitable environments. For example, managers could promote J. monosperma individuals that currently exist in P. ponderosa stands, thereby providing a seed source to passively facilitate the upward migration. Given that P. ponderosa is forecast to dominate higher elevation sites that are predicted to burn more frequently in a warmer climate (Westerling et al. 2006), P. ponderosa should be favoured in any silvicultural treatment in mixed-conifer forests to assist this upward migration. These results suggest that the MaxEnt model has practical uses in applied ecology, but this forecast suggests an extremely rapid shift in species distributions.

The approach used here likely overestimates the rate of vegetation change that will occur by the year 2060 because it did not incorporate other important climatic factors and demographical processes known to influence species migration. For example, the increasing CO2 concentration may offset potentially negative consequences of increasing temperatures by increasing water use efficiency (Long et al. 2004). Changes in precipitation will also control range shifts, but we did not incorporate precipitation into the model because future changes in precipitation are far less predictable than changes in temperature (IPCC 2007) and because the WorldClim model-predicted normals of precipitation are strongly correlated with temperature.

The MaxEnt approach used here did not account for dispersal limitation, trait plasticity or evolutionary adaptation (Dullinger, Dirnböck & Grabherr 2004; Morin, Viner & Chuine 2008). Forecasts of rapid migration rates are common to niche-based approaches (e.g. Iverson & Prasad 1998), and strict niche-based forecasts likely need tempering because dispersal limitation will limit migration rates (Morin, Viner & Chuine 2008; Cole 2010; Moser et al. 2011). MaxEnt can potentially account for dispersal limitation by using more informative prior distributions that reflect local abundance patterns (Sonnier, Shipley & Navas 2010). We restricted our analyses to models with uniform (i.e. uninformative) prior distributions. Trait plasticity and adaptation could be incorporated into MaxEnt by altering trait values of species, but it is uncertain how species’ traits will adapt to such rapid climate change.

Another limitation of the MaxEnt model is that it lacks an explicit mechanism relating plant traits to performance in different environments (Webb et al. 2010). We assessed the performance filter using nonlinear regression models to develop equations for predicting community-weighted mean trait values from climatic conditions. We acknowledge that this approach is largely phenomenological; that is, we relied on empirical fits to observed data to learn inductively how community-weighted mean traits vary along climatic gradients, rather than building a model from first principles. Such models built from first principles have not yet been fully developed, but recent theoretical advances suggest a promising way forward (Falster et al. 2010). Until this theory is more fully developed, empirical models built from real data as a first approximation to the assessment of the performance filter must be used.

Why should ecologists bother with a trait-based approach when classical species distribution modelling approaches are easier to apply and often yield better predictions? First, trait-based approaches allow ecologists to statistically evaluate the importance of interspecific trait variation in community assembly and therefore attempt to explain observed distributional patterns based on physiology-based trait–environment constraints. Classic modelling approaches lack a physiology-based link between species and environment. Secondly, the MaxEnt approach attempts to predict the relative abundance of every species in the species pool simultaneously (including those that never actually successfully establish), in contrast to the classic approach, which models either a single species at a time or just the species that are known to occur in a local site. Lastly, a predictive model based on trait–climate relationships is better suited for making predictions outside the range of where the model was developed (Webb et al. 2010). Given that climate can predict biome types across the planet (Whittaker 1975), trait–climate relationships developed in one region may be similar to trait–climate relationships in other regions. Using a performance filter that is developed in one region to predict the relative abundances of a different set of species in another region is the natural next step for evaluating this trait-based model of community assembly.

Acknowledgements

This work was supported by a Joint Venture Agreement (#08-JV-11221633-233) with the USDA Forest Service Rocky Mountain Research Station.

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