The relationship between wood density and mortality in a global tropical forest data set


  • Nathan J. B. Kraft,

    1. Department of Integrative Biology, University of California, Berkeley, CA 94720, USA
    2. Present address: Biodiversity Research Centre, University of British Columbia, Vancouver, BC, Canada
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    • These authors contributed equally to this work.

  • Margaret R. Metz,

    1. Department of Plant Pathology, University of California, Davis, CA 95616, USA
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    • These authors contributed equally to this work.

  • Richard S. Condit,

    1. Smithsonian Tropical Research Institute, Panama City, Republic of Panama
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  • Jérôme Chave

    1. Laboratoire Evolution et Diversité Biologique, Université Paul Sabatier/CNRS, Toulouse, France
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Author for correspondence:
Nathan J. B. Kraft
Tel: +1 604 822 6438


  • Wood density is thought to be an important indicator of plant life history because it is coupled to many aspects of whole-plant form and function. We used a hierarchical Bayesian approach to explain variation in mortality rates with wood density, drawing on data for 765 500 trees from 1639 species at 10 sites located across the Old and New World tropics.
  • Mortality rates declined with increasing wood density at five of 10 sites. Similar negative trends were detected at four additional sites, while one site showed no relationship. Our model explained 40% of variation in mortality on average. Both wood density and mortality rates show a high degree of phylogenetic conservatism.
  • Grouping species by family across sites in a second analysis, we found considerable variation in the relationship between wood density and mortality, with 10 of 27 families demonstrating a strong negative relationship.
  • Our results highlight the importance of wood density as a functional trait in tropical forests, as it is strongly linked to variation in survival. However, the relationship varied among families, plots, and even census intervals within sites, indicating that the factors responsible for the relationship between wood density and mortality vary spatially, taxonomically and temporally.


A central goal of ecology is to understand how variation in the morphological and physiological characteristics of species relates to differences in growth, survival, and, ultimately, patterns in the distribution and abundance of organisms across landscapes (McGill et al., 2006; Westoby & Wright, 2006). Growing consensus among plant ecologists now permits the quantification of woody plant strategies along several often orthogonal axes of variation related to characteristics of the leaves, seeds, wood, and growth form (Westoby, 1998; Westoby et al., 2002; Cornelissen et al., 2003; Wright et al., 2004). These attributes, or functional traits, are most ecologically meaningful when they correlate with variation in vital rates and performance, both of which contribute to lifetime fitness (Ackerly, 2003; Violle et al., 2007).

Wood density is thought to be an important functional trait because it is directly coupled to many aspects of whole-plant form and function (Cornelissen et al., 2003; Chave et al., 2009). Species with denser wood tend to grow more slowly (in height or diameter) because they invest more carbon in a given volume of stem relative to species with lighter wood, and because high sapwood density is associated with reduced conductance and thus reduced photosynthetic carbon gain (Enquist et al., 1999; Bucci et al., 2004; King et al., 2005; Chave et al., 2009; O’Grady et al., 2009). Species with dense wood tend to occur later in succession than species with low-density wood (ter Steege & Hammond, 2001; Falster & Westoby, 2005). High wood density is known to correlate with resistance to drought-induced embolism, minimum seasonal water potential, mechanical breakage, and attack by pathogens and fungi (Augspurger & Kelly, 1984; Niklas, 1992; Clark & Clark, 2001; Hacke et al., 2001; Ackerly, 2004; Jacobsen et al., 2005; Preston et al., 2006; Alvarez-Clare & Kitajima, 2007; Chave et al., 2009; Zanne et al., 2010). These benefits of denser wood should lead to reduced mortality.

As causes of mortality may vary among regions, it is reasonable to expect that the relationship between wood density and mortality will differ among sites. Similarly, plant functional traits such as wood density are often broadly conserved within related taxa, so we expect there to be variation in the wood density–mortality relationship across lineages as well (Prinzing et al., 2001; Chave et al., 2006; Swenson & Enquist, 2007; Donoghue, 2008).

A negative relationship between wood density and mortality has been documented at local sites (e.g. Muller-Landau, 2004; Nascimento et al., 2005; King et al., 2006; Chao et al., 2008; Poorter, 2008; Wright et al., In press) and in 140 tree species across five neotropical sites (Poorter et al., 2008), but this relationship has yet to be explored at a pan-tropical scale. Here, we present the results of analyses exploring the relationship between wood density and mortality in over 765 500 trees from 1639 species at 10 long-term forest census plots located across the Old and New World tropics. Our study improves on previous efforts by including a broad range of tropical forests across continents, a large standardized sampling effort within forests, and a single analytic framework.

We use a hierarchical Bayesian modeling approach (e.g. Clark, 2005; Gelman & Hill, 2007), which assumes that process model parameters of interest (such as species’ mortality rates) are drawn from broader distributions. One goal of the approach is to produce accurate estimates of the parameters that describe these distributions, as opposed to simply estimating process model parameters directly from the data. There are several advantages to this approach. First, it permits us to incorporate the hierarchical structure of our data into the model, which allows us to separate variation among geographic locations, families and species from sampling error (Clark, 2005); standard frequentist methods often confound these sources of variation and overestimate true variance. Secondly, it permits us to include rare species with sparse sample data in our estimates of species mortality rates (Condit et al., 2006). Recent analyses suggest that rare tree species within tropical forests tend to have functional trait values that are somewhat distinct from those of more common species (Baraloto et al., 2009), indicating that rare species should be included in analyses in order to capture the full spectrum of trait variation within communities. Finally, the ability of hierarchal Bayesian approaches to characterize distributions of parameters at various levels within analyses permits the discussion of both the central tendencies and the degree of variation present within distinct components of our model.

Specifically, we ask three questions. (1) Is there support for a pan-tropical relationship between wood density and mortality rates across forest sites, and, if so, how variable is the relationship across sites? (2) Is there variation in the strength of the relationship across families? Finally, as the evolutionary nonindependence of related taxa can impact correlations between traits when taxa are analyzed out of phylogenetic context (Felsenstein, 1985), we ask (3) does the evolutionary history of taxa included in the study influence the relationship?

Materials and Methods

Data sources

We used previously published forest census data (Condit et al., 2006) from 10 permanent tropical forest dynamics plots that are part of the Center for Tropical Forest Science (CTFS) network. The plots range in size from 20 to 52 hectares (Supporting Information Table S1), and are located in forests largely free from human disturbance. Details of the sites and the census protocols can be found elsewhere (Condit, 1998; Losos & Leigh, 2004; Condit et al., 2006). At three sites (Barro Colorado Island, Panama; Pasoh, Malaysia; Mudumalai, India), data for multiple census intervals were available. We chose to use the longest census interval at these sites, although we present separate analyses of the intermediate census intervals for comparison in case census interval affects mortality rates (Sheil & May, 1996; Lewis et al., 2004). In all analyses we expressed mortality in terms of annual rates. The Ituri forest site in the Democratic Republic of Congo has two plots, Edoro and Lenda, which we treated separately. Mean wood density, defined as the ratio of wood dry mass to fresh volume (Niklas, 1992; Chave et al., 2006; Williamson & Wiemann, 2010), was taken largely from published compilations (Chave et al., 2006, 2009; Zanne et al., 2009) and unpublished data from J. Chave and N. Swenson. These database values are the best estimates of wood density currently available for many of the species in the study, although it may be valuable to revisit these analyses as more locally collected data become available. Only taxa for which we had species-level wood density determinations were included in our analyses; that is, we did not apply genus-level or family-level means to species lacking published wood density data. Species-level wood density estimates were available for 20–72% (mean 43%) of the species present at a site (Table S1).

Model 1: site-based analyses

First, we estimated parameters describing the relationship between wood density and mortality rates across species at each forest site. We used a hierarchical Bayesian approach and Metropolis–Hastings algorithms (e.g. Clark, 2005; Gelman & Hill, 2007) with noninformative (i.e. uniform) priors to estimate parameters describing the relationship between wood density and mortality rates across species at each forest site (cf. Condit et al., 2006; Metz et al., 2008). Sites were analyzed independently. Across all species i at a site, we modeled a linear relationship with lognormal errors between the mortality rate constants, mi, and wood density, wdi, as:

image( Eqn 1)

For analysis, we subtracted the global mean wood density value (across all species in all sites in the study) from each species’ wood density (wdi) to produce a centered wood density value wdi′. Once mortality rates were estimated, wood density values were uncentered (as wdi), and intercepts (bj′) were adjusted accordingly for presentation (as bj). We assumed that the species mortality rate constants, mi, followed a lognormal distribution about a predicted mortality rate, μi, for a given wood density, wdi. The parameters μi and σ describe the mean and standard deviation, respectively, of the logarithm of this distribution and capture the residual error (ε ∼ lognormal(0, σ)) in the wood density–mortality relationship not captured elsewhere by other components of the model. The predicted mortality rate (μi) was not a parameter in the model but was calculated directly using a, wdi′ and b′.

The simple relationship between wood density and mortality described by Eqn 1 is the core of our analysis; however, we also wanted to partition variance in the relationship into several specific sources. By using a hierarchical approach, we are able to estimate parameters that describe variation in the relationship at different levels in the structure of our data: the census level, the family level, and the site level.

Census data  In our model, mortality rate estimates (mi) were assumed to depend both on the relationship of wood density and mortality, described above in Eqn 1, and on the observations of the survival of individual trees across a census period. These observations of tree survival can be subject to high error, particularly for rare species. Instead of using these observations as a direct measure of mortality, we used a probability model in the form of a binomial distribution (Condit et al., 2006). We estimated a survival probability (θi) for individuals of each species i, based on the observed number of trees at the beginning of a census, Ni, and the observed number of survivors across the census interval, Si. The binomial distribution permits the estimation of a finite and nonzero survival probability for a species even if all or none of the starting individuals survive over the census interval, as can be seen by comparing the observed vs fitted mortality rate constants in the supporting data set of a related analysis by Condit et al. (2006). This feature allows us to include many rarer species that would be excluded from traditional analyses. The annual survival probability is related to the annual mortality rate by the exponential function (θ = em). Thus, the probability of observing S survivors from N individuals for any species i is:

image( Eqn 2)

Family level  As preliminary results suggested that there is both a site and a taxonomic component to the relationship between wood density and mortality, we allowed the slope and intercept of the relationship between wood density and mortality to vary across families within a site. Thus, we expanded our model from Eqn 1 to include variation in the relationship attributable to family differences:

image( Eqn 3)

Here aj represents the slope of the relationship for family j to which species i belongs. Similarly , bj′ represents the intercept of the relationship for family j, and is an estimate of the mortality rate of a hypothetical species within the family at the global average wood density. One limitation of our approach is that plant family delineations are somewhat arbitrary, in that they represent clades of different ages. A more natural approach would consider phylogenetic relatedness in a continuous fashion; however, practical modeling constraints limited us to placing species into clades, and families were the most recognizable and tractable level at which to group species.

Site-wide parameters  Family-level slopes (aj) and log-transformed family-level intercepts (loge(bj′)) were assumed to be jointly distributed in a bivariate normal distribution across all families at a site. This distribution was described by five plot-wide hyperparameters: the mean (α) and variance (SDα2) of the slopes of the families, the mean (β) and variance (SDβ2) of the logarithms of the intercepts of the families, and the covariance between slope and intercept (Covα,β). The means of this bivariate distribution (α, β) describe the relationship of an average family at a site, while the variances (SDα2 and SDβ2) capture family-to-family variation. If family variation is unimportant at a site, the variances in slope and intercept across families (SDα2 and SDβ2) should be estimated as 0. We assumed that residual unexplained error, σ, first introduced in the description of Eqn 1, was constant across all families at a site.

Thus, variation in the relationship between wood density and mortality is partitioned into several different sources. At the census level, the binomial distribution accounts for sampling error, including cases where species lost all or no individuals in a given census interval. At the site-wide level, the bivariate distribution of family slopes and intercepts allows for variation among families, and the lognormal distribution of mortality rates accounts for variation in mortality at a given wood density.

We ran 101 000 iterations of the Metropolis–Hastings algorithms for each forest over each census interval, discarding the first 1000 iterations (the ‘burn-in’ period) from the final analysis. In each step all parameters were updated in turn. The site-wide parameters (α, SDα2, β, SDβ2 and Covα,β) were updated using the bivariate normal distribution of family slopes and intercepts that they describe. The family-level parameters (aj,bj′ and σ) were updated using Eqn 3. The mortality rate constant, mi, of each species was updated using the census-data level relationship described in Eqn 2.

To ensure that the Metropolis–Hastings algorithms thoroughly explored the range of possible parameter values, the step size used to propose a random new value of each parameter was adjusted during the initial 1000-iteration burn-in period until approx. 25% of the proposed steps were accepted. The step size was then held constant for the following 100 000 iterations, which were used to estimate the posterior distributions of the parameters. Visual inspection of the Markov-chain Monte Carlo (MCMC) chains for each site-wide parameter and the log likelihood values revealed that the posterior distributions had converged well before 1000 iterations.

We ran the Bayesian analyses with data for each site, using all tree species for which wood density data were available. While our plot network data included all trees ≥ 10 mm diameter at breast height (dbh), many tropical forest census plots work exclusively with trees ≥ 100 mm dbh. To check if our results were robust to this difference, we repeated our analysis after removing all stems of 10–99 mm dbh from our data. We also explored running the model with log-transformed mortality rates in order to permit comparisons with prior analyses, many of which have log-transformed mortality observations to meet the assumptions of parametric analyses. All analyses were performed in R version 2.7.2 (R Development Core Team, 2008), and code for Model 1 and a sample dataset are available as Supporting Notes S1 and S2.

Following these analyses, we used the 95% credible intervals of parameter estimates to determine which sites had nonzero slopes (α values) and to compare results across sites. To facilitate comparison with other studies, we evaluated the goodness of fit of the model at each forest by calculating Bayesian R2 (Gelman & Pardoe, 2006; Gelman & Hill, 2007). This calculation compares the variance in the estimated species’ mortality rates (mi) in a forest to the variance of the residual errors about the predicted linear relationship defined by species’ wood density and the corresponding family-level slope (aj) and intercept (bj′) parameters. It does not account for variation explained at the census data level of the model (Eqn 2). Note that Bayesian R2 averages over uncertainty in the regression coefficients and therefore usually produces lower estimates of the amount of variance explained by a model relative to a ‘traditional’ coefficient of determination R2 (Gelman & Pardoe, 2006).

Finally, for graphical purposes we calculated the 95% confidence interval for the family and site-wide parameter portions of the model by sampling the bivariate normal distribution of family-level slopes and intercepts (defined by α, SDα2, β, SDβ2 and Covα,β), calculating predicted mortality at a range of wood density values, and adding within-family variation to each estimate using σ. This process was repeated 10 000 times and the 97.5% and 2.5% quantiles of the resulting distribution were calculated (shaded areas in Fig. 1). This procedure allows us to determine where 95% of randomly chosen species from randomly chosen families would be predicted to fall, and thus provides an estimate of the range of variability in the wood density–mortality relationship.

Figure 1.

 The relationship between wood density (WD) and annual mortality rates for individual species (black points) from 10 forest census plots across the tropics, as described by Model 1. The solid line indicates the average family relationship as described by the site-wide slope α and intercept β; lines curve because the y-axis has been log-transformed for presentation. Dashed lines denote ± 2σ (within-family error) around the average family relationship. The shaded area indicates the 95% confidence interval in the model, reflecting variation both within and across families. At some sites the shaded area contracts around the global mean wood density (0.58 g cm−3), reflecting the fact that data were centered on this value before analysis. An asterisk (*) denotes plots where site-wide slope (α) 95% credible interval estimates do not overlap 0 (see Tables 1 and S4). Note that the intercept of the average family relationship at Sinharaja is strongly influenced by two species, each the sole representative of their family (Melastomataceae and Vitaceae), with elevated mortality rates relative to the rest of the plot.

Model 2: family-based analyses

To address our second question about the role of family-level variation, we ran a second model that grouped species across sites by family. We then conducted a similar analysis for each family as we had done for each plot in Model 1, but Model 2 did not have the site-wide parameter portion of the model. Each family j was analyzed separately. The census data level of the model remains the same, but the family level was simplified to estimate a single slope (aj), intercept (bj′) and residual error (σj). In cases where species occurred at multiple sites, only the data from the site with the most individuals were included, although our main conclusions were insensitive to including these extra observations (results not shown). We chose to restrict our analyses to families with 15 or more species in the data set.

Phylogenetic analyses

As a last step, we explored the phylogenetic component of the relationship between wood density and mortality in two ways. First, we tested the degree of phylogenetic conservatism (Lord et al., 1995; Blomberg et al., 2003) of wood density and estimated mortality rates using the Analysis of Traits (AOT) routine in the program phylocom (Webb et al., 2008). In order to do this, we created a phylogenetic tree of all taxa using phylomatic (Webb & Donoghue, 2005) and the angiosperm phylogeny R20050610 (archived at Unresolved relationships between genera within families and species within genera were treated as polytomies. We used log-transformed estimates of mortality from Model 1, and averaged mortality rates across sites for species that occurred in multiple locations. Secondly, to control for phylogenetic nonindependence, we tested for a pan-tropical relationship between wood density and mortality with a phylogenetic independent contrasts (PICs) analysis of all taxa in the study (Felsenstein, 1985; Garland et al., 1992), again implemented in the AOT module of phylocom (Webb et al., 2008).


Mortality rates declined with increasing wood density at five of the 10 sites in our study (Figs 1 and 2), where the 95% credible interval (CI) of the plot-wide slope (α) was < 0 (Table 1). Almost all of the individual families at these five sites (95–100%) had negative slope parameter (aj) estimates (Fig. 3). Four sites (Edoro and Lenda in the Democratic Republic of Congo, Sinharaja in Sri Lanka, and La Planada in Colombia) had negative plot-wide slope (α) estimates, but the 95% CI included 0. At these four sites the majority of families (52–100%) had negative slopes (Fig. 3). One site (Mudumalai, India) had a positive plot-wide slope with a 95% CI including 0 (Table 1). The slope of the relationship was indistinguishable among the five sites with clear negative relationships (all slope 95% CIs for α overlapped; Table 1, Fig. 2a), although these sites did differ in the plot-wide intercept (β) of the relationship (Table 1, Fig. 2b). Specifically, BCI (Panama) and HKK (Thailand) had higher intercepts (corresponding to higher mortality rates at the global mean wood density) than Lambir (Malaysia), Pasoh (Malaysia), and Yasuní (Ecuador) (Table 1, Fig. 2b). These main results were also seen in an alternative version of the model operating on log-transformed mortality rates (Table S5 and Fig. S2).

Figure 2.

 A comparison of the fitted hyperdistributions of family slopes (a) and intercepts (b) of the relationship between wood density and mortality rates from the 10 forest plots in our study, as described by Model 1. Gaussian curves are plotted using the slope mean and standard deviation (α and SDα) in (a) and the intercept mean and standard deviation (β and SDβ) in (b). The area underneath each normalized curve sums to 1. Intercepts have been converted to a normal scale for presentation. Dashed lines indicate a slope or intercept of 0. Labels are placed at the same height as the apex of each distribution. Broader distributions indicate a greater family-to-family variation in the relationship at a given site. In (a), forests with slope hyperdistribution means (α) with 95% credible intervals that did not include 0 are plotted and labeled in black; those that did include 0 are plotted and labeled in gray. Note that the credible intervals themselves are not depicted in the figure – see Table 1.

Table 1.   Site-wide parameter estimates and measures of goodness-of-fit (Bayesian R2) for the relationship between wood density and mortality at 10 sites as described in Model 1
SiteCountryYearαSDαβSDβCovα,βσBayesian R2
  1. Site-wide parameters include the mean (α) and standard deviation (SDα) of the family slopes, the mean (β) and standard deviation (SDβ) of the family intercepts (converted to a normal scale for presentation here), and the covariance (Covα,β) between slope and intercept. The parameter σ describes the residual error in log annual mortality rates about each family’s relationship. Parameters were estimated using the longest interval of survival data available at each site. Values are the mean of the posterior distributions for each parameter, estimated using Metropolis–Hastings algorithms in a Bayesian hierarchical model. The 95% credible interval for each parameter’s distribution is given in parentheses. Slopes (aj) and intercepts (bj) for individual families within plots are shown in Supporting Information Table S4.

Barro Colorado Island (BCI)Panama1982–2005−0.041 (−0.068 to −0.016)0.034 (0.012 to 0.067)0.0512 (0.047 to 0.0578)0.0056 (0.0017 to 0.014)0 (−0.004 to 0.003)0.698 (0.604 to 0.807)0.14
Huai Kha Kaeng (HKK)Thailand1993–1999−0.034 (−0.067 to 0)0.045 (0.016 to 0.086)0.0488 (0.0428 to 0.0583)0.0084 (0.0024 to 0.0217)0 (−0.007 to 0.006)0.735 (0.606 to 0.888)0.20
Ituri-EdoroDemocratic Republic of Congo1994–2000−0.01 (−0.042 to 0.025)0.046 (0.013 to 0.092)0.0255 (0.018 to 0.0454)0.0115 (0.0018 to 0.053)−0.003 (−0.022 to 0.011)0.761 (0.561 to 0.992)0.39
Ituri-LendaDemocratic Republic of Congo1994–2000−0.015 (−0.048 to 0.016)0.043 (0.01 to 0.102)0.0303 (0.0203 to 0.06)0.0192 (0.0043 to 0.0996)−0.004 (−0.026 to 0.013)0.651 (0.458 to 0.869)0.56
La PlanadaColombia1997–2003−0.046 (−0.102 to 0.003)0.065 (0.018 to 0.135)0.0532 (0.0399 to 0.0979)0.0233 (0.0048 to 0.1558)0.002 (−0.031 to 0.038)0.661 (0.507 to 0.862)0.46
LambirMalaysia1992–1997−0.02 (−0.032 to −0.009)0.026 (0.015 to 0.04)0.0267 (0.0246 to 0.0298)0.0048 (0.0026 to 0.0089)−0.001 (−0.004 to 0.002)0.544 (0.488 to 0.603)0.39
MudumalaiIndia1988–20000.006 (−0.096 to 0.114)0.113 (0.029 to 0.282)0.0373 (0.0163 to 0.1331)0.0306 (0.0041 to 0.3219)0 (−0.065 to 0.069)1.026 (0.749 to 1.379)0.26
PasohMalaysia1987–2000−0.021 (−0.03 to −0.012)0.018 (0.01 to 0.028)0.029 (0.0269 to 0.0319)0.0054 (0.0033 to 0.009)−0.001 (−0.003 to 0.001)0.417 (0.378 to 0.46)0.44
SinharajaSri Lanka1995–2001−0.003 (−0.062 to 0.043)0.061 (0.015 to 0.141)0.0322 (0.0107 to 0.1781)0.0538 (0.0061 to 1.1745)−0.007 (−0.067 to 0.044)0.356 (0.061 to 0.811)0.83
YasuniEcuador1996–2003−0.022 (−0.032 to −0.011)0.017 (0.007 to 0.032)0.0293 (0.0258 to 0.035)0.0077 (0.0037 to 0.0162)−0.001 (−0.005 to 0.002)0.637 (0.564 to 0.718)0.39
Figure 3.

 Summary of family-to-family variation in the slope of the wood density–mortality relationship across 10 different forest plots, as described by Model 1. Histograms of the family-level slope (aj) estimate for families with four or more species at the site are shown as filled bars; additional families with fewer species are shown as open bars. The fitted hyperdistribution of family slopes (see Fig. 2a), described by α and SDα, is traced above each histogram, and a slope of 0 is indicated by the dashed line. Note that the scale of the y-axis differs across panels. The proportion of families with negative slope (aj) estimates is indicated underneath the site label for each panel. Note that at three sites (La Planada, Edoro and Lenda) the majority of families were estimated as having negative slopes (aj), even though the credible interval on the mean of the hyperdistribution of slopes (α) included 0 (see Table 1).

Site-based Model 1 explained an average of 40% of the variation in mortality rates across all sites (Bayesian R2; Table 1), ranging from 13% at BCI to 83% at Sinharaja. Several of the sites with weak plot-wide relationships (α CI estimates include 0) had high Bayesian R2 values relative to other sites (e.g. Sinharaja). If just the five sites with a clear site-wide negative relationship are considered, the average Bayesian R2 is lower (0.31).

The three sites with multiple censuses exhibited noticeable variation in the wood density–mortality relationship among sample intervals (Table S2). For example, the goodness of fit (Bayesian R2) at BCI was the highest in our study in the initial 1982–1985 census interval (0.32), which corresponds to a period of elevated mortality associated with the severe 1983 El Niño-driven drought (Condit et al., 1995), but declined steadily in subsequent censuses to 0.22 in the most recent (2000–2005) interval (Table S2). The slopes did not show a clear trend across intervals. In contrast, the relationship between wood density and mortality at Pasoh became more strongly negative (lower α estimates) over the three census intervals in our data set. Restricting our analysis to trees of ≥ 100 mm dbh produced comparable estimates of the relationship between wood density and mortality (Table S3), albeit with larger credible intervals on some parameters, which is not surprising given the smaller number of species and individuals present in this reduced sample.

When we grouped species by family instead of site in Model 2, we found considerable variation in the relationship between wood density and mortality. Ten of the 27 most species-rich families in our study (with ≥ 15 species) had a negative relationship (aj 95% CIs < 0), with Euphorbiaceae and Melastomataceae having the most negative slopes. Two families (Ebenaceae and Combretaceae) had a moderately positive slope (Figs 4 and S1; Table 2) and one (Myrtaceae) had a flat slope. The remaining 14 families had negative estimated slopes with a CI including 0 (Table 2). The average Bayesian R2 across families was 13%.

Figure 4.

 Examples of the variation in the relationship between wood density and mortality for species in four families (black points), as estimated by Model 2. Gray points represent the entire global data set. The solid line indicates the family relationship as described by the slope (aj) and intercept (bj) parameters; dashed lines indicate the 95% confidence interval of the model, reflecting within-family variation (σ). Lines curve because the y-axis has been log-transformed for presentation. An asterisk (*) denotes families where slope (aj) 95% credible interval estimates do not overlap 0 (see Tables 2). For additional families see plots in Supporting Information Fig. S1 and parameter estimates in Table 2.

Table 2.   Parameter estimates, species per family (N) and measures of goodness-of-fit (Bayesian R2) for the relationship between wood density and mortality rates for species grouped by families across 10 tropical forest sites, as described by Model 2
OrderFamilyNabσBayesian R2Slope group
  1. Only families with ≥ 15 species are presented here. We estimated the slope (a), intercept (b) and standard deviation of the logarithm of annual mortality rates (σ) using Metropolis–Hastings algorithms in a Bayesian hierarchical model. Values are the mean of the posterior distributions for each parameter with the 95% credible interval (CI) for each parameter’s distribution shown in parentheses. Families with nonzero overlapping slope CIs are grouped by letters; an n.s. in this column indicates that the slope CIs include 0.

EricalesEbenaceae340.014 (0.029 to 0)−0.0004 (0.0014 to −0.002)0.341 (0.509 to 0.219)0.14n.s.
Lecythidaceae18−0.005 (0.019 to −0.028)0.0117 (0.0166 to 0.0082)0.617 (1.105 to 0.306)0.10n.s.
Sapotaceae68−0.002 (0.01 to −0.014)0.0103 (0.0125 to 0.0084)0.452 (0.596 to 0.336)0.01n.s.
FabalesFabaceae138−0.024 (−0.005 to −0.043)0.0322 (0.0355 to 0.0292)0.828 (0.962 to 0.711)0.05a,b
GentianalesApocynaceae21−0.027 (−0.003 to −0.053)0.0273 (0.0315 to 0.0242)0.355 (0.721 to 0.046)0.49a,b
Rubiaceae52−0.01 (0.027 to −0.046)0.0244 (0.0293 to 0.0201)0.68 (0.88 to 0.523)0.00n.s.
LamialesBignoniaceae16−0.028 (0.026 to −0.082)0.0378 (0.0543 to 0.0275)0.973 (1.65 to 0.596)0.14n.s.
Lamiaceae19−0.03 (0.029 to −0.078)0.0368 (0.0503 to 0.0288)0.842 (1.466 to 0.426)0.14n.s.
LauralesLauraceae95−0.032 (−0.02 to −0.04)0.0353 (0.0373 to 0.0335)0.44 (0.542 to 0.353)0.29a,b
MagnolialesAnnonaceae54−0.017 (0.003 to −0.036)0.0251 (0.0283 to 0.0222)0.68 (0.851 to 0.539)0.05n.s.
Myristicaceae43−0.006 (0.015 to −0.024)0.0158 (0.0183 to 0.0137)0.428 (0.58 to 0.31)0.00n.s.
MalpighialesChrysobalanaceae19−0.044 (0.002 to −0.09)0.0494 (0.0609 to 0.0394)0.509 (0.827 to 0.303)0.21n.s.
Clusiaceae42−0.035 (0.005 to −0.069)0.0411 (0.0483 to 0.0353)0.845 (1.118 to 0.643)0.08n.s.
Euphorbiaceae61−0.093 (−0.064 to −0.123)0.0789 (0.0847 to 0.0739)0.792 (0.986 to 0.638)0.39a,c
Phyllanthaceae44−0.03 (0.022 to −0.082)0.0395 (0.0466 to 0.034)0.656 (0.876 to 0.487)0.03n.s.
Salicaceae27−0.038 (0.079 to −0.157)0.0525 (0.0679 to 0.041)0.728 (1.057 to 0.496)−0.01n.s.
MalvalesDipterocarpaceae89−0.034 (−0.016 to −0.053)0.039 (0.0421 to 0.0363)0.613 (0.743 to 0.506)0.16a,b
Malvaceae77−0.029 (−0.005 to −0.051)0.0302 (0.034 to 0.0272)0.845 (1.036 to 0.691)0.09a,b
MyrtalesCombretaceae170.015 (0.071 to −0.035)0.0022 (0.0114 to −0.004)0.659 (1.174 to 0.359)0.05n.s.
Melastomataceae26−0.106 (−0.009 to −0.204)0.1128 (0.1408 to 0.0935)1.046 (1.467 to 0.755)0.18a,b,c
Myrtaceae380 (0.023 to −0.024)0.0131 (0.0168 to 0.01)0.358 (0.518 to 0.239)−0.01n.s.
OxalidalesElaeocarpaceae15−0.033 (0.031 to −0.075)0.0381 (0.0494 to 0.0307)0.739 (1.326 to 0.399)0.19n.s.
RosalesMoraceae105−0.045 (−0.029 to −0.058)0.0442 (0.048 to 0.0409)0.833 (1.013 to 0.68)0.22a,b
SapindalesAnacardiaceae37−0.015 (0.006 to −0.032)0.0213 (0.025 to 0.0184)0.623 (0.875 to 0.441)0.07n.s.
Burseraceae60−0.018 (−0.001 to −0.034)0.0237 (0.0253 to 0.0221)0.391 (0.503 to 0.302)0.11a,b
Meliaceae95−0.017 (0.008 to −0.042)0.0274 (0.0306 to 0.0246)0.631 (0.765 to 0.522)0.03n.s.
Sapindaceae36−0.06 (−0.026 to −0.097)0.0605 (0.0683 to 0.0543)0.604 (0.888 to 0.403)0.32a,b,c

Our phylogenetic analyses found strong phylogenetic conservatism of both wood density (phylocom AOT test, P = 0.001) and mortality rate constants (P = 0.001). The analysis of phylogenetic independent contrasts (PICs) revealed that the pan-tropical relationship between wood density and mortality remained significantly negative after accounting for phylogenetic relationships (phylocom PICS test: 447 contrasts, 168 positive, sign test P < 0.0001, correlation coefficient of contrasts = −0.295).


Our results show that there is support across the tropics for a negative relationship between wood density and annual mortality rates within forest communities (Figs 1–3). An average of 31% of the variation in mortality at a site with a negative relationship can be explained by variation in wood density (Table 1). In addition to the five sites with significantly negative plot-wide slopes, four sites exhibited negative trends with CIs on the slope that included 0. Within these four sites the majority of individual families had negative relationships (Fig. 3). It should be noted that there was a geographic pattern to the strength of the relationship; the patterns were strongest at sites in South America and Southeast Asia, intermediate in Africa, and weakest on the Indian subcontinent (Fig. 1). This variation may be attributable to differences in sample size among sites that mirrored these trends (Table S1, although the correlation between richness and plot-wide slope or richness and Bayesian R2 was not significant), or to real differences in mortality agents and mechanisms across forests. For example, the biggest outlier in our study, Mudumalai in India (Fig. 1), has a set of mortality agents that is unique relative to other sites in our study, including frequent fires that disproportionately kill small trees (Sukumar et al., 1998) and a very high density of large browsing mammals such as the Asian elephant (Sukumar et al., 2004). The sites in our study vary in climatic conditions such as mean annual rainfall and length of dry season (Losos & Leigh, 2004), and, while there was no significant relationship between these attributes and the slope or Bayesian R2 values from Model 1 (linear regression, P > 0.05), it would be valuable to re-examine this relationship as data from more sites become available.

While there are some obvious limitations (see discussion in Materials and Methods) to grouping species into families within sites and allowing families to vary, as we did in Model 1, we would argue that the limitations are outweighed by our ability to include some evolutionary information in our estimation of the relationship between wood density and mortality at individual sites. It is important to note that our model was free to estimate that individual family distinctions were unimportant; were this the case, the distribution of family slopes and intercepts within a site would have no variance (SDα2 and SDβ2 would be estimated as 0). This was not the case in our results – Model 1 estimated a range of family relationships within plots (e.g. Figs 2 and 3), and many families had slope (aj) or intercept (bj) estimates that differed from the overall plot slope (α) and intercept (β) estimates (Tables 1 and S4). Simplifying Model 1 to remove family effects entirely did not significantly alter the plot-wide results presented here (results not shown).


The relationship that we observed may occur because wood density is an indicator of features of the stem that reduced mortality risk, or because wood density is a correlate of other traits beyond the stem itself that impact mortality rates. Several lines of evidence support the former, more direct connection. Species with dense wood are thought to have reduced vulnerability to the mortality agents of drought-induced embolism (Hacke et al., 2001; Jacobsen et al., 2005), pathogen attack (Augspurger & Kelly, 1984), and mechanical breakage (Niklas, 1992). In tropical forests, wood density is often relatively uncorrelated with other key functional traits such as leaf economics traits and seed size (with the exception of leaf size; see Wright et al., 2007; Kraft et al., 2008), further suggesting a direct, mechanistic connection between wood density and mortality.

The negative relationship between wood density and tree mortality may occur as a result of different constraints operating on opposing corners of the bivariate space defined by wood density and mortality. That species do not have both low wood density and low mortality rates (Figs 1 and 4) may result from the increased susceptibility light-wooded species have to a range of mortality agents, as outlined in the preceding paragraph. In contrast, the lack of species demonstrating both high wood density and high mortality rates may reflect a physiological constraint; dense wood is expensive (in terms of carbon) to construct. Species with a high mortality rate, and therefore a short life, would have little time to accumulate the carbon to invest in the construction of dense wood, and would do so at the expense of allocating resources to reproduction or other strategies to offset the fitness costs of high mortality.

Evolutionary history

The relationship between wood density and mortality that we observed at the plot level (Table 1) was generally more consistent than the within-family relationships (Table 2). Some families exhibited strong negative relationships that mirrored our plot-level results (e.g. Euphorbiaceae and Fabaceae), and many exhibited a weak negative relationship (e.g. Annonaceae and Clusiaceae). However, in certain families mortality is apparently insensitive to variation in wood density (e.g. Myrtaceae and Sapotaceae). This result is also reflected in the fact that the hyperdistribution of family slopes for each site from Model 1 crosses zero (Fig. 2), indicating that our model estimated that there are families at each site (whether or not they were measured in our data set) that do have a flat or moderately positive relationship between wood density and mortality. The lack of relationship within certain families may result from higher within-family susceptibility to mortality agents that are unrelated to wood density (e.g. herbivory pressure), from low within-family variation in wood density (e.g. Salicaceae), or from consistently low mortality rates across the family. For example, both Myrtaceae and Sapotaceae are composed of species with relatively high wood density and generally low mortality rates that may be attributable in part to additional investment in defenses (cytotoxic organic compounds in Myrtaceae and latex borne in phloem canals in Sapotaceae; McNair, 1932; Regnault-Roger, 1997; Smith et al., 2004). A lack of a relationship may also be attributable to poor statistical power resulting from low within-family species sampling; however, the fact that some of the most species-rich families (e.g. Sapotaceae) had slopes that were indistinguishable from 0 suggests that power was not the culprit in all cases. Further, we would not expect to see the observed variation in the family-level parameter estimates in the plot-wide analyses (Fig. 3) if variation in sample size was the sole cause of variation among families. Rather, family-level estimates would collapse to the side-wide mean estimate, and variation attributable to sample size would be accounted for elsewhere.

Finally, it should be noted that many families occupied a distinct and relatively restricted portion of the bivariate space defined by wood density and mortality (Figs 4 and S1), a pattern that is consistent with the high degree of phylogenetic conservatism that we detected for both traits. Taken together, our family-level analysis suggests that the consistent negative relationship we observed within communities results from two related but distinct family-level components: negative wood density–mortality relationships within many families, and turnover across families where mortality varies little with wood density.

Future directions

As plant ecology moves toward an increasing emphasis on functional traits, there is a growing need to solidify our understanding of connections between traits and variation in plant performance. Our results indicate that wood density is a functional trait that is well worth considering in studies focused on life history strategies, even though wood density was not a component of some early plant strategy schema (e.g. Westoby, 1998). Collecting wood density data may require increased effort relative to other commonly measured functional traits (Cornelissen et al., 2003; Williamson & Wiemann, 2010), but these data are correlated with substantial variation in demographic rates among species.

Here we have outlined a straightforward application of a hierarchical Bayesian approach to a relatively focused question at the intersection of functional ecology and demography. As additional trait and demographic data become available, this type of analysis can easily be applied to them separately or in a multivariate context. It remains to be seen whether other commonly measured functional traits are as strongly related to mortality as wood density, although several analyses with multiple traits suggest that wood density may be a better predictor than many other traits (Poorter et al., 2008; Wright et al., In press). Large geographic-scale analyses will play an important role in efforts to characterize strategy variation among plant species.


N.J.B.K. acknowledges funding from the NSERC CREATE Training Program in Biodiversity Research. This manuscript was improved by discussion and suggestions from D. Ackerly, B. Choat, W. Cornwell, P. Cowan, S. Kembel, D. King, L. Poorter, K. Simonin, E. Sudderth, A. Zanne and one anonymous reviewer. N. Swenson generously contributed unpublished wood density data. We are grateful for the efforts of everyone who has contributed to the forest census plots associated with the Center for Tropical Forest Science of the Smithsonian Tropical Research Institute, as well as to people of the countries in which the plots are located for permitting this ongoing research.