For cases in which total tree height is unavailable, we developed a diameter-height allometric equation of the form of Eq. (3). Using forward selection (see Methods), we found that among-site variation in diameter-height allometries was best explained by TS (temperature seasonality), CWD (climatic water deficit), and PS (precipitation seasonality), with only small further declines in model RSE with the sequential inclusion of additional bioclimatic variables (Fig. S5). We thus propose the following pantropical diameter-height allometric model (6a) (AIC=47, RSE=0.243, df=3998), where E is defined as (6b) Formula (6b) has an intuitive interpretation. E is a measure of environmental stress. Indeed, E increases with temperature seasonality, which relates to the amount of time a plant is exposed to stressful temperature, and CWD (a negative quantity) increases in magnitude with increasing annualized water stress. The dependence of E on PS (precipitation seasonality) is less obvious but appears to be mostly driven by monsoon-dominated rainfall regime (Nemani et al. 2003). The dependence of diameter-height allometry on E is illustrated in Fig. 4. A global gridded layer of E at 2.5 arc-second resolution is available at Equation (6a) predicts that the log-transform of tree height for a given diameter declines with both water and temperature stress. We also verified that the functional form of Eq. (3) is biologically consistent: for all E, the quadratic function in ln(D) reaches a maximum at a value that far exceeds biologically realistic values for D. Combining Eqs. (4) and (6a) directly, AGB can be inferred in the absence of height measurements (RSE=0.431, df=3999). Here, we prefer to fit the data directly, yielding the following model: (7)
hydraulics in regulating the height of trees at a given trunk diameter (see also Kempes et al. 2011). Recently, Feldpausch et al. (2011) conducted a pantropical analysis of diameter-height tree allometries and concluded that regional variation in this allometry was an important source of variation in tree AGB. They then developed a set of region-specific diameter-height allometries to minimize bias due to the variation in canopy height across tropical forest regions (see also Banin et al., 2012). They investigated whether some of the climatic variables in the WorldClim database may predict a significant fraction of the variation in the relationship. For a given trunk diameter, they found a positive correlation between tree height and precipitation seasonality only. Their finding is counter-intuitive because height should peak at intermediate precipitation seasonality values, and be lower in both dry and ever-wet forests (see e.g. Hall & Swaine, 1981, Fig. 5.1; Wang et al., 2006). This is probably because the Feldpausch et al. (2011) database did not include many dry-vegetation sites. Here, we readdressed the question of the bioclimatic dependency of the relationship in tropical trees. Our dataset had only a limited overlap with that used in Feldpausch et al. (2011) and Banin et al. (2012), and we found different results. Our major finding is that the diameter-height relationship depends linearly on a compound bioclimatic variable E, which itself is a linear function of climatic water deficit, temperature seasonality, and precipitation seasonality. Indeed, we found that a large fraction of the residual variation in the diameter-height relationship is attributable to the variable E, and that a single model (Eq. 6) may be used to predict total tree height from trunk diameter and E across the tropics.