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Forests function as the main sinks and reservoirs of terrestrial carbon as well as providers of several environmental services (Hui et al. 2016). Global increases in atmospheric carbon dioxide and their effect on climate are driving a growing interest in quantifying forest carbon storage (Pan et al. 2011). Tropical forests contain almost 55 % of the carbon stored in terrestrial vegetation but experience high rates of deforestation and degradation (Hui et al. 2016) which are estimated to cause 6-20 % of anthropogenic greenhouse gas emissions (Dixon et al. 1994, Pan et al. 2011, Baccini et al. 2012, Le Quéré et al. 2015). This releases the carbon that was stored to the atmosphere, transforming the vegetation from a carbon sink into a carbon source. Understanding the magnitude of the greenhouse gas emissions associated with these processes requires accurate quantifications of tropical forest biomass and emission factors (Chaplin-Kramer et al. 2015).
Precise estimation of tropical forest biomass is vital for commercial lumber production and for understanding and modeling the global carbon cycle. The vast majority of the world’s nations are committed to provide periodic reports on the condition of their forest resources and on forest emissions and absorptions of green-house gases under the United Nations Framework Convention on Climate Change (UNFCCC 2007). In addition, implementation of climate-change mitigation mechanisms such as the Reduction of Emissions from Deforestation and Degradation (REDD+) requires accurate data on forest carbon reservoirs and emission factors (Angelsen et al. 2012). Secondary tropical forests re-growing after abandonment of agricultural lands currently account for over half of the tropical forest area worldwide (FAO 2010) and are increasingly recognized as playing an important role in the global carbon cycle (Poorter et al. 2016, Chazdon et al. 2016), yet no global estimates of the carbon stock in secondary tropical forests are currently available (Bongers et al. 2015).
Most forest biomass studies focus on above-ground biomass (AGB) since it is relatively easy to estimate, monitor and tie in to remote sensing data (Timothy et al. 2016). However, efforts to quantify AGB and the carbon stored therein in tropical forests have been plagued by uncertainty. For example, estimates made for tropical forests in Africa vary by more than 100 % and in the Amazonian rainforest may vary by up to 60 % (Baccini et al. 2012).
Accurately estimating AGB involves choosing an appropriate biomass allometric model. Allometry allows prediction of one tree measurement (e.g., AGB) as a function of another (e.g., diameter) (Gayon 2000, Picard et al. 2012) which can be further improved by including height and wood density in the models (Chave et al. 2005, Návar-Cháidez et al. 2013, Ramírez-Ramírez et al. 2017). The errors associated with AGB estimation such as the uncertainty inherent in inferring individual tree height without direct and exact measurements should also be reported (Chave et al. 2004, Molto et al. 2013, Chen et al. 2015, Mermoz et al. 2015). Empirical models of AGB estimation have been proposed for a whole region (Feldpausch et al. 2012) or even a biome (Chave et al. 2014). However, local-level allometric studies that evaluate tree height-diameter relationships (H-D) can provide better estimates than regional or global models because tree growth and competition between individuals can vary under different biotic and abiotic conditions (Feldpausch et al. 2012). Yet, locally-developed allometric models are not always validated in secondary forests, which can differ in forest structure and composition from old-growth forests (Stas et al. 2017).
Moreover, resource allocation to different tree parameters (i.e., diameter, height, crown- and/or root cover) can change during tree growth in response to changes in resource availability and environmental and biotic conditions (Weiner 2004) and vary as a function of tree size. For instance, small trees may assign more resources to growth in height in order to reduce the risk of suppression by competitors. Once a height has been reached at which suppression is a minimal risk, resources may be assigned to horizontal growth (diameter, crown and root cover) to guarantee greater stability and resource access. In other words, the allometry of forest trees can change as a function of size (Weiner 2004), implying that different allometric models may be needed for small vs large trees and for young secondary-growth vs older forest stands.
The objectives of the present study were threefold: 1) to develop general allometric equations of AGB for a seasonally dry secondary tropical forest in Yucatán, Mexico; 2) evaluate if the allometric relationship of AGB to tree diameter and/or height changes with tree size; 3) evaluate if the combined use of different general allometric equations (for different tree-size categories) produces more accurate estimations of AGB than one general equation that assumes a single allometric relationship.
Materials and methods
Study area. The study was conducted in the “Ejido” (communally-owned land) San Agustín, in the municipalities of Oxkutzcab and Tekax, in the southern portion of the state of Yucatán, Mexico (19° 58’ 43” N; 89° 29’ 18” W) in July 2016. The landscape consists of rolling, low-elevation (60-190 m asl) hills and enclosed plains (Flores-Guido & Espejel-Carvajal 1994). Climate is warm sub-humid (Aw1 in the Köppen classification as modified by García 1973) with summer rain (May-October) and a marked dry season (November-April). Annual mean temperature is 26 °C, and annual mean precipitation ranges from 1,000 to 1,100 mm (Dupuy et al. 2012). Vegetation type is seasonally dry tropical forest (50 to 75 % of the trees shed their leaves during the dry season). Mean canopy height varies from 10 to 15 m, although species such as Vitex gaumeri Greem and Caesalpinia mollis (Kunth) Spreng can reach up to 18 m in height (López-Martínez et al. 2013). Virtually all forests in the study region are secondary, but differ in successional age, following abandonment of traditional slash-and-burn agriculture, practiced from pre-Columbian Mayas to current inhabitants (Barrera-Bassols & Toledo 2005). Soils vary depending on topographic conditions: shallow Leptosols predominate on the hills while deeper Luvisols and Cambisols are found in the plains (Bautista et al. 2015).
Established in 1968, the San Agustín Ejido encompasses 34,506 ha, of which 7,127 ha are subject to hydrological services incentive payments, 2,254 ha are under timber exploitation, and 92 ha are human settlement. Constructing allometric equations of AGB requires destructive sampling of trees in order to obtain precise measurements of AGB that can subsequently be related to other more easily obtained dasometric measures (e.g., diameter, height). Tree felling for this study was done with the permission of ejido members in the timber exploitation area (Figure 1).
Figure 1 Location of the Timber Exploitation Area, San Agustín Ejido, Yucatán, México, where trees were harvested to construct allometric equations of above ground biomass. Source: Mexico REDD+ Alliance, 2016.
Tree sampling. Since the aim of this study was to develop general allometric equation(s) of AGB for the secondary tropical dry forests of San Agustín, we used data from three 1 ha conglomerates (four 400 m2 plots each) in ≥ 50 year-old secondary forest stands from a community forest inventory (Dupuy, unpublished data), following the National Forest and Soils Inventory protocol (CONAFOR 2013) to identify the dominant tree species in the studied area. Tree species were sorted by decreasing value of total AGB estimated from these conglomerates following the methodology of Hernández-Stefanoni et al. (2014), and the top 25 species that accounted for 95 % of total AGB were identified. To ensure representativeness of landscape conditions, trees were sampled both on plains and on hills, covering a total area of approximately 0.2 ha. At the request of ejido members, sampling of trees > 10 cm DBH was also done along the main road -at a distance of 10 m or more from the road to minimize edge effects. The entire sampling area consisted of 60-70 years-old secondary forests following abandonment of traditional slash-and-burn agriculture, where large-sized trees can be found. The following tree selection criteria were used: 1) belongs to a dominant species (i.e., one of the top 25 species that account for 95 % of AGB); 2) encompasses the widest possible range of DBH found in the sampling area; 3) has a straight minimally branched trunk; and 4) has permission to fell granted by ejido members.
A total of 47 trees (DBH = 2.5-41.5 cm) from 18 species were sampled (Table 1). This is just under the minimum sample size of n = 50 recommended by previous studies to construct accurate AGB allometric models (Chave et al. 2004, van Breugel et al. 2011, Picard et al. 2012), but it is the most that our human and funding resources, as well as permission of ejido members, allowed. Diameter at breast height (DBH) was measured at 1.3 m above ground level before felling, and tree height (H) was measured after felling. The trunk and main branches were divided into 1-1.5 m sections; all trunk sections, branches and leaves were weighed in the field, and samples were taken of each section and component: stems (10-15 cm pieces), branches (20-25 cm pieces) and leaves (ca 1 kg samples). All samples were dried at 70 °C to constant weight. The dry weight/fresh weight ratio was used to estimate total biomass for each individual (adding all components and sections), based on the total fresh weight measured in the field.
Table 1 Characteristics of tree species sampled with the destructive method. No. Indiv. = number of individuals; DBH = (range of) diameter at breast height (1.3 m); AGB = (range of) above ground biomass values measured in this study. Ref. wood density = reference for wood density value.
| Scientific name | No. Indiv. | DBH (cm) |
Height (m) |
Wood density (g/cm3) |
Ref. wood density |
AGB (kg) |
|---|---|---|---|---|---|---|
| Bunchosia swartziana Griseb. | 1 | 2.9 | 4.6 | 0.58 | 1* | 1.83 |
| Bursera simaruba (L.) Sarg. | 5 | 3.3 - 38.5 | 5 - 13.64 | 0.36 | 1* | 0.67 - 736.56 |
| Caesalpinia gaumeri (Britton & Rose) Greenm. | 2 | 6 - 6.1 | 6.9 - 7.95 | 0.9 | 1* | 6.58 - 9.04 |
| Coccoloba diversifolia Jacq. | 2 | 5.5 - 6.3 | 8.25 - 8.76 | 0.8 | 2* | 9.58 - 10.25 |
| Coccoloba spicata Lundell | 2 | 4.1 - 6 | 5.93 - 8.1 | 0.86 | 1* | 2.96 - 7.93 |
| Cochlospermun vitifolium (Willd.) Spreng. | 2 | 10.4 - 20 | 10.1 - 11.35 | 0.23 | 1* | 22.41 - 60.9 |
| Exostema caribaeum (Jacq.) Roem. & Schult. | 1 | 6.7 | 8.55 | 0.88 | 1* | 21.15 |
| Gymnopodium floribundum Rolfe. | 2 | 4 - 6.3 | 6 - 8.1 | 0.79 | 1* | 1.54 - 13.51 |
| Lonchocarpus rugosus Benth. | 1 | 6.6 | 10.5 | 0.95 | 1* | 15.65 |
| Lonchocarpus xuul Lundell | 7 | 3.3 - 11.3 | 5.86 - 13.2 | 0.82 | 1* | 2.48 - 119.2 |
| Lysiloma latisiliquum (L.) Benth. | 4 | 19.9 - 37.3 | 12.2 - 14.53 | 0.55 | 1* | 171.06 - 724.34 |
| Mimosa bahamensis Benth. | 2 | 5.4 - 6.5 | 7 - 7.31 | 0.71 | 1* | 11.81 - 17.24 |
| Melicoccus oliviformis Kunth ssp. oliviformis | 1 | 4.4 | 8.3 | 0.91 | 1* | 7.86 |
| Piscidia piscipula (L.) Sarg. | 6 | 4.7 - 41.5 | 4.7 - 12.99 | 0.78 | 1* | 2.64 - 545.31 |
| Platymiscium yucatanum Standl. | 2 | 27.6 - 28.5 | 13.25 13.55 | 0.9 | 1* | 608.38 - 777.88 |
| Psidium sartorianum (O. Berg) Nied. | 2 | 2.5 - 6.5 | 4.44 - 8.24 | 0.85 | 1* | 1.45 - 17.82 |
| Thouinia paucidentata Radlk. | 3 | 6 - 7.5 | 7 - 9.57 | 0.94 | 1* | 10.72 - 16.34 |
| Vitex gaumeri Greenm. | 2 | 17.3 - 38.5 | 11.28 - 14.43 | 0.65 | 1* | 106.29 - 563.91 |
Statistical analyses. Pairwise relationships between AGB, tree height and DBH were analyzed to assess changes in slope. We used segmented regression in R-studio implemented in the segmented package (Muggeo 2008), which consists of detecting an inflection or break point (bp) in the data and, where found, applying a different linear regression to each segment. Davies’ test was applied to identify inflection or break points and to test for significant differences in the slope of the segments (Muggeo 2008). The regression lines were fitted to the data by minimizing the sum of the squared differences (SSD) between the observed value (X i ) and the value calculated by regression (Y i ) of the dependent variable, using the following formulas:
Where
θ 1 and θ 2 are the regression coefficients indicating the slope of the lines in the respective segments. β 0 and β 1 are the intercepts of each segment, indicating the values of Y i when X i = 0.
Different allometric equations were then explored for the tree size categories identified with the segmented regressions. These took various functional forms, mainly logarithmic and power, based on common published models (Chave et al. 2005, Picard et al. 2012, Návar-Cháidez et al. 2013, Ramírez-Ramírez et al. 2017). After formally testing that the residuals of each regression equation met the assumptions of normality (Shapiro-Wilk’s test) and homoscedasticity (Breusch-Pagan’s test), the sign of the coefficients of the explanatory variables was verified because a positive relationship is expected between AGB and DBH, H and wood density (Pw), and their combinations (e.g., D2H). Data on Pw were obtained from previous studies in the region and from the literature (Table 1).
Following the methodologies proposed by Hernández-Stefanoni & Dupuy (2008), Segura & Andrade (2008), Fonseca et al. (2009), and Ramírez-Ramírez et al. (2017), selection of those equations with the best goodness of fit and lowest prediction error for each category followed two steps using R (R Core Team 2018):
i. Calculation of equation fit indicators: root mean square error (RMSE); Akaike’s Information Criterion (AIC); delta AIC (Δ); and Akaike weight (ω i ) (Caballero 2011). All equations with ω i < 0.1 and/or Δ > 2 were excluded (Hernández-Stefanoni & Dupuy 2008).
where:
k is the number of parameters and L is the likelihood function.
Delta AIC (Δ)
Akaike weight (ω i ):
ii. Cross-validation: following Hernández-Stefanoni et al. (2014), we used leave-one-out cross-validation, in which one datum is excluded at a time and the remaining data are used to generate the corresponding predicted value. This was done for all the data points such that, for each equation, one predicted value was generated for each observed value. A linear regression was then run using the observed and predicted values to select the best equation based on the coefficient of determination (R 2), the agreement coefficient (AC) and the root mean square error (RMSE).
The following is the formula for calculating the agreement coefficient (AC):
where
Xi are the observed values of AGB and Yi are the predicted values of AGB,
The equations thus developed for each tree size category were then combined to assess the accuracy of AGB estimation obtained with combinations of equations for the different tree size categories. First, the combination of the most accurate equation for each category was compared to the most accurate single equation developed for the same data set. Second, the most accurate equation developed in the present study was combined with the equations of Brown (1997), Chave et al. (2005) and Urquiza-Haas et al. (2007), all developed and/or validated, and used to estimate AGB in the forests of the Yucatan Peninsula. The most accurate combination was identified by comparing deviation measurements of the models: modelling efficiency (MEF); model coefficient of determination (CD); and coefficient of error (CE) (Medina-Peralta et al. 2010). The MEF statistic is equivalent to the Pearson’s correlation coefficient (r) and represents the proportion of the variation expressed by the line y = z; in a perfect fit both statistics would have a value of one (Tedeschi 2006, Medina-Peralta et al. 2010). Modelling efficiency (MEF) was calculated as follows:
Where yi
is the i-th observed value;
The coefficient of determination (CD) was calculated as follows:
It indicates the proportion of the total variation in the observed data that is explained by the predicted data (Loague & Green, 1991). A CD value near one indicates an accurate prediction by the model, CD < 1 indicates overestimation, and CD > 1 indicates underestimation (Tedeschi 2006).
The coefficient of error (CE) was calculated using this formula:
It is a measure of the average of the absolute differences and is expressed as a proportion of the mean of the observed values (Klepper & Rouse 1991, Medina-Peralta et al. 2010). A value for C very near zero indicates the model combination yields negligible estimation errors (Yang et al. 2000, Medina-Peralta et al. 2010).
Results
Allometric relationships between AGB, diameter and height. Diameter at breast height (DBH) of the 47 sampled trees averaged 12.67 cm (range = 2.5 - 41.5 cm), height (H) averaged 9.48 m (range = 4.44 - 14.53 m), and AGB averaged 134.25 kg (range = 0.67 - 777.88 kg), equivalent to 63.1 kg of carbon (range = 0.31 - 365.60 kg).
The segmented regression analysis indicated a continuous relationship (without segments) between AGB and DBH (Figure 2a), as well as between H and DBH (Figure 2c), and identified a discontinuity or segmentation in the relationship between H and AGB (Figure 2b). This analysis identified a break point at 12.18 m in H (corresponding to 9.95 cm in DBH), defining two tree size categories: category 1 containing 30 individuals with DBH between 2.5 and 9.95 cm, and category 2 containing 17 individuals with DBH ≥ 10 cm. Davies’ test confirmed that two equations with significantly different slopes should be applied to the AGB-H relationship (Table 2; Figure 2).
Figure 2 Segmented or linear regression analyses of tree above-ground biomass (AGB) vs diameter at breast height (DBH) (A), AGB vs height (H) (B), and height (H) vs DBH (C) in a seasonally dry tropical forest in Yucatán, México. *** = p < 0.001; NS = not significant.
Table 2 Slopes of the two equations for above-ground biomass (AGB) as a function of tree height (H) defined by segmented regression and Davies’ test.
| Description | Estimate | Std. Error | t value | Pr(> |t|) |
|---|---|---|---|---|
| Intercept | 3.018 | 1.072 | -2.815 | 0.007*** |
| logH | 2.702 | 0.579 | 4.664 | 3.02e-05*** |
| U1.logH | 4.215 | 1.132 | 3.722 | NS |
Allometric equations by diameter category. Three allometric equations that met methodological criteria were chosen for tree size category 1 (trees 2.5 - 9.95 cm DBH; Table 3). The best goodness of fit corresponded to equation 1: AGB = exp(-2.769+0.937ln(D2HPw) (R 2 adj = 0.85, AIC = 28.31, ωi = 0.847). This equation is based on an exponential relationship, considers a quadratic term for DBH and assumes a multiplicative relationship. The remaining equations were excluded because they had Akaike weight (ωi) values < 0.1 and/or a Δ AIC > 2 (Table 3). Equation 1 also provided the most accurate prediction according to the cross-validation analyses (R 2 adj = 0.708; AC = 0.671, indicative of a good agreement), as well as the lowest error (RMSE = 3.26 kg). This equation deviated little from the 1:1 relationship line between observed and predicted values, indicating that the estimation bias was negligible (Figure 3a).
Table 3 General allometric equations developed for tree size category 1 (2.5-9.95 cm in DBH) in a seasonally dry tropical forest in Yucatán, México; n = 30.
| No | Equation | R 2 adj | RMSE | AIC | Δ | ωi |
|---|---|---|---|---|---|---|
| 1 | AGB = exp(-2.769+0.937ln(D2HrPw)) | 0.85 | 1.42 | 28.31 | 0.00 | 0.847 |
| 2 | AGB = exp(-2.937+1.737ln(D)+1.133ln(Hr)+0.913ln(Pw)) | 0.84 | 1.42 | 32.14 | 3.83 | 0.125 |
| 3 | AGB = exp(-1.857+2.458ln(D)+1.029ln(Pw)) | 0.82 | 1.47 | 35.33 | 7.02 | 0.025 |
AGB= above-ground biomass (kg); D = tree diameter (cm); H = total tree height (m); Pw = wood density (g/cm3); R 2 adj = adjusted coefficient of determination; RMSE = root mean square error; AIC = Akaike information criterion; Δ = deltaAIC; ωi = Akaike weight.
Figure 3 Cross-validation analyses of equations 1 and 4 used to compare observed and predicted tree AGB (kg) values in a seasonally dry tropical forest in Yucatán, México. R 2 adj = adjusted coefficient of determination; AC = agreement coefficient; RMSE = root mean square error. The dashed line represents the 1:1 relationship between observed and predicted values. If the fitted line falls above the dashed line, the fitted model overestimates the observed value, and if the fitted line falls below the dashed line, the model underestimates it.
Three allometric equations (4 to 6) met the methodological criteria for tree size category 2 (trees ≥ 10 cm DBH). Equation 4 had the best fit (R 2 adj = 0.92, AIC= 15.67, ωi = 0.965), while the remaining equations were excluded because they had a Δ AIC > 2 and Akaike weight (ωi) values < 0.1 (Table 4). Equation 4 assumes an additive relationship and includes H even though the segmented regression indicated that this variable does not significantly explain biomass variation in this diameter category. The cross-validation analysis produced an AC value of 0.365 for equation 4, which is indicative of a weak agreement, meaning it has a poor predictive power. Moreover, the estimation error for this equation was very large (RMSE = 147.65 kg), and the fitted regression line deviated from the 1:1 relationship between predicted and observed values, indicating a bias in AGB estimation: slight overestimation for small trees and larger underestimation for large trees (Figure 3b).
Table 4 General allometric equations developed for tree size category 2 (≥10 cm in DBH) in a seasonally dry tropical forest in Yucatán, México; n = 17.
| No | Equation | R 2 adj | RMSE | AIC | Δ | ωi |
|---|---|---|---|---|---|---|
| 4 | AGB = exp(-9.171+1.591lnD+3.902lnHr+0.496lnPw) | 0.92 | 1.33 | 15.67 | 0.00 | 0.965 |
| 5 | AGB = exp(-1.113+2.223lnD+0.748lnPw) | 0.84 | 1.53 | 27.30 | 11.64 | 0.003 |
| 6 | AGB = exp(-4.063+1.079ln(D2Hr)) | 0.82 | 1.60 | 28.37 | 12.70 | 0.001 |
AGB = above-ground biomass (kg); D = tree diameter (cm); H = total tree height (m); Pw = wood density (g/cm3); R 2 adj = adjusted coefficient of determination; RMSE = root mean square error; AIC = Akaike information criterion; Δ = deltaAIC; ωi = Akaike weight.
Performance of equation combinations versus a single equation. The best single general equation developed using the whole data set (without separating tree-size categories) was AGB = exp (-3.073+1.024 ln(D2HPw). Cross validation analyses for this equation and for the combination of equations 1 and 4 clearly showed that the single equation had lower accuracy (R 2 = 0.68 versus R 2 = 0.84) and higher prediction error (RMSE = 127.77 kg versus RMSE = 92.33 kg) than the 1-4 equation combination (Table 5). Measures of deviation (MEF, CD and CE) confirmed the better performance of the 1-4 equation combination, compared to the best single equation.
Table 5 Measures of goodness of fit and deviation to evaluate allometric equations of tree AGB in a seasonally dry tropical forest in Yucatán, México.
| Equations | R 2 adj | RMSE | MEF | CD | C |
|---|---|---|---|---|---|
| Single Equation | 0.677 | 127.773 | 0.753 | 0.938 | 0.337 |
| Eq1-4 | 0.835 | 92.33 | 0.835 | 1.197 | 0.337 |
| Eq1-Bro | 0.784 | 105.71 | 0.784 | 1.275 | 0.432 |
| Eq1-Cha | 0.842 | 90.55 | 0.842 | 1.188 | 0.339 |
| Eq1-Urq | 0.813 | 98.55 | 0.812 | 1.231 | 0.342 |
Eq1-4: combination of equations 1 and 4; Eq1-Bro: combination of equations 1 and Brown (1997); Eq1-Cha: combination of equations 1 and Chave et al. (2005); Eq1-Urq: combination of equations 1 and Urquiza-Haas et al. (2007); RMSE = root mean square error; MEF: modeling efficiency; CD: equation coefficient of determination; CE: coefficient of error.
Comparison of combinations of local allometric equations to equations developed or used in the Yucatan Peninsula. The combination of equation 1 with that of Chave et al. (2005) showed slightly higher accuracy than the 1-4 equation combination (R 2 = 0.84 and R 2 = 0.83, respectively) and smaller prediction error (RMSE = 90.55 kg, and RMSE = 92.33 kg, respectively; Figure 4). However, the 1- Chave et al. (2005) equation combination greatly underestimated AGB, especially for large trees, as evidenced by the large deviation of the fitted regression line from the 1:1 relationship between predicted and observed values (Figure 4c). The combination of equation 1 with that of Urquiza-Haas et al. (2007) yielded slightly lower accuracy than the 1-4 equation combination (R 2 = 0.81 and R 2 = 0.83, respectively) and higher estimation error (RMSE = 98.55 kg, and RMSE = 92.33 kg, respectively). Moreover, compared to the 1-4 equation combination, the1- Urquiza-Haas et al. (2007) combination showed a slightly higher bias, with a tendency towards overestimating AGB, particularly for larger trees (Figure 5a, d). Although the 1- Brown (1997) equation combination showed the lowest accuracy (R 2 = 0.78) and highest prediction error (RMSE = 105.71 kg), it also showed the lowest prediction bias, as shown by the very small deviation of the fitted line from the 1:1 relationship (Figure 5b).
Figure 4 Cross-validation analysis comparing observed and predicted tree AGB (kg) values in a seasonally dry tropical forest in Yucatán, México, for the combination of equations 1 and 4 (A), and for the combinations of equation 1 with those of Brown 1997 (B), Chave et al. 2005 (C) and Urquiza-Haas et al. 2007 (D). R 2 adj = adjusted coefficient of determination, RMSE = root mean square error. The dashed line represents the 1:1 relationship between observed and predicted values. If the fitted line falls above the dashed line, the fitted model overestimates the observed value, and if the fitted line falls below the dashed line, the model underestimates it.
Discussion
Allometric relationships between AGB, diameter and height. Exploration of the allometric relationships between AGB, DBH and H for the sampled trees identified a discontinuity only in the AGB-H relationship, which suggests a change in tree allometry between AGB and H (Figure 2b). This highlights the importance of analyzing all relationships between the different measurements included in allometric equations. The discontinuity or change in the AGB-H relationship occurred at a height of 12.2 m, which corresponds to average canopy height in old-growth (≥ 50-year-old) forests in the study area (Dupuy et al. 2012). That the segmented regression identified two different segments or relationships between AGB and H, suggests a change in tree growth strategy as a function of height. In particular, the lower slope of the first segment indicates a small increase in AGB for any given increase in H in trees shorter than the inflexion point of 12.2 m height, i.e. the average forest canopy height. In other words, small trees (< 10 cm DBH) seem to assign resources mainly to growth in height (rather than in AGB), which may allow them to reach the canopy in short time periods and avoid suppression by competitors. Once they have reached the canopy, trees may assign resources to horizontal growth (in AGB, diameter, and crown and root cover). This could provide greater mechanical resistance against possible disturbances such as wind, as well as greater access to resources, both above-ground (light) and below-ground (water, nutrients). In agreement with this interpretation, branches contributed a lower percentage of total ABG (28.9 %) in the small tree size category (DBH = 2.5-9.95 cm; corresponding to trees of H < 12.2 m), compared to 42 % for the large size category (DBH > 10 cm; H > 12.2 m; data not shown).
Previous studies (Niklas 1995, Midgley 2003) indicate that trees that assign resources to diameter growth have marginal increases in height, suggesting the existence of mechanical and physiological limits in trees to increasing growth in height. No significant discontinuity between DBH and H was observed in the present study, although, compared to small trees, larger ones tended to show smaller increases in H for a given increase in DBH (Figure 2 c). The change in tree allometry detected in this study implies that using two different allometric equations could be more appropriate and produce more accurate AGB estimations than using a single equation.
Comparisons of allometric equations. The low predictive power of equation 4 (tree size category 2: ≥ 10 cm in DBH) evidenced by the cross-validation analysis may be due in part to the small sample size of this category (17 trees) and highlights the need to increase the sample size of large trees in the studied area. Návar-Cháidez et al. (2013) also found greater uncertainty in AGB estimation for larger (> 10 cm DBH) trees than for smaller ones in a tropical dry forest in northern Mexico. However, when equation 4 was combined with equation 1 (tree size category 1: 2.5 cm - 9.9 cm in DBH), the combination yielded fairly accurate estimates of AGB (Figure 4, Table 5). This was partly due to the good fit and high accuracy of equation 1 (Figure 3), which partly compensated the low accuracy of equation 4. More importantly, the better fit and predictive power of the equations 1-4 combination compared to the best single equation developed for the same data set (Table 5) clearly shows that combining different equations for two tree-size classes can provide more precise estimates of AGB than using a single equation. We propose that this is because using two different equations allows greater flexibility to model shifts in allometry (and resource allocation to growth) before vs after trees reach the forest canopy -as evidenced by the previously discussed discontinuity in the AGB-H relationship. Indeed, the best equations for the two tree size categories (equations 1 and 4, respectively) differ not only in their parameter values, but also in the type of relationship between dependent and independent variables -multiplicative in the case of equation 1, additive in the case of equation 4 (Tables 3, 4).
Since the allometric equations developed for diameter category 2 were based on a small sample size and showed a low predictive power, we tested if combining equation 1 of this study with other general equations developed and/or validated and used to estimate AGB in the forests of the Yucatan Peninsula, and generally based on larger sample sizes, would yield more accurate estimates. The comparatively low accuracy and high prediction error of the equations 1- Brown (1997) combination vis a vis the equations 1-4 combination (Table 5; Figure 4) was expected, since Brown’s equation was developed in a different continent (Asia), based on a small sample size (28 trees) and a narrow range of tree sizes (5 - 40 cm in DBH), and did not include tree height or wood density. However, the small estimation bias of this equations combination is surprising, but agrees with the good performance of Brown’s (1997) equation compared to a single equation developed using almost the same data set (Ramírez-Ramírez et al. 2017). Conversely, the slightly higher accuracy and lower prediction error of the equations 1- Chave et al. (2005) combination compared to the 1-4 combination may be partly due to the very large sample size (n = 1,808) of the Chave et al. (2005) equation, develop for pantropical seasonally dry forests, including those from the Yucatan Peninsula. Nevertheless, the equations 1- Chave et al. (2005) combination largely underestimates AGB, especially for large trees, and therefore should not be applied to our studied area. Finally, the relatively similar overall performance of the equations 1- Urquiza-Haas et al. (2007) combination compared to the 1-4 combination, may be partly related to the fact that both equations were developed in the Yucatan Peninsula (although in different locations), and consequently share some dominant tree species (e.g. Coccoloba diversifolia Jacq, Melicoccus oliviformis Kunth ssp. oliviformis), as well as similar climatic and edaphic conditions. Overall, these results suggest that local equations are better suited to local data, even if they are based on relatively small sample sizes.
Caveats, implications for and applications to forest management. Our results have important implications for and applications to forest management. First, our results indicate that using different allometric equations for small (2.5-9.9 cm in DBH) than for larger trees (≥ 10 cm in DBH) improved the precision of AGB estimation in the studied forest, compared to a single equation, likely because different equations capture shifts in tree allometry and resource allocation to growth. Appropriate and precise allometric equations for AGB estimation are a crucial tool for accurately quantifying forest carbon stocks and emission factors (Malhi et al. 2006, Pan et al. 2011, Anderson-Teixeira et al. 2015, Jucker et al. 2017). Thus, the equations developed in this study may improve estimates of AGB and emission factors in the studied tropical dry forest and, potentially, in similar tropical dry forests of the Yucatán Peninsula.
However, we would like to acknowledge two important caveats of this study: sample size and among-species variation in tree allometry. Due to human and funding constraints, as well as to permission of ejido members to fell only a limited number of trees, the sample size of this study (n = 47) fell just short of the minimum (n = 50) recommended by previous studies for constructing accurate allometric equations of AGB (Chave et al. 2004, van Breugel et al. 2011, Picard et al. 2012). This problem was particularly evident for large trees, since only 17 trees with DBH ≥ 10 cm could be harvested, resulting in a low estimation accuracy (R 2 ajd = 0.55) and a very large estimation error (RMSE = 147.65 kg: Figure 3b). This means that our estimates may not accurately represent actual AGB values of the seasonally dry tropical forests studied -at least for large trees. However, cross validation of equation 1 (for trees < 10 cm in DBH) showed a relatively high accuracy (R 2 ajd = 0.71) and a very low estimation error (RMSE = 3.26 kg: Figure 3a), although the sample size (n = 30) was still considerably lower than the minimum recommended (n = 50). Besides, previous studies have successfully developed and validated general allometric equations based on small sample sizes (n = 28 in Brown 1997; n = 39 in Návar-Cháidez et al. 2013).
Moreover, since species differ from one another in tree allometry (Niklas 1995, Chave et al. 2005, Picard et al. 2012), AGB estimates may vary slightly with species representation in a sample. Although we included 18 tree species belonging to the top 25 species that accounted for 95 % of AGB in the studied area, each of these 18 species was represented by only one to seven individuals. This means that our estimates may be slightly biased by the best sampled species (e.g., Lonchocarpus xuul Lundell, Piscidia piscipula (L) Sarg. see Table 1). Thus, the generality of our findings and their potential applicability to other tropical dry forests should be further investigated (ideally using larger, more representative sample sizes) -particularly for large trees (DBH ≥ 10 cm). However, we believe that equation 1 provides accurate estimation of AGB for smaller trees and may be more widely applicable, especially to secondary dry forests, since, compared to old-growth forests, small trees make up a greater proportion of AGB in these forests (van Breugel et al. 2011) -which currently make up most of the forested area worldwide (FAO 2010).
Our results also have potential applications to current forest management practices in the Ejido San Agustín, which are based on two harvest cycles: a short cycle of 10 years with a 5 cm in DBH minimum harvest diameter of almost all tree and shrub species mostly for charcoal production; and long cycle of 20 years with a 25 cm in DBH minimum harvest diameter of a few valuable timber species. The results of this study suggest that these harvest practices could be modified to maximize carbon storage, without compromising charcoal production or timber extraction. Thus, instead of harvesting almost all individuals with a minimum DBH of 5 cm for charcoal or biofuel production, all but one stem of tree species could be harvested (including branches), leaving the straightest and least branched stem to continue growing towards the size threshold (12.2 m H; 9.9 cm DBH) at which allocation to AGB growth (hence carbon storage) increases. Once the individuals of timber species attain the minimum diameter for the long cycle, those with the appropriate characteristics could be harvested, leaving all other trees for long-term carbon storage. This would allow maintaining charcoal or biofuel production, selecting the best individuals and stems for timber harvest in the long cycle, and at the same time would reduce forest degradation, to comply with climate change mitigation strategies such as REDD+ -thereby diversifying and potentially increasing revenues from forest management.
Our results show that using segmented regression to study individual relationships between variables included in allometric models of AGB allowed identifying a shift in allometry and defining tree size categories for which different equations should be applied. The combined use of these equations produced more precise estimations of AGB than a single equation that assumes unchanging allometric relationships. The shift in allometry detected in this study involved tree height with an inflection point corresponding to the average forest canopy height (12.2 m). Our results suggest a shift in resource allocation to growth: mostly to height for small (2.5-9.95 cm DBH) trees vs mostly to AGB for larger (≥ 10 cm DBH) trees. These findings have potential applications to forest management and clear implications for monitoring, reporting and verification (MRV) of forest emission factors, especially in secondary forests, which are increasing in extent and importance worldwide. Clearly, their generality and applicability need further investigation and validation using larger, more representative samples.
