Accounting for smallsize tree biomass is critical to improve total stand biomass estimates of secondary tropical forests, and is essential to quantify their vital role in mitigating climate change. However, owing to the scarcity of equations available for smallsize trees, their contribution to total biomass is unknown. The objective of this study was to generate allometric equations to estimate total biomass of 22 tree species ≤ 10 cm in diameter at breast height (DBH), in the Yucatan peninsula, Mexico, by using two methods. First, the additive approach involved the development of biomass equations by tree component (stem, branch and foliage) with simultaneous fit. In the treelevel approach, total tree biomass equations were fit for multispecies and wood density groups. Further, we compared the performance of total tree biomass equations that we generated with multispecies equations of previous studies. Data of total and by tree component biomass were fitted from eight nonlinear models as a function of DBH, total height (H) and wood density (ρ). Results showed that two models, identified as model I and II, best fitted our data. Model I has the form AGB = β_{0 }(ρ·DBH^{2}·H)β_{1 }+ ε and model II: AGB = exp(β_{0})(DBH^{2}·H)β_{1 }+ ε, where AGB is biomass (kg). Both models explained between 53% and 95% of the total observed variance in biomass, by treestructural component and total tree biomass. The variance of total tree biomass explained by fit models related to wood density group was 96%97%. Compared foreign equations showed between 30% and 45% mean error in total biomass estimation compared to 0.05%0.36% error showed by equations developed in this study. At the local level, the biomass contribution of small trees based on foreign models was between 24.38 and 29.51 Mg ha^{1}, and model I was 35.97 Mg ha^{1}. Thus, from 6.5 up to 11.59 Mg ha^{1 }could be excluded when using foreign equations, which account for about 21.8% of the total stand biomass. Local equations provided more accurate biomass estimates with the inclusion of ρ and H as predictors variables and proved to be better than foreign equations. Therefore, our equations are suitable to improve the accuracy estimates of carbon forest stocks in the secondary forests of the Yucatan peninsula.
The importance of tropical secondary forests for biodiversity conservation, provision of ecosystem services and climate change mitigation is globally recognized (
Smalldiameter trees are an important component of total tree density and biomass in tropical forests in the Yucatan peninsula, Mexico. This component represents between 2.4% to 60% of the total tree density in forests of the state of Campeche, Mexico (
Tree biomass is commonly estimated with allometric models that use easily measured tree variables as predictors, namely DBH, total height and wood density (
Biomass equations generated at the local scale might become a reliable tool to reduce uncertainty of carbon stock estimates. For instance, biomass errors ranging from 10% to 40%, and in extreme cases up to 70% have been reported for neotropical regions (
In Mexican tropical forests, the study and analysis of the biomass of smallsize trees and their contribution to the ecosystem is limited, though many nonlinear and exponential type biomass equations have been developed. Indeed, most equations have been generated for temperate forests, especially for valuable timber species of the Pinaceae and Fagaceae families (
In this study, we developed allometric equations to estimate the biomass of small diameter trees (DBH ≤ 10 cm) for 22 tree species that are structurally important in secondary tropical forests of the southern Yucatan peninsula, Mexico. The main objectives were to: (i) generate biomass equations by tree structural components (
This study was performed in secondary tropical forests ranging from nine to 35 yearsold and in an oldgrowth stands. The stand age corresponds to the time (years) elapsed after the last application of slash and burn agriculture system (maize, beans and squash as main products). Stands were located in the southeast region of the Yucatan peninsula, Mexico, between the Sian Ka’an Biosphere Reserve in Quintana Roo (19° 05′ and 20° 06′ N, 87° 30’ and 87° 58’ W) and Calakmul Reserve in Campeche (19° 15′ and 17° 45′ N, 90° 10′ and 89° 15’ W 
The dominant vegetation type is midstature, semi evergreen tropical forest (
We performed a preassessment on each stand to collect information to estimate the Structural Importance Index (IVI) of each tree species (
We selected and harvested between 12 and 18 trees by species (311 trees in total  Tab. S1 in Supplementary material) for biomass calculations. The fresh weight of each structural component of the selected trees (
Wood samples (cubes) were taken from each tree at 1.30 m from the base of the stem to determine wood basic density (g cm^{3}). Each sample included the pith, heartwood, sapwood and cambium because the distribution of these elements influences the wood density along the stem (
Scatter plots of total biomass against DBH by species were used to explore data trends, and decide whether a linear or a nonlinear model would be more suitable to fit the data. Based on scatter plots, we tested eight allometric regression model types that were previously reported in other studies to estimate total tree biomass (Tab. S2 in Supplementary material).
We performed independent fitting for each model to estimate their parameters by structural component and for total tree biomass. Model fitting was performed by applying the Newton’s iterative method with Ordinary Least Squares (OLS) using the PROC MODEL in SAS (
After we selected the models following the independent fitting, they were fitted by tree structural components (
where AGB is aboveground biomass (kg), β is the vector of regression parameters to be estimated, DBH is diameter at breast height (cm), H is total tree height (m), ρ is wood density (g cm^{3}) by species. We assumed that the error terms are independent and identically distributed as ε~ N(0,σ^{2}_{e}).
The simultaneous fit, without analytical relations among equations, was solved with the NSUR technique (nonlinear seemingly unrelated regressions) and iteratively applying the ITSUR option of PROC MODEL in SAS using Newton Algorithm (
Multispecies (
where AGB is the aboveground biomass (kg), β_{0} and β_{1} are regression coefficients of the parameters to be estimated, ρ is the wood density (g cm^{3}) by species, DBH is the diameter at breast height (cm), H = total tree height (m), ln is the natural logarithm function, CF is the correction factor, σ is the residual standard error, and β′_{0} is the regression coefficient estimated in model fitted. We assumed that the error terms are independent and identically distributed as ε~N(0,σ^{2}_{e}).
We used the independent model approach with weighted regression to fit multispecies and wood density group models to improve homogeneity of variance and goodness of fit. Model’s predictive ability was assessed with the “kfold crossvalidation” method (
where RME% and MAPE% are the relative mean error and absolute bias, respectively, AGB_{est }and AGB_{obs} are predicted (or estimated) and observed biomass, respectively, and
We compared the RME% and MAPE% of biomass estimated with equations used in this study against equations generated for other tropical regions to assess uncertainty and select a final model. For example, multispecies equations were compared with
where AGB_{pred} is the predicted aboveground biomass (kg), DBH is the diameter at breast height (cm), ρ is the wood density (g cm^{3}) by species, and ρ_{av} is the mean wood density (0.54 g cm^{3}) of the plot and ln is the natural logarithm function.
We selected
The RME% and MAPE% of equations fitted by wood density groups was compared to
where AGB_{pred} is the predicted aboveground biomass (kg), DBH is the diameter at breast height (cm), H is the total tree height, ln is the natural logarithm function, and ρ is the wood density (g cm^{3}) by species.
Our main interest was to assess the performance of
The RME% and MAPE% of equations generated in other tropical regions was calculated from “Kfoldcrossvalidation” tests (
Lastly, we evaluated the accuracy of estimations of total biomass stored in smallsize trees (≤ 10 in DBH) with the equations of
We tested eight regression models to predict aboveground biomass (Tab. S2 in Supplementary material). The adjusted R^{2} values for these models ranged from 80% to 94%. Model I (named as Model 7 in Tab. S2) and model II (named as Model 8 in Tab. S2) showed the highest adjusted R^{2} and the smallest RMSE and AIC (Tab. S5). We selected these models based on their best goodnessoffit statistics.
Equations fitted with models I and II accounted for 53% to 95% of the biomass variance observed by structural components, and from 92% to 95% of the total tree biomass (
The biomass of structural components and total tree for multispecies calculated with models I and II of
Both the RME% and bias (MAPE%) for estimating the biomass by structural component (
Total tree biomass estimated with multispecies equations of
Model I and II showed less error and bias in the estimation of total tree biomass compared to the
The distribution of residuals and models goodnessoffit statistics for species with high and intermediate wood density improved with the weighting factor 1/DBH^{2}H. The equations fit by wood density groups (
Results of the linear regression analysis also showed the existence of a stronger association between the biomass estimated for species with high and intermediate wood density than for species with low wood density (
Furthermore, the equations fit by wood density group estimated total tree biomass with a smaller error and bias (
Based on inventory data, the biomass average of trees with DBH >10 cm was 128.97 ± 14.46 Mg ha^{1}. Small trees (2.510 cm in DBH) biomass estimated with Model I was greater (p < 0.05) than the biomass estimated with
We developed allometric equations to estimate total aboveground biomass of small trees in tropical forests of the Yucatan peninsula, by structural components (
The use of NSUR to fit models by tree structural component (
Model I showed a lower relative mean error for stem (0.03%), branch (2.5%) and foliage (0.17%) biomass than model II (
The inclusion of wood density in addition to DBH and total height in the multispecies models I and II improved total tree biomass predictions as showed by their lowest biomass estimation error (
The large error in the biomass estimated with
Regarding the sample size,
The
In general, generic equations developed for a different region and applied at the local level, give results similar to those obtained in this study. For example,
Biomass models for wood density groups are not common for tropical regions and particularly for the Yucatan peninsula. In this study, we developed three biomass equations for species with high (0.610.80 g cm^{3}), intermediate (0.420.52 g cm^{3}) and low (0.250.29 g cm^{3}) wood density (
The pantropical model by Djomo et al. (
The model by Van Breugel et al. (
We observed that model I had the best accuracy in estimating the contribution of small trees to total biomass (
We developed allometric equations to estimate biomass by tree component (stem, branch, and foliage), and total tree biomass for 22 smallsize (≤ 10 cm DBH) tree species in secondary forests of the Yucatan peninsula, Mexico. We confirmed the hypothesis that the inclusion of total height and wood density in allometric models improve equations fit and biomass estimation compared with models including a single predictor variable such as DBH.
The equations used in this study yielded more accurate biomass estimations than those developed for other tropical regions. These results support the hypothesis that local equations can better explain the biomass variability in a region when both total height and wood density are included in the fitting process, since these parameters are highly correlated with growth type and wood physical properties of trees.
The equations developed in this study can be conveniently used to reduce uncertainty in biomass and carbon stocks estimations in secondary forests of the Yucatan peninsula, where a large proportion of the community is composed by smallsize trees and the sites are constantly affected by natural and anthropogenic disturbances. Managing tropical secondary forests for climate change mitigation requires the estimation of biomass/carbon stocks with a low level of uncertainty; therefore, these equations can be a useful tool in the context of climate change within the projects implemented by REDD+ in Mexico, and similar regions in developing countries.
This study was financially supported by the Sustainable Landscapes Program of the Agency for International Development of the United States of America, through the USDA Forest Service International Programs Office and the Northern Research Station (Agreement No. 12IJ11242306033).
Location of biomass harvest points in the southern Yucatan peninsula.
Relationship between observed and predicted biomass. Model I: total biomass (a), stem biomass (b), branch biomass (c), and foliage biomass (d). Model II: total biomass (e), stem biomass (f), branch biomass (g), and foliage biomass (h). The gray solid line represents the 1:1 ratio between the biomass values. The black dotted line represents the linear regression between observed and predicted biomass.
Comparison between observed total tree and predicted total tree biomass. (a): Model I; (b): model II; (c):
Comparison between observed versus estimated total tree biomass by wood density groups. High (a) intermediate (b) and low (c). The gray solid line represents the 1:1 ratio between the biomass values. The black dotted line represents the linear regression between observed and predicted biomass.
Aboveground biomass at the stand level of small trees estimated with
Allometric equations for biomass estimation by tree structural component and total tree biomass derived with simultaneous fit and multispecies equations. (Model I): AGB = β_{0}(ρ·DBH^{2}·H)^{β1}; (Model II): AGB = exp(β_{0})(DBH^{2}H)^{β1}. (AGB): stem, branches, foliage or total tree estimated aboveground biomass (kg); (ρ): wood density (g cm^{3}); (DBH): diameter at breast height (cm); (H): total tree height (m); (β_{0}, β_{1}): regression coefficients of the models to be estimated; (RMSE): root mean square error of the estimate; (adjR^{2 }): proportion of variance explained by the model. We assumed that the error terms are independent and identically distributed: ε~N(0,σ^{2}_{e}).
Model  No.  Allometric model  RMSE  adjR^{2} 

Model I  1  AGB_{stem}=0.057541(ρ·DBH^{2}·H)^{0.916963}  1.6538  0.95 
2  AGB_{branches}=0.019758(ρ·DBH^{2}·H)^{0.980837}  1.6293  0.73  
3  AGB_{foliage}=0.022462(ρ·DBH^{2}·H)^{0.724191}  0.4491  0.71  
4  AGB_{totaltree}=AGB_{stem}+AGB_{branches}+ AGB_{foliage}  2.6009  0.95  
5  AGB_{totaltree multispecies}=0.078479(ρ·DBH^{2}·H)^{0.945339}  0.1389  0.96  
Model II  6  AGB_{stem}= exp(3.471635)(DBH^{2}·H)^{0.956893}  2.1974  0.93 
7  AGB_{branches}=exp(4.047339)(DBH^{2}·H)^{0.954151}  2.4432  0.76  
8  AGB_{foliage}=exp(3.838296)(DBH^{2}·H)^{0.712222}  0.8329  0.53  
9  AGB_{totaltree}=AGB_{stem}+AGB_{branches}+ AGB_{foliage}  3.7892  0.92  
10  AGB_{totaltree multispecies}= exp(2.97501)(DBH^{2}·H)^{0.957051}  0.1552  0.95 
Comparison of the relative mean error (RME, %) and bias (MAPE, %) of biomass estimations by structural component and total tree among multispecies equations (derived from models I and model II),
Parms  Structuralcomponent  Model I  Model II  Hughes et al.  Chave et al. 

RME  Stem  0.20 ± 1.57 ^{a}  0.02 ± 1.65 ^{a}     
Branch  0.41 ± 2.56 ^{a}  0.14 ± 2.78 ^{b}      
Foliage  0.93 ± 4.86 ^{a}  2.41 ± 6.18 ^{b}      
Totaltree  0.36 ± 2.08 ^{a}  0.05 ± 1.92 ^{a}  44.51 ± 0.92 ^{b}  30.36 ± 1.21 ^{c}  
MAPE  Stem  0.08 ± 0.06 ^{a}  0.008 ± 0.05 ^{a}     
Branch  0.15 ± 0.10 ^{a}  0.05 ± 0.09 ^{a}      
Foliage  0.32 ± 0.18 ^{a}  0.84 ± 0.17 ^{a}      
Totaltree  0.13 ± 0.07 ^{a}  0.01 ± 0.07 ^{a}  15.57 ± 0.04 ^{b}  10.63 ± 0.05 ^{c} 
Allometric equations for total tree biomass estimation for tree species with high, intermediate and low wood density. (n): sample size (number of trees); (AGB): total tree estimated aboveground biomass (kg); (ρ): wood density (g cm^{3}); (DBH): diameter at breast height (cm); (H): total tree height (m); (RMSE): root mean square error of the estimate; (adjR^{2}): proportion of variance explained by the model. A correction factor (CF) of 1.05 was used to reduce the bias of logtransformation for the biomass equation for low wood density species.
No  Wood densitygroup  n  Equation  RMSE  adjR^{2} 

1  High  234  AGB_{totaltree}=0.077022(ρ·DBH^{2}·H)^{0.947669}  0.1421  0.96 
2  Intermediate  21  AGB_{totaltree}=0.079603(ρ·DBH^{2}·H)^{0.962061}  1.0873  0.97 
3  Low  20  AGB_{totaltree}=0.0814549(ρ·DBH^{2}·H)^{0.971735}  0.3083  0.97 
Comparison of the relative mean error (EMR, %) and bias (MAPE, %) of total tree biomass estimated with equations fit by wood density groups (this study) and foreign equations. Different letters indicate significant statistical differences (p < 0.05) between structural components, result of Duncan’s multiple range test (± standard error).
Parms  Model  High  Intermediate  Low 

EMR  This study  0.34 ± 0.99 ^{a}  0.65 ± 4.74 ^{a}  2.66 ± 15.97 ^{a} 

98.70 ± 0.05 ^{c}  98.31 ± 0.14 ^{c}  97.45 ± 0.05 ^{b}  

1.23 ± 1.34 ^{a}  10.15 ± 3.19 ^{ad}  14.38 ± 5.23 ^{ac}  
MAPE  This study  0.03 ± 0.02 ^{a}  9.50 ± 0.01 ^{b}  0.11 ± 0.03 ^{a} 

0.31 ± 0.42 ^{a}  34.14 ± 0.34 ^{b}  3.53 ± 0.28 ^{a}  

0.14 ± 1.98 ^{a}  35.58 ± 1.03 ^{b}  5.57 ± 0.83 ^{a} 
Tab. S1  Distribution of trees sampled by species harvested to fit allometric biomass equations in secondary tropical forests of the southeast Yucatan peninsula.
Tab. S2  Allometric regression models tested for estimating biomass from 22 species with high structural importance in secondary tropical forests.
Tab. S3  Program that can be used to fit a system of biomass estimation equations by tree structural component, stem, branches and foliage, using SAS/ETS.
Tab. S4  Program to fit an equation to estimate the totaltree biomass under an independent approach using SAS/ETS.
Tab. S5  Goodness of fit statistics for the regression models fit to 22 tree species.