Allometric Modelling of the Stem Carbon Content of Rhizophora mucronata in a Tropical Mangrove Ecosystem

Mangrove ecosystems are identiﬁed as important blue carbon ecosystems because they play an important role in carbon sequestration among the coastal ecosystems. The present study was conducted to develop an allometric model to determine the stem carbon content of Rhizophora mucronata in a conserved tropical mangrove ecosystem. The stepwise regression with backward elimination was used to identify the best ﬁt model to predict the stem carbon content of Rhizophora mucronata . The allometric equation, Ln C �− 2.403+2.247 Ln DBH, where C : stem carbon content and DBH: diameter at breast height, was constructed to be evaluated and validated as the most suitable and practically applicable model. The reliability of the model was 76.7%, and the model was signiﬁcant at 95% level of signiﬁcance. The model bias values and the model eﬃciency values for the best ﬁt model suggested that the model is suitable to be used practically. The present study used a nondestructive method of measuring individual tree parameters to develop this allometric equation to predict the stem carbon content and it is considered as an environmentally friendly approach with minimum damage to the tree.


Introduction
Mangroves play an important role in carbon sequestration in tropical and subtropical coastal areas, and they have a considerable contribution of carbon dioxide mitigation. e mangrove forests are very diverse ecosystems and they consist of true mangroves, mangrove-associated plants, and other organisms [1]. Most mangrove forests are located in tropical areas, although there are some expansions into subtropical regions as well.
e approximate global area covered by mangrove forests is estimated to be 140,000 km 2 with the highest extent of mangroves occurring in Asia (42%), followed by Africa (20%) and North and Central America (15%) [2]. e most common tropical mangrove genera include Avicennia, Rhizophora, Bruguiera, and Sonneratia.
ese genera are identified as most suitable species to be used in tropical mangrove replantation programmes due to their ability to distribute in a wide range of soil and hydrological conditions [3].
In addition, Rhizophora mucronata is commonly used in the tropical mangrove replantation programmes due to its adaptability and rapid growth rate. When selecting mangrove species for replantation, the factors such as their adaptability, growth rate, and the extent of the root system are considered as high-priority characteristics. However, considering the current global warming conditions in the world, it is important to consider the carbon sequestration capacity of the selected species for replantation as the mangrove plants are considered to be excellent carbon dioxide removers from the atmosphere [11,12].
Coastal ecosystems such as mangrove forests are identified as blue carbon ecosystems and they store more carbon per unit area than terrestrial forests and therefore are recognized as highly important ecosystems to mitigate climate change [12].
However, the carbon sequestration potential of Rhizophora mucronata is not widely researched in the tropical mangrove ecosystems. e studies that have been conducted so far have followed a destructive method of sampling, which involves the removal of sampled trees from the ecosystem and measuring the carbon content stored in the plant parts. However, the removal of plants from their natural ecosystem can have detrimental effects to the global climate and therefore currently it is not encouraged to remove plants even for the research purposes. erefore, the present study was conducted with the objective of using a nondestructive method to estimate the stem carbon content of Rhizophora mucronata in conserved tropical mangrove ecosystems.

Methodology
is study was conducted in a major mangrove conservation forest, e Kadol Kale mangrove forest located in Sri Lanka. Seventy individual trees of Rhizophora mucronata were selected from the study area based on purposive sampling. Damaged trees and trees devoid of leaves were not sampled during the study to avoid the effects on biomass accumulation process. A diameter tape was used to measure the diameter at breast height (DBH) of each tree, and the clinometer method was used to measure the total tree height, tree crown height, and merchantable stem height. e method described by Sabin was used to measure the stem volume of each plant [13]. ImageJ software was used to measure the leaf area of each tree (https://imagej.nih. gov/ij/).

Determination of the Stem Carbon Biomass.
Increment borer was used to collect core samples of tree trunk from each tree at breast height with relatively minor injury to the tree. e Archimedes displacement principle was used to measure the initial volume of the collected core samples. e fixed stem carbon biomass of all the core samples was determined by loss on the ignition method as described by Guendehou and Leehtonen [14].
Considering the diameter at breast height of all the trees, the trees were grouped into classes as follows: Carbon sequestration performance at each diameter class was determined by calculating the mean stem carbon content at each diameter class. e percentage increase of mean stem carbon content compared to previous diameter class was also calculated. e data were tested for normality using the Anderson Darling test, and the nonnormalized data were log transformed as appropriate. e correlation between the stem carbon content and the individual tree parameters was assessed using person's correlation analysis. e transformed data were used in model construction, evaluation, and validation.

Construction Evaluation and Validation of the Allometric Model.
Stepwise regression with backward elimination was used to construct an allometric equation for the stem carbon content of Rhizophora mucronata. Only 75% of data were used in construction of the model while other 25% of data were used in model validation. e best fitted model was evaluated using quantitative and qualitative evaluation methods as described by Subasinghe and Haripriya [15]. e best fitted model was used to estimate the stem carbon content of reserved 25% of trees. e model was validated using the diagram between the actual values and the residual values and Student's t test was used to compare the predicted stem carbon content from the allometric equation and the measured stem carbon content. MINITAB 14 software was used for statistical analysis.

Results and Discussion
e mean DBH, stem height, merchantable stem height, crown height leaf area and the stem carbon content of Rhizophora mucronata are given in Table 1. e diameter at breast height of the sampled trees ranged from 4.7 cm to 15. 9 cm. e total height ranged from 3.5 m to 12.1 m. e merchantable stem height and crown height ranged from 2.3 m to 8.8 m and 0.5 m to 6.9 m respectively. e total leaf area of the sampled trees ranged from 1.7 m 2 to 50.5 m 2 . e stem carbon content of the sampled trees ranged from 3.5 kg to 109.6 kg (Table 1).
e variations of stem carbon content at different DBH classes are given in Table 2. e mean stem carbon content at the lowest diameter class was significantly lower than the other diameter classes. e significantly highest stem carbon content was recorded from the Rhizophora mucronata trees at DBH class 5 (12.1 cm-14.00 cm). However, there was no significant difference in the mean stem carbon content of the trees at the DBH classes 4 and 6. e highest percentage increase of mean stem carbon content was observed between the DBH classes 1 and 2. e percentage increase of mean 2 International Journal of Forestry Research stem carbon content decreased in the other successive DBH classes (Table 2). Generally, mature trees are expected to have long carbon residence time. However, there is no consensus on the contribution of old trees to carbon storage due to lack of long-term individual tree data [16]. Declining tree growth over time is caused due to changes in the supply rate of required resources (light, nutrients, and water), change in balance between photosynthesis and respiration, increased hydraulic resistance, decreased nutrient supply, or genetic changes with meristem age which can result in increased carbon storage capacity of the mature trees compared to the new trees [17][18][19][20][21]. e results of the correlation analysis are given in Table 3. e stem carbon content of Rhizophora mucronata showed significant positive correlations with DBH (R 2 � 0.797, p ≤ 0.001), total stem height (R 2 � 0.648, ≤0.001) and merchantable stem height (R 2 � 0.697, ≤0.001) ( Table 3).

Model Construction.
Stepwise regression with backward elimination was used to identify the major predictors of stem carbon content of Rhizophora mucronata. To construct the model, 75% of data were used. e predictor variables used were DBH (diameter at breast height), total height, crown height, merchantable stem height, and leaf area. Two models (Model A and Model B) were constructed from the stepwise regression with backward elimination method: e constructed models, their regression coefficients, and VIFs (variance inflation factors) are given in Table 4. For Rhizophora mucronata DBH, crown height, total height, and stem height (p ≤ 0.001) were statistically significant with stem carbon content. Leaf area was not statistically significant. In order to find whether the explanatory variables were related to each other, multicollinearity was checked.
e VIF values were used to measure the effect of multicollinearity among the explanatory variables. e VIF > 5 suggests that the regression coefficient is poorly estimated due to severe multicollinearity, and 1 < VIF < 5 suggests that regression coefficient is poorly estimated due to severe multicollinearity. e VIF � 1 means that there is no multicollinearity among the explanatory variables, and therefore, these variables are best suited to fit into the model. In the model A, total height (VIF � 22.20), stem height (VIF � 10.22), and crown height (VIF � 9.75) indicate high multicollinearity. erefore, total height, stem height, and crown height were eliminated to refit the model. In model B, DBH (VIF � 1) showed a good fit for the model (R 2 � 76.7%) ( Table 4). As it is always better to keep the model simple in the real-world application, the model B was selected as the best model for Rhizophora mucronata.

Evaluation of the Model.
Model fit was examined using p value, R 2 value, and residual diagram. e p value of the best fit model for Rhizophora mucronata was statistically significant as it was lower than the alpha level of 0.01 (Table 4, stepwise regression analysis with backward elimination method). For the best fit model, the explanatory variable DBH was statistically significant and the high R 2 value of the best fit model indicated that the dependent variable which is the stem carbon content of Rhizophora mucronata can be explained up to high percentage (more than 60%) by the selected explanatory variable, which is DBH. e residual distribution diagrams for the best model for Rhizophora mucronata is given in Figure 1. Distribution of the residuals for the models indicated a random pattern, and the distribution were between +1 and 1 implying a good fit for linear model (Figure 1). e model bias and modelling efficiency values for the best fitted model of Rhizophora mucronata was used for the evaluation of the model. e model bias value and the model efficiency values for Rhizophora mucronata were −0.002563323 and 0.7665, respectively. e model bias value was very close to 0, and the modelling efficiency value was close to one indicating that the selected model is well suited to predict the stem carbon content of Rhizophora mucronata.

Validation of the Model.
e reserved 25% of data were used for model validation. e residuals values for Rhizophora mucronata were calculated as the difference between the actual stem carbon content and predicted stem carbon content from the model. e residual diagram of residual versus actual values for Rhizophora mucronata is given in Figure 2. e residual diagram showed a random pattern indicating that the model can be proved to use in the real world ( Figure 2). e mean values of the measured stem carbon content and the predicted stem carbon content using the prediction model for Rhizophora mucronata are given in Table 5. e measured stem carbon content of the Rhizophora mucronata trees used for model validation ranged from 1.3 kg to 4.3 kg and their predicted values ranged from 1.3 kg to 3.6 kg. ere was no significant difference of the mean measured stem carbon content and the mean predicted stem carbon content from the allometric equations developed for Rhizophora mucronata (Table 5, Student's t test, p > 0.05).

International Journal of Forestry Research
Tree allometry is an important tool for estimating tree weight from independent variables such as trunk diameter, tree height, crown height, total height that are easily measurable in the field. e basic concept of allometric relationships is that the growth rate of one or more measurements of the tree is proportional to that of other parameters [22]. Most of these allometric equations are used for the biomass related studies in terrestrial forest ecosystems. However, few studies have used tree allometric modelling to determine the above ground biomass of mangrove trees in some regions of the world [22][23][24][25][26][27].
Determination of the stem carbon content of individual species is very important and can play a key role when assessing     the carbon sequestration capacity of the ecosystems. e actively growing trees can store more carbon in their stem. is carbon is fixed by photosynthesis and comparatively high carbon content can be stored in the stem of the trees compared to the leaves. As trees mature, they sequester less carbon but gain the capacity to store carbon in their stems [28][29][30]. erefore, it is very important to measure the carbon content of the tree stems, in order to estimate the role of a particular tree species in removal of excessive carbon dioxide from the atmosphere. However, use of destructive methods for this purpose is not advisable as they can disrupt the balance of the carbon removal process. Previous studies conducted in this part of the country to assess the mangrove carbon sequestration capacity have used destructive methods [31,32]. e present study can be considered as the initial attempt to use a nondestructive method to construct an allometric equation to predict the stem carbon content of Rhizophora mucronata in a tropical conserved mangrove forest. erefore, it is recommended to extend this allometric equation development method to estimate the stem carbon content of other common tropical mangrove species in order to get an accurate estimate on the contribution of tropical mangrove stem carbon storage capacity for mitigation of global warming.

Conclusion
e present study identifies that the allometric model, Ln C � −2.403 + 2.247 Ln DBH as the best fit and practical model to estimate the stem carbon content of Rhizophora mucronata. e stem carbon content can be easily estimated from this model by using an easily measurable tree parameter. is is a non-destructive method and it is environmentally friendly as it does not require the tree to be removed from its natural environment. Furthermore, the results of the present study identifies that the Rhizophora mucronata as a suitable species to be used in mangrove replantation programs as it has the maximum carbon storage capacity when the trees are at a DBH range of 12-14 cm. Findings of the present study can be extended to estimate the functional capacities carbon sequestration by other Sri Lankan mangroves, and therefore encourage rational decision making on conservation and management of mangrove areas for their ecological services including their carbon sequestration capacity and influence to mitigate predicted climatic changes.

Data Availability
e raw data of the study are available upon request from the corresponding author. e data are presented as mean ± standard deviation. e values within parentheses indicate the range of variation of the measured and predicted stem carbon content. a Measured and predicted stem carbon content of Rhizophora mucronata at 95%level of significance. p >0.05 indicates that there is no significant difference in the actual stem carbon content and the predicted stem carbon content from the developed model at 95% level of significance.
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