Biomass Distribution and Development of Allometric Equations for Non-Destructive Estimation of Carbon Sequestration in Grafted Mango Trees

The general equations available/developed for forest/wild mango trees based on measurement of diameter at breast height (DBH) (cannot be used) are not applicable for mango orchards which are predominantly established with grafted plants. Hence allometric equations were developed with destructive sampling of grafted mango trees. The selected parameters showed that allometric parameters were significantly related with age of the trees. The proportion of roots (22%) in grafted mangos was found to be higher than those reported for tropical forest trees (18%) with a R ratio of 0.291. The biomass expansion factor (BEF) varied with age. Initially the BEF was very high followed by a decreasing phase and finally a steady phase by and large attained stability beyond 20 years. The equations generally fitted the data well, and in most cases more than 50% of the observed variation in biomass was explained by primary branch girth (PBG) × number of primary branches (NPB). All equations were statistically significant (p < 0.05) for both scaling parameters, a and b. Based on the R values the best fit model for estimation of above ground biomass of grafted mango trees is a power model using PBG × NPB as the best dimension: There was a good agreement between the observed and the predicted biomass using this equation.


Introduction
Non-destructive estimates of tree biomass are essential for several purposes.For example, it is essential in assessing forest structure and conditions (Westman & Rogers, 1977); estimating forest productivity and carbon fluxes (Chambers et al., 2001); for sequestration of carbon in wood, leaves, and roots (Specht & West, 2003); for estimating carbon sequestration and for assessing site productivity.All these depend on sequential changes in biomass.
Tree allometry is a statistical tool to relate some fairly easy to measure parameters of trees like DBH to such parameters which are often more difficult to assess.To obtain such relationships detailed measurements on a small sample of typical trees are made and then relationships are worked out such that they permit extrapolations and estimations of a host of dendrometric quantities on the basis of a single (or at most a few) measurements.This approach eases out difficult field work and enhances the speed of data collection and estimating tree biomass.This approach is very commonly practiced in forestry, but the same is not true in perennial horticulture.The data base in perennial horticulture are very poor to develop allometric relationship that relate, if any, existing between the parts of the subject measured and the quantities of parameters of interest (Smith & Brand, 1983).This should also take in to account the factors which affect tree growth such as age, species, site location, etc. (Avery & Burkhart, 2002).Once all these guidelines are met, one may attempt to develop an allometric equation.
In forestry many attempts have been made to develop biomass-prediction equations from mixtures of tropical species.But use of such relationships are not successful because the species especially dicotyledonous trees differ in allometry, wood density, and architecture, all of which can affect the relationship between the measurements taken during forest inventories and the biomass of individual trees (e.g., Chambers et al., 2001;Ketterings et al., 2001;Chave et al., 2005).jas.ccsenet.

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Allometric Measurements
Allometric parameters such as number of primary and secondary branches, girth of primary and secondary branches, tree height, tree volume, basal diameter, diameter below graft union (DBGU), were measured on 74 randomly selected mango trees of different age groups : 3,5,8,10,12,15,16,20, was measured with a diameter tape.The height of the tree and the diameter of the crown were measured with a Spiegel relaskop.

Tree Harvesting
Trees were measured for all allometric parameters and felled.The harvested biomass was segregated into foliage, Stem & primary branches and secondary branches.The foliage, branches and small stem were weighed separately, taking a subsample to obtain dry matter content (60 °C).Wood samples were taken to estimate specific gravity.Biomass was estimated based on volume and specific gravity.Total aboveground biomass was calculated as the sum of the biomass of all components.

Biomass Expansion Factor (BEF)
The BEF was calculated as the ratio of the biomass tothe volume, resulting in a dimensional variable (Mg m -3 ): Where, W is the stand biomass (Mg ha -1 ), ρ is the dry matter basic wood density (Mg m -3 ) and V is the stand volume (m 3 ha -1 ) (Soares & Tome, 2012).

Statistical Modelling
Logistic Model: the rate of growth of population size is given by a model represented by the differential equation: Where, N(t) denotes the population size or biomass at time t and r is the intrinsic growth rate.
Integrating, we get, Gompertz Model: Unlike the logistic model, this is not symmetric about its point of inflexion.The differential equation for this model is, Integration of this equation yields, The equation may equally return as, , Power Model: A model represented by an equation, As all these three models are a class of nonlinear regression model, as the derivatives of Y t with respect to unknown parameters are functions of either of them, suitable nonlinear estimation procedure was followed for parameter estimation (Venugopalan & Shamasundaran, 2003).SAS codes were developed to fit these non-linear regression models.

Component Biomass Distribution
Stem wood in grafted plants is very low as the tree branches from the ground just above the graft union.Hence stem and primary branches were combined for calculating the biomass distribution.The majority of the aboveground biomass constituted stem and primary branch wood with dry weight on an average representing, 49.82% of the total (Table 1).Secondary branch wood and foliage accounted for a further 17.02 and 10.62%, respectively.The belowground biomass accounted for the remaining 22.54% (i.e.small, medium and large roots).
Stem and primary branches accounted for the largest proportion of the total aboveground biomass by weight (49.82%).and was fairly similar to those reported earlier (Normand et al., 2007;Normand & Lauri, 2012;Eneji et al., 2013).This component was 47.9% in young plants and showed an increasing trend with age and crossed 50% after 20 years.The proportion of Secondary branch wood showed a declining trend with age and declined from 21% in young plants to 15.6% at 45 th year of age.One of the reasons for this may be the practice of pruning the secondary branches for ease of management.Contrary to this the foliage biomass showed a marginal increasing trend up to 20 years and declined slightly beyond this age.The proportion of roots (22%) was found to be higher than those reported for tropical forest trees (18%).The general above ground to below ground ration reported for tropical forest trees is 0.26 (Cairns et al., 1997) while we found it to be 0.29 in this study.Grafting, planting density and differences in site conditions like micro climate, soil and management would account for these slight variations in the biomass distribution between the studies.Further our interest was to extract maximum possible portion of the roots from soil profiles as our aim was to work out the carbon sequestration rather than from other commercial objectives of wood as in case of forestry studies.

Relationship between Tree Age and Allometric Parameters
Table 2 lists means and standard deviations of all the biometric parameters of the eight age groups examined.Tree age is used as the independent variable to predict the changes of biometric parameters with time.We applied several equations to select an appropriate growth model.Logarithmic and nonlinear exponential equations proposed by Peper et al. (2001aPeper et al. ( , 2001b) ) were first tested as these equations showed a good prediction in other environments.The logarithmic regression model was therefore applied to predict DBGU, tree volume, tree height and PBG X NPB from age: The summary of the best predictive growth models is presented in Figures 2a-2d.These relationships showed that allometric parameters were significantly related with age of the trees.The tree height was correlated better with age of tree (R 2 = 0.795) followed by DBGU (R 2 = 0.726), tree volume (R 2 = 0.644) and PBG × NPB (R 2 = 0.563).

Biomass Expansion Factor (BEF)
The BEF of mango is presented in Table 3. BEFs are needed as a complement of growth models that do not include biomass predictions.In spite of the fact that the BEFs vary with the phase of stand development, constant BEFs are applied in forestry and agro-forestry studies (Löwe et al., 2000;Lehtonen et al., 2007).But to reduce the uncertainty associated with the use of BEFs for biomass estimation, we estimated the BEF of different age groups as the ratio of the biomass to the volume, resulting in a dimensional variable and expressed in Mg m -3 .The BEF varied with age.Initially the BEF was very high followed by a decreasing phase and finally a steady phase.The BEF increased from 0.904 (Mg m -3 ) in third year, increased gradually to 1.63 (Mg m -3 ) at 8 th year.
Then the BEF started declining gradually and reached 1.12 (Mg m -3 ) at age 20.The BEF by and large attained stability beyond 20 years and attained 0.45 (Mg m -3 ) at 85 th year.Similar observations were made by several authors (e.g.Brown, 2002;Jalkanen et al., 2005;Lehtonen et al., 2007;Tobin & Nieuwenhuis, 2007) in other species.These reports support the findings concerning resource allocation during the growth process:

Biomass Estimation
Use of height-diameter relationships is very common in most allometric equations and in dicotyledonous tree species these are quite similar and have a slope very close to unity and may differ most among larger trees.This is true with mangos grown from seeds but not so in case of commercially grown grafted trees for fruit purpose.
A basic scatter plot examination was conducted while analysing the data.The field and laboratory data and all calculations were verified again and retained only those correct data remained in the data set.We opted for use of three forms of models viz., power model (Y = aX b ), logistic model (Y = a/(1 + be -0.042x)) and Gompertz model (Y = a × exp(be -x )) for allometric equations.Where, Y = biomass of tree and a and b are scaling factors (Table 4).As already mentioned the dimensions used were DBGU, Tree height, Tree volume and PBG × NPB.The equations generally fitted the data well, and in most cases more than 50% of the observed variation in biomass explained by PBG × NPB.All equations were statistically significant (p < 0.05) for both scaling parameters, a and b.Based on the R 2 values the best fit model for estimation of above ground biomass of grafted mango trees is a power model using PBG × NPB as the best dimension: A plot between estimated AGB and predicted AGB using this equation is presented in Figure 4.There is a good agreement between the observed and the predicted biomass using this equation.

Table 1 .
Component dry weight (Kgs) of harvested mango trees of different age (data in the parenthesis represents %)

Table 2 .
Means and standard deviations of the biometric parameters of the different age trees examined in grafted mangos

Table 4 .
Allometric equations for estimation of grafted mango above ground biomass 2.