Development of Allometric Models for Estimating the Biomass of Sclerocarya birrea (A.Rich) Hoscht and Boscia senegalensis (Pers.) Lam. ex

The objective of this study was to develop allometric models for estimating the biomass of Sclerocarya birrea (A.Rich) Hoscht and Boscia senegalensis (Pers.) Lam. ex Poir. The inventory of these ligneous was carried out at Widou Thiengoly (North of Senegal). The sample consists of 43 individuals of Boscia senegalensis and 15 individuals of Sclerocarya birrea. The selected individuals were dendrometrically characterized before being cut, compartmentalized (trunk, branches, and twigs) and weighed entirely. Simple regression tests were performed to examine the most explanatory dendrometric parameter (x) for biomass (y) according to two types of models: the linear sequestered carbon assessment study and will play a role in monitoring the carbon market in Africa.


Introduction
In the current context of increased anthropization, the world's ecosystems are undergoing intense deforestation, causing a significant increase in greenhouse gas emissions to the atmosphere and global warming [1]. To address this major challenge, greenhouse gas (GHG) reduction mechanisms were introduced as part of the Kyoto Protocol in 2005, in which carbon appears to be at the center of economic, environmental and social issues in the world. In the Sahel, the recurrence of droughts in recent decades, relating to rainfall deficits, has led to a reduction in the productivity of vegetation [2]. At the same time, natural ecosystems are subject to overexploitation by local populations and overgrazing by livestock [3] [4]. In Senegal, in the Sahelian zone, certain woody trees play a primordial environmental and socio-economic role. As part of the Sahel regreening project in the context of the Great Green Wall (GMV), the main plant species used in this program to combat desertification are, among others, Balanites aegyptiaca (L.) Del, Acacia tortilis (forsk.) Hayne ssp. raddiana (Savi) Brenan, Acacia senegal (L.), Sclerocarya birrea (A.Rich) Hoscht and Boscia senegalensis (Pers.) Lam. ex Poir. [5] [6]. The productivity of these species in the Senegalese Sahel will directly contribute to the increase of their biomass in reforested ecosystems and indirectly their capacity to sequester atmospheric carbon. Indeed, the study of woody biomass provides information on the atmospheric carbon sequestration potential of a species [7] [8]. This therefore responds particularly to the global concern of mitigating climate change due to emissions of greenhouse gases, notably carbon [9] [10]. Previous work has been the subject of biomass studies of species such as Acacia senegal with [11] and [12] and Afzelia africana, Ficus gnaphalocarpa and Pterocarpus erinaceus with [13]. Our study is part of this continuity, as it complements the work already carried out in the area [14]. In addition, the literature review reveals almost no data on Sclerocarya birrea (A.Rich) Hoscht and Boscia senegalensis (Pers.) Lam. ex Poir.
The objective of this study is to develop allometric models for the estimation of the biomass of these two Sahelian species in the Ferlo.

Presentation of the Study Area
The study was conducted in Widou Thiengoly, a village in the north of Senegal in the Sylvopastoral area of Ferlo ( Figure 1). The choice of site is justified by the  [17].
The region's climate, of a semi-arid tropical type, is characterized by an alternation of a long dry season from October to June and a short rainy season between July and September. Average annual precipitation in recent decades has rarely reached 300 mm [18] and is unevenly distributed in time and space. The months of August and September, which record the maximum rainfall (around 150 mm), are considered to be the heart of the rainy season. Temperatures vary throughout the year with minimums of 15˚C and maximums of 46˚C to 48˚C [19]. Ferlo shelters a steppe with shrubby dominated by woody trees such as Balanites aegyptiaca (L.) Del, Boscia senegalensis (Pers.) Lam. ex Poir., Acacia senegal (L.), Acacia tortilis (forsk.) Hayne ssp. raddiana (Savi) Brenan, and Calotropis procera (Aiton) W. T. Aiton [18] [20]. In terms of soil morphology, the study area belongs to the sandy Ferlo, characterized by a succession of dunes and shallows with little accident, with a different type of soil depending on whether one is on a dune summit or below slope [21]. to 5 m high, conical in shape, the crowns are very dense and the trunks of small diameters very branchy. These two species have a wide distribution in the Sahelian to Sudanian zone, on dry stations, rocky, lateritic, sandy soils (dunes). They returned from Mauritania to Senegal and can be found as far as Ethiopia. They are fairly common, locally abundant and gregarious [22]. The above-ground biomass of its two woody species was used to develop an allometric model for the evaluation of their biomass.

Sampling and Dendrometric Characterization of Woody Species
The sample size was calculated from Dagnélie's formula [23]: P = percentage of the species; A = (the ratio of the density of the species studied to the total density of woody species); d = is the error rate; U = is the u of the normal law which is read on the table.
Based on this calculation, the study focused on 43 individuals of the species Boscia senegalensis and on 15 individuals of Sclerocarya birrea; randomly selected from Widou Thiengoly village routes. Dendrometric measurements of standing individuals were carried out to characterize the species. They concern: the diameter at chest height (1.30 m from the ground) and the diameter at the base (0.30 m from the ground), the total height and the two crossed diameters of the crown (d1 and d2). It is then possible to calculate the area of the crown (m 2 ) by the following formula [24]:

Biomass Measurement in the Field
To develop allometric models, the direct method based on tree felling and was used. The sampled subjects are cut down and compartmentalized (trunk, branches, twigs and twigs-leaves). The total fresh mass of each part is weighed with a balance of 200 kg and that of the compartments with a precision balance of 7 kg. These different weighings are noted in the statement sheet. From each compartment, samples were taken and stored in plastic bags to determine the dry biomass.

Determination of Dry Biomass
In the laboratory, the samples from the different compartments were weighed again and then dried in an oven at 70˚C to constant weight. The dry biomass (Ms) of small sample was determined which made it possible to calculate the humidity rate of the different parts of each individual according to the formula

Data Processing
The dry biomass data were processed using the Excel spreadsheet and the R x 64 Software version 3.5.1 was used as the basis for the statistical tests. Simple regression tests were performed using XLSTAT 2014 software in Excel to see the relationship between the calculated dry biomass and the various dendrometric parameters measured. With these tools, several allometric equations were tested in order to retain those which seem to be the most explanatory of aboveground biomass according to dendrometric parameters.
The allometric equations were subjected to a series of statistical tests in order to meet all the validation conditions [25] [26]. Thus, each model is subject, at the probability threshold of 5%, respectively to: • Normality test (Shapiro-Wilk test) to check the normality of the residuals; • Test of the zero mean (One Sample Test) to check the nullity of the residuals; • Heteroscedasticity test (studentized Breusch-Pagan) to check the heterogeneity of the residues; • Autocorrelation test (Durbin-Watson test) for the independence of the residues.
When an equation meets these tests, an analysis of the information criterion (AIC) of the residual error (E) and especially of the standard residual error (CSR) is carried out. AIC establishes a compromise between bias and variance for a model [27]. The residual error (E) expresses the error linked to the prediction of a model. It is expressed as a percentage [28]. For each fraction of the biomass, we prioritized the models using the correlation coefficient (R) of the regression between the predicted biomass and the observed biomass.

Dendrometric Characteristics of the Sample
The results of the population structure of the sampled Sclerocarya birrea and

Development of Allometric Model for Biomass
A correlation matrix ( The results of the correlation showed that the most explanatory dendrometric parameter of the biomass of the species Boscia senegalensis is the surface of the crown and that of the species Sclerocarya birrea is the diameter at 1.30. These two parameters for each species subjected to tests on five (5) models of equations (polynomial, linear, power, exponential and logarithmic) for a possible prediction of the biomass. Table 3 shows the results obtained.
The tests are carried out with a probability calculated at the threshold of 0.001; well below the critical threshold of 5% for all models. This indicates that all of the allometric equations have good correlation coefficients overall. Thus, the regressions whose coefficient of determination R 2 is greater than or equal to 0.80 have been retained.
The best models are then the polynomial regressions of order 2 (y = ax 2 + bx + c) and linear (y = ax + b) which are highly significant (P-value > 0.0001) and which have the best coefficients of determination (R 2 ) close to 1. Figure 3 show the results obtained for Boscia senegalensis (E1 and E2) and for Sclerocarya birrea (E3 and E4) for the linear and polynomial order model.

Discussion
The approach based on allometric equations which make it possible to directly estimate the total or partial biomass of a tree as a function of predictors was recommended in this study. Thus, to develop allometric models of the two species, the sample size was 43 individuals for Boscia senegalensis and 15 individuals for Sclerocarya birrea. This seems sufficient to us because [25] [37] in which the number of individuals retained was less than 20 due to the limited availability of trees. This same case applies to Sclerocarya birrea, a species which has significantly decreased in the Ferlo area since the beginning of the drought in the 1970 [38].
This study showed that the most important predictor of the biomass of Boscia senegalensis in Ferlo is the area of the crown (m 2 ). Our results are in line with those of [30] who developed regressions to estimate the biomass of two species of shrubs native to the Sahel morphologically very close to B. senegalensis; these are Guiera senegalensis JF Gmel (Gs) and Piliostigma reticulatum (DC.) Hochst (Pr). However, these authors used the mean crown diameter as an explanatory factor for the biomass. Other authors like [39] and [40], have shown that the crossed crown diameter explains part of the variance of the residues in the Amazon basin and in the Congo basin. [40] indicates that taking crown dimensions into account significantly improves biomass estimates. These words are confirmed by recent work by Panzou [41].
However, estimating the diameter of the crown or the crown surface of these species poses risks in terms of confusion between individuals. The difficulty with this method is to obtain precise measurements of the diameter of the crowns of these very gregarious species and widely spread on the ground. However, the diameter at the base of the subjects is just as difficult to measure, because the species B. senegalensis is most often multi-stemmed, low-branched with very small trunks, often exploited for their wood; so that the residual branches are only regrowth [29]. Indeed, the introduction of crown mass in the reference models illustrates the interest that should be given to the architecture of trees.
For the species S. birrea, the total dry aerial biomass of the species was determined according to the diameter at breast height (DHP or diameter at 1.30 m).
[31] states that DHP is the most used parameter in allometric equations. Recent work by [42] confirmed that the best predictor of tree biomass was diameter at breast height. Several equations were tested (linear, logarithmic, power, exponential, polynomial of degree 2) with the dendrometric parameters measured in the field. The best prediction models are the second order polynomial allometric These observations were decisive in choosing the polynomial equation of order 2 for which the residual error and the AIC were lower; at the expense of the linear equation Similar studies were conducted by Kuyah et al. [44] and selections were made based on the Akaike criterion. Likewise Mbow et al. [28] developed allometric equations, the selection of which was based mainly on the low value of the standard residual error. For each model they developed, the CSR is less than 0.19. Fayolle et al. [45], for their part, selected cubic rate models by combining CSR with AIC. According to them, the best model is the one with the lowest AIC value and a low CSR value. The same procedure was applied in this study for the validation of the polynomial equations of the two species Boscia senegalensis and Sclerocarya Birrea.

Conclusions
This study made it possible to develop efficient models for estimating the biomass of the two woody species at Ferlo: Boscia senegalensis and Sclerocarya birrea by testing two mathematical models; linear and polynomial. The results of various statistical validation tests made it possible to select the polynomial equation of degrees 2 expressing the total dry aerial biomass of the species as a function: of diameter at breast height for S. birrea and of the crown surface for B. senegalensis. This work enabled us to retain the diameter at 1.30 m for the prediction of the aerial biomass of S. birrea and the crown surface for B. senegalensis.
These results could be very useful in assessing the amount of carbon sequestered by these species in the Ferlo area. In one way or another, they are a springboard for decision-making on climate change and adaptation policy.