Development of Allometric Equations to Determine the Biomass of Plant Components and the Total Storage of Carbon Dioxide in Young Mediterranean Argan Trees

Abstract

Morocco’s argan trees, native to forests, are now cultivated in large orchards within the Argan Biosphere Reserve, transforming “Arganiculture”. These orchards are anticipated to bolster carbon storage, but their precise contribution to carbon storage remains unclear. This study introduces for the first time allometric equations for estimating biomass in different components of argan plants within orchards. A total of 89 plant individuals, aged 2 to 6 years, were collected. Their diameter and total height were measured. The biomass, carbon content, and biomass carbon stock of each component were determined. The best-fit allometric equation incorporates diameter, height, growing years, and root-to-shoot ratio to estimate total biomass (R² = 0.95). The estimated total carbon biomass stock ranged from 0.01 to 0.82 t CO₂ ha⁻¹ for plants, at a density of 200 plants ha⁻¹. Between 2021 and 2023, the average annual carbon sequestration was 0.20 t CO₂ ha⁻¹ year⁻¹. This model offers valuable tools for use when species-specific equations during the establishment growing stage are unavailable, enhancing carbon sequestration quantification for more reliable results and informing climate change mitigation strategies. The allometric parameters serve as benchmarks for trees resembling the argan tree. The methodology could be adapted for other forest plants undergoing conversion to orchard cultivation.

1. Introduction

Biomass estimation is one of the most crucial steps in estimating carbon sequestration in different biomass components [1,2]. It is important to determine the future projections of carbon dioxide (CO₂) stored by biomass over the years [3]. This information is useful in ecology as it provides insights into ecosystem structure and function, serves as an indicator for sustainability, and helps in assessing ecosystem productivity and the global carbon budget [4,5].

Biomass estimation can be achieved using different methods, including the direct application of allometric equations, the multiplication of stand volume by wood density, or the use of the biomass expansion factor, which is a measure of volume-to-biomass ratio [4,5,6]. These methodologies have a common requirement for generalized allometric equations, although they differ in terms of predictor variables. The former method is often used for younger plants, while the latter is more appropriate for mature forest trees due to its rarity and adherence to ethical guidelines and regulations, aiming to mitigate any potential ecological impact on ecosystems [4,7].

There has been recent interest in the development of the allometric equation method for biomass estimation, which is a cost-effective technique and uses easily measurable variables such as diameter and height. Additionally, it has the potential to adapt to specific species, taking into account their unique characteristics and growth patterns [8]. These specialized models can also include site-specific factors, such as soil type, climate, and topography, which can enhance the accuracy, efficiency, and conciseness of biomass estimates and reduce errors in carbon biomass stock assessments [9,10,11,12].

This study focuses on creating allometric equations for estimating biomass in different components of the argan plant (Argania spinosa (L) Skeels), a vital species in Morocco supporting local economies and ecosystems. Argan trees, predominantly found in the 830,000-hectare Argan Biosphere Reserve (ABR), face challenges due to the increased demand for argan oil, impacting forest density and sustainability. To address this, Morocco has initiated the domestication of forest-origin species by establishing argan orchard perimeters in vulnerable areas [13]. This innovative project, based around the Arganiculture concept, aims to meet national commitments for environmental protection and sustainability outlined in the nationally determined contributions (NDCs). Arganiculture is expected to enhance carbon storage, mitigate soil erosion, and sustain the agroforestry system, supporting both mitigation and adaptation efforts. The development of allometric equations to estimate Argania biomass holds immense potential for quantifying the carbon sequestration capabilities within established orchards. These data would significantly contribute to policy formulation, enabling informed decisions on land use, conservation strategies, and carbon offset initiatives [14].

In earlier studies, Benzyane [15] and Belghazi [16] employed a semi-destructive method to estimate the biomass of argan trees in the Haha plateau (Essaouira region). Benzyane [15] generalized the equation for mature trees considered as part of a high forest, while Belghazi [16] focused on young stands classified as coppice pushed on old and already-well-established root systems. Determining the age of Argania trees in forest stands posed challenges; however, these studies relied on parameters like tree height and trunk circumference. The published biomass equations focus on large argan trees with diameters > 10 cm. No attempt has been made to explore the biomass estimation of argan trees at the establishment growing stage; these are considerably smaller and contribute little to the total stand biomass. In our current research, allometric equations focus on argan plants of known ages and are derived from nursery seedlings subsequently transplanted into the newly established Arganiculture orchards. By deriving allometric equations from nursery seedlings, this research aims to provide a more comprehensive understanding of the biomass of argan trees at the established growth stage, which can be identified as young argan plants. This approach contributes to a more accurate assessment of total stand biomass in argan forests. It enables more informed forest management and conservation strategies, improves carbon sequestration assessments, and contributes to better modeling of forest growth and development [14].

Accordingly, the present study attempts to (1) develop allometric equations for young argan plants and their components (e.g., leaves, stem, small branches, roots) to estimate their biomass, (2) apply these equations to estimate the total biomass in selected studied orchards, and (3) convert the estimated biomass to total carbon dioxide storage.

2. Materials and Methods

2.1. Study Area

The study was conducted in argan orchards across the marginal and vulnerable areas within the regions of Souss Massa, Marrakech-Safi, and Guelmim Oued Noun, all located within the ABR in the North Africa region. Figure 1 presents the orchard’s locations in the ABR. These areas are within three different climatic zones, including the semi-arid climatic zone, the arid climatic zone, and the pre-arid or Saharan climatic zone. The mean annual temperature is 18.05 °C, with average monthly temperatures ranging between 9.4 °C (December, January) and 26 °C (July, August). The mean annual precipitation is 301.6 mm, with the highest rainfall occurring from October to April, with extremely low precipitation occurring between June and August [17]. The argan soils in these areas are mostly lithosols and regosols, associated with fluvisols and saline soils on lowlands [18]. The argan plants studied exhibit different growing stages, ranging from 2 to 6 years.

2.2. Sampling and Field Measurement

At the beginning of the study in 2021, six individual argan plant samples were randomly collected from 11 experimental plots (each 0.5 ha) across 6 distinct argan orchard perimeters within the ABR, following the experimental design (Figure 2). In total, 66 young argan plants were collected. Plants in newly transplanted orchards were only 2, 3, and 6 years old, creating a data gap. The biomass trend of plants aged between 3 and 6 years could be difficult to interpret without data on intermediate ages. To avoid the risk of a false biomass trend due to missing age groups, additional plants were collected later in 2023, when they had reached 4 and 5 years of age. A total of 36 plants were collected from 6 plots, distributed across 3 distinct perimeters within the ABR. The potential seasonal differences between the initial and later data collection were considered. The plots maintained a density of 200 argan plants per hectare. The total height (H) and diameter (D) of the sampled plants were measured using a measuring tape and calliper. The diameter was measured at the base of the stem. Degraded plants without leaves or with broken stems were removed, resulting in a sample size of 89 young plants.

2.3. Laboratory Analysis

The leaves, stems, small branches, and roots were separated from each harvested plant. In the case of very small individuals, the stem and small branches were considered as one part [19]. The fresh biomass of each component was weighed separately. Roots were washed and cleaned of adhering soil, drained, and air-dried, and their weight were recorded. A sub-sample were then oven-dried at 70 °C (leaves) and 105 °C (stems, branches, and roots) until a constant weight was achieved. Root-to-shoot ratio was calculated in argan plants by dividing the root weight by the shoot weight. The carbon concentration of each component was measured using the ignition loss method [20]. The above- and below-ground carbon stock was calculated by multiplying the tree’s biomass by its carbon content [21]. To convert carbon stock to CO₂ emissions, we multiplied it by 3.67.

2.4. Allometric Model Development and Statistical Analysis

The study analysed the relationship between leaf, stem, and root biomass as dependent variable, and specific independent variables including diameter (D), height (H), growing years (age), and root-to-shoot ratio [22]. A linear regression was applied (Equation (1)) and the data were checked for linear relationship, independence, homoscedasticity, and normality following the protocol described by Zuur et al. [23]. To enhance linearity and homoscedasticity, the regression models underwent the natural logarithm transformation of the variables (Equation (2)) [4,24]. Possible sources of error were checked for, and outliers were identified. Only data that were correctly identified were retained for this study. To remove bias when converting natural logarithmic values to biomass, a correction factor (CF) was derived for each equation (Equation (3)), following Sprugel’s [25] method. The correction factor is determined by the standard error of estimate (SEE) of the regression.

$$\mathrm{B}\mathrm{i}\mathrm{o}\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}=\mathrm{a}\mathrm{X}$$

(1)

$$\mathrm{L}\mathrm{n}\left(\mathrm{B}\mathrm{i}\mathrm{o}\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\right)=\mathrm{l}\mathrm{n}\left(\mathrm{a}\right)+\mathrm{b}\mathrm{L}\mathrm{n}\left(\mathrm{X}\right)$$

(2)

$$\mathrm{B}\mathrm{i}\mathrm{o}\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}=e^a{\mathrm{X}}^{\mathrm{b}}\mathrm{C}\mathrm{F}$$

(3)

where X is the independent variable (e.g., D), a and b are empirically estimated scaling factors, and CF is the correction factor.

Several studies have referred to the allometric models frequently used to estimate biomass [9,21,26,27,28]. The best allometric models were evaluated and selected based on the primary criteria as outlined by Chave et al. [4].

Table 1. Goodness-of-fit indicators and model-selection criteria.

Criteria	Description	Best Selection	Reference
Coefficient of determination (R2)	Measures the proportion of the variance in the dependent variable (R2) that is explained by the independent variables in the model	Highest value	[4,19,30]
Adjusted coefficient of determination (R2)	Adjusts R2 by acknowledging the number of independent variables in the model	Highest value
Residual standard deviation (RSE)	Describes the difference between the standard deviations of the observed values compared with the predicted values	Lowest value
Root-mean-square error (RMSE)	Measures the average distance between the predicted values and the observed values	Lowest value
Akaike information criteria (AIC)	Minimizes issues associated with overfitting	Lowest value	[31]
Durbin–Watson (DW)	Tests the autocorrelation of residuals in a linear regression model and reflect the independence of the residuals	0 < DW < 2 indicates a positive correlation between successive residues 2 < DW < 4 indicates a negative correlation between residues. DW = 2 indicates no correlation	[32]
Mean squared error (MSE)	Measure the average difference between the predicted and observed values in LOOCV data	Lowest value	[29]

summarises the primary criteria and their descriptions and interpretations. The allometric models was validated using the leave-one-out cross-validation (LOOCV) technique, in which one data point at a time is systematically left out and the model is trained on the remaining data points [29,30]. This iterative process is repeated for each data point in the dataset, enabling multiple rounds of training and validation to assess the models’ performance. The LOOCV technique assesses its predictive accuracy and reliability. The mean squared error (MSE) was adopted as robust metric for evaluating model performance within the LOOCV framework. The statistical modelling was performed using the lm() function from the R package, and the statistical comparisons were made using the basic R package under version R 3.2.3.

The study analyzed the effect of growing years and argan plant components on carbon content using a two-way analysis of variance (ANOVA) after checking for normality and homogeneity of variance. The statistical analysis was conducted using the SPSS program (IBM Corp. Released in 2019, Version 26), and significance was determined at p < 0.05 level.

3. Results

3.1. Biomass and Carbon Content

Table 2. Descriptive statistics of young plants’ dry biomass components (kg), diameter (D), and total height (H), collected from argan orchards located within the Argan Biosphere Reserve in North Africa.

	Dry Biomass (kg/Plant)					D (cm)	H (m)
	Leaf	Stem	Root	Total	Shoot-to-Root Ratio
Min.	0.0008	0.002	0.0006	0.006	0.08	0.34	0.29
Max.	1.02	2.05	1.42	4.48	2.67	7.91	1.42
Mean	0.14	0.22	0.12	0.48	0.64	1.61	0.68
SD	0.22	0.39	0.26	0.85	0.51	1.28	0.25
n *	89	89	89	89	89	89	89

* Min, minimal; Max, maximal; SD, standard deviation; n, number of young plants sampled.

shows that the mean D, H, and total dry biomass for selected young argan plants were 1.61 ± 1.28 cm, 0.68 ± 0.25 m, and 0.48 ± 0.85 kg, respectively. The biomass distribution was concentrated mainly in the stems, which represented 49% of the total dry biomass, with an average of 0.22 ± 0.39 kg. Roots represented 27% of the total dry biomass, with an average of 0.12 ± 0.26 kg, while the leaves represented 24% of the total dry biomass, with an average of 0.14 ± 0.22 kg. The mean root-to-shoot ratio for the study was 0.64, with a range of 2.67 for the smallest diameter classes and 0.69 for the largest.

Figure 3 illustrates the relationship between diameter and measured dry biomass, alongside height and measured biomass for different components of young argan plants. The analysis indicates that biomass is directly affected by both diameter and height. However, this effect is non-linear.

Figure 4 shows the mean carbon content among different components of young plants. The carbon content varied significantly (p < 0.001) based on the tree component and its age (

Table 3. Two-way ANOVA results on the effect of growing years and argan plant components on carbon content.

Source	Type III Sum of Squares	df	Mean Square	F	Sig.
Growing years	1413.21	4	353.30	26.89	0.000
Plant components	3383.92	2	1691.96	128.80	0.000
Growing years × plant components	2365.67	8	295.71	22.51	0.000

). The root had a lower carbon concentration (33–55%), while the stem and leaf of the argan tree had a significantly higher carbon content (52–56%).

The study found a medium, yet significant, correlation (0.5 < r < 0.9) between the biomass of young argan plant components and growing years, which were the dependent and the independent variables, respectively, as shown in Figure 5. Additionally, a large, significant correlation was observed between root and stem biomass (r = 0.95) and between diameter and both stem and leaf biomass (r = 0.90 and r = 0.92, respectively). The results also indicated a negative correlation between the shoot-to-root ratio and years of growth (r = −0.30).

3.2. Biomass Model Generation

Table 4. Regression models of allometric equation and associated coefficients used for the estimation of dry biomass in different components of argan plants including leaf, stem, root, and total biomass. n is the number of young plants studied.

	Note	Allometric Equation Model	n	Coefficients
				a	b	c	d	e
Leaf	1	Ln b = a + b Ln (D)	89	−4.35 *	2.89 *	-	-	-
	2	Ln b = a + b Ln (D) + c Ln (H)	89	−3.57 *	2.27 *	1.44 *	-	-
	3	Ln b = a + b Ln (D) + c Ln (H) + d Ln (age)	89	−6.95 *	0.88 *	1.21 *	3.29 *	-
	4	Ln b = a + b Ln (D × age)	89	−6.39 *	2.04 *	-	-	-
	5	Ln b = a + b Ln (D × H)	89	−3.26 *	2.00 *	-	-	-
	6	Ln b = a + b Ln (D × H × age)	89	−5.07 *	1.56 *	-	-	-
	7	Ln b = a + b Ln (D2 × H)	89	−3.71 *	1.20 *	-	-	-
	8	Ln b = a + b Ln (D2 × H × age)	89	−4.83 *	1.02 *	-	-	-
	9	Ln b = a + b Ln (D2 × H) + c ln (age)	89	−7.21 *	0.60 *	3.21 *	-	-
	10	Ln b = a + b (D) × c (H)	89	−9.92 *	2.84 *	6.18 *	−1.90 *	-
	11	Ln b = a + b (D) × c (age)	89	−10.83 *	2.79 *	1.81 *	−0.50 *	-
	12	Ln b = a + b (D) × c (H) × d (age)	89	−10.08 *	1.38	0.43	1.33 *	-
Stem	1	Ln b = a + b Ln (D)	89	−3.40 *	2.39 *	-	-	-
	2	Ln b = a + b Ln (D) + c Ln (H)	89	−3.02 *	2.08 *	0.71 *	-	-
	3	Ln b = a + b Ln (D) + c Ln (H) + d Ln (age)	89	−4.90 *	1.30 *	0.58	-	-
	4	Ln b = a + b Ln (D × age)	89	−5.04 *	1.65 *	-	-	-
	5	Ln b = a + b Ln (D × H)	89	−2.50 *	1.63 *	-	-	-
	6	Ln b = a + b Ln (D × H × age)	89	−3.97 *	1.26 *	-	-	-
	7	Ln b = a + b Ln (D2 × H)	89	−2.87 *	0.98 *	-	-	-
	8	Ln b = a + b Ln (D2 × H × age)	89	−3.78 *	0.83 *	-	-	-
	9	Ln b = a + b Ln (D2 × H) + ln (age)	89	−4.88 *	0.63 *	1.84 *	-	-
	10	Ln b = a + b (D × H)	89	−7.59 *	2.36 *	4.21 *	−1.45 *	-
	11	Ln b = a + b (D × age)	89	−8.15 *	2.20 *	1.25 *	−0.35 *	-
	12	Ln b = a + b (D × H × age)	89	−7.09 *	1.11	−0.17	0.63	-
Root	1	Ln b = a + b Ln (D)	89	−4.06 *	2.23 *	-	-	-
	2	Ln b = a + b Ln (D) + c Ln (H)	89	−3.84 *	2.06 *	0.40 *	-	-
	3	Ln b = a + b Ln (D) + c Ln (H) + d Ln (age)	89	−5.05 *	1.56 *	0.32	-	-
	4	Ln b = a + b Ln (D × age)	89	−5.56 *	1.52 *	-	-	-
	5	Ln b = a + b Ln (D × H)	89	−3.22 *	1.52 *	-	-	-
	6	Ln b = a + b Ln (D × H × age)	89	−4.57 *	1.16 *	-	-	-
	7	Ln b = a + b Ln (D2 × H)	89	−3.56 *	0.91 *	-	-	-
	8	Ln b = a + b Ln (D2 × H × age)	89	−4.40 *	0.77 *	-	-	-
	9	Ln b = a + b Ln (D2 × H) + ln (age)	89	−4.89 *	0.68 *	1.22 *	-	-
	10	Ln b = a + b (D × H)	89	−7.56 *	2.01 *	3.30 *	-	-
	11	Ln b = a + b (D × age)	89	−7.95 *	1.78 *	0.97 *	-	-
	12	Ln b = a + b (D × H × age)	89	−7.78 *	3.93 *	−3.08	-	-
	13	Ln b = a + b Ln (D) + c Ln (H) + d Ln (age) + e Ln (root-to-shoot ratio)	89	−5.00 *	1.48 *	0.40 *	1.38 *	0.31 *
	14	Ln b = a + b Ln (D) + c Ln (H) + d Ln (ABG)	89	−2.81 *	1.20 *	0.01	0.41 *	-

* Significant difference of 0.05.

presents models of allometric equations and their corresponding coefficients used to estimate the biomass of leaf, stem, and root. The statistical parameters of these allometric equation models for each young plant’s components are compared in

Table 5. Statistical properties of regression models to estimate dry biomass in different components of argan plants including leaf, stem, root, and total biomass. Initials refer to statistical parameters mentioned in Table 1; CF stands for the correction factor.

	Note	R2	R2 Adjusted	RSE	AIC	RSME	DW	CF	MSE
Leaf	1	0.85	0.85	0.85	−26.31	4.29	1	1.53	0.74
	2	0.87	0.87	0.80	−35.53	4.30	2	1.49	0.67
	3	0.95	0.95	0.50	−120.2	4.35	2	1.28	0.26
	4	0.93	0.93	0.61	−85.98	4.33	2	1.36	0.38
	5	0.87	0.87	0.81	−35.70	4.30	2	1.50	0.67
	6	0.93	0.92	0.60	−90.01	4.33	2	1.34	0.36
	7	0.87	0.87	0.80	−37.18	4.30	2	1.49	0.66
	8	0.91	0.91	0.66	−71.43	4.33	2	1.39	0.45
	9	0.95	0.95	0.51	−116.45	4.35	2	1.28	0.27
	10	0.87	0.87	0.82	−32.41	4.30	2	1.50	0.69
	11	0.94	0.94	0.54	−106.19	4.35	2	1.30	0.30
	12	0.96	0.95	0.48	−127.84	4.35	2	1.26	0.23
Stem	1	0.84	0.83	0.75	−46.99	3.42	2	1.46	0.59
	2	0.84	0.84	0.74	−48.31	3.42	2	1.45	0.58
	3	0.88	0.87	0.66	−68.88	3.44	2	1.39	0.47
	4	0.87	0.87	0.66	−69.63	3.44	2	1.40	0.45
	5	0.83	0.83	0.76	−44.63	3.42	2	1.46	0.60
	6	0.87	0.86	0.67	−67.07	3.43	2	1.40	0.47
	7	0.84	0.84	0.74	−49.83	3.42	2	1.45	0.57
	8	0.87	0.86	0.68	−65.27	3.44	2	1.41	0.47
	9	0.88	0.87	0.66	−70.86	3.44	1	1.39	0.45
	10	0.83	0.82	0.78	−39.26	3.42	1	1.47	0.64
	11	0.86	0.86	0.70	−60.06	3.44	2	1.41	0.51
	12	0.88	0.86	0.68	−59.36	3.44	1	1.39	0.51
Root	1	0.89	0.89	0.56	−99.52	3.95	2	1.32	0.33
	2	0.89	0.89	0.56	−99.42	3.95	2	1.32	0.33
	3	0.91	0.90	0.52	−113.36	3.96	2	1.29	0.28
	4	0.90	0.90	0.52	−114.61	3.96	2	1.29	0.27
	5	0.87	0.87	0.60	−87.38	3.95	2	1.35	0.37
	6	0.90	0.90	0.54	−107.61	3.96	2	1.31	0.30
	7	0.89	0.89	0.57	−98.38	3.95	2	1.33	0.33
	8	0.90	0.90	0.52	−112.87	3.96	2	1.30	0.28
	9	0.91	0.90	0.52	−113.41	3.96	2	1.30	0.28
	10	0.86	0.86	0.63	−77.58	3.94	2	1.36	0.44
	11	0.89	0.89	0.55	−100.26	3.95	2	1.32	0.34
	12	0.91	0.91	0.52	−108.49	3.96	2	1.28	0.29
	13	0.93	0.92	0.47	−127.6	3.97	2	1.26	0.24
	14	0.92	0.91	0.49	−124.04	3.96	2	1.27	0.25
Total biomass		0.95	0.94	0.42	−148	2.78	2	1.23	0.19

. This study reported higher values of R² and adjusted R² (0.85 to 0.96 and 0.86 to 0.93, respectively) for leaf and root parts, while lower values (0.82 to 0.88) were recorded for stem parts of young plants.

For leaf biomass, model 9 was identified as the best-fitting regression equation, explaining 95% of the variance. It had the lowest values of RSE, AIC, and RSME compared to other models (RSE = 0.51, AIC= −116.45, RSME = 4.35) and no potential for heteroskedasticity. For stem biomass, only models 1, 2, 10, and 11 showed no heteroskedasticity of variance. Model 11 was selected as the best allometric model with the highest R² and R²-adjusted value of 0.86 and the lowest RSE and AIC (RSE = 0.70, AIC= −60.06, RSME = 3.44). For root biomass, model 4 with three variables (D, H, and age) met all the selection criteria with an R² of 0.90. However, when specific variables such as the root-to-shoot ratio (model 13) and aboveground biomass (ABG) (model 14) were added, the R² increased to 0.93 and 0.92, respectively, while RSE decreased from 0.51 to 0.47 and 0.49, respectively. Furthermore, the AIC, RMSE, and MSE parameters decreased. Model 13 was selected as the most reliable and strong model for predicting root biomass.

The residuals of the three selected models were considered independent, as indicated by a Durbin–Watson statistic of 2 (DW = 2). Model 9 had an MSE of 0.27 for leaf biomass, Model 11 had an MSE of 0.51 for stem biomass, and Model 13 had an MSE of 0.24, representing the lowest values among the models presented in Table 5. The selected allometric models for leaf and roots were more reliable and efficient compared to the stem model (Table 5).

In all fitted models for all three biomass components, the residuals did not reveal heterogeneity of variance, as shown in Figure 6. Q-Q plots demonstrate a close alignment of residuals with the theoretical normal distribution, which supports model assumptions. Predicted vs. observed values plots show a strong linear relationship, indicating good model-prediction accuracy.

3.3. Biomass Carbon Stock

The average biomass per plant of different components varied across growing years, with a total biomass range of 0.03 to 2.34 kg per plant (Figure 7).

Table 6. Total biomass of leaves, stems, and roots of argan plants in the orchards studied.

Growing Years	Biomass (t ha−1)
	Leaf	Stem	Root	Total
2	0.001 ± 0.001	0.003 ± 0.002	0.002 ± 0.002	0.006 ± 0.002
3	0.003 ± 0.002	0.009 ± 0.004	0.004 ± 0.003	0.017 ± 0.003
4	0.013 ± 0.011	0.032 ± 0.024	0.01 ± 0.009	0.055 ± 0.015
5	0.082 ± 0.063	0.125 ± 0.065	0.046 ± 0.036	0.253 ± 0.055
6	0.201 ± 0.106	0.185 ± 0.023	0.083 ± 0.051	0.469 ± 0.060

presents the total biomass of leaves, stems, roots of argan plants in the studied orchards. The total carbon biomass of 200 argan plants per hectare at the ages of 2 to 6 years ranges from 0.003 to 0.22 t C ha⁻¹, corresponding to 0.01 to 0.82 t CO₂ ha⁻¹ (Figure 8). From 2021 to 2023, the average annual carbon sequestration was 0.20 tonnes of CO₂ per hectare per year.

4. Discussion

Allometric models were developed to estimate the biomass of different components. including stems, leaves, roots, and the total biomass of argan plants within recently established argan orchards perimeters across different regions within the Argan Biosphere Reserve. The studied plants were 2 to 6 years old, corresponding to the establishment growing stage (encompassing the lag phase and the very early part of the exponential growth phase). They exhibited diameters ranging from 0.33 to 7.91 cm and a height between 0.29 and 1.42 m. The mean root-to-shoot ratio obtained was 0.64. The root-to-shoot ratio indicates that there are on average 0.64 units of root per 1 unit of aboveground biomass across the plants in the study. The variation in the root-to-shoot ratio across diameter classes indicates that smaller plants allocate a larger proportion of their resources to belowground structures compared to larger plants.

Young plants with smaller stems may require larger root systems for stability and support in arid and semi-arid climates. This could be explained by the need to acquire resources such as water and nutrients in the soil [33]. The ratio varies with environmental conditions such as precipitation, soil moisture, texture, and fertility and stand conditions such as age, height, forest type, or origin [34,35].

The study of carbon content in plant components identified differences in the mean carbon content of roots based on the age of the argan plants. In particular, the carbon content of the roots of argan plants aged between 4 and 5 years old was higher than that of other growing years. This variation could be attributed to natural fluctuations in carbon content throughout the growing season and across years, which are influenced by environmental factors such as temperature, rainfall, and nutrient availability. Harvesting at different times (2021 vs. 2023) may capture these variations. Furthermore, differences in management practices may also be a contributing factor. If there had been changes in management practices, such as fertilization or irrigation, between 2021 and 2023, then this could have had a greater impact on the root C content.

The study revealed that the roots of argan trees have a lower carbon concentration (33–55%) compared to the stems and leaves (52–56%). This could be explained by argan plant roots concentrating on acquiring resources and water directing less carbon towards the belowground parts of the plant. Additionally, age-related variations in carbon content can occur, with younger plants investing more carbon in rapid growth and development [33,36]. Mahmood et al. [26] found that the carbon content was between 42% and 47% in leaves and between 40 and 49% in branches, bark, and stems in tropical evergreen forests. Thomas et al. [37] reported a wide variation in carbon concentration of 45.7–60.7% in subtropical/Mediterranean species, and Ma et al. [38] found that the carbon content in crop roots was 38.20 ± 5.23%. In the global assessments, carbon content has been assumed to be 50% of tree biomass; however, recent studies indicate that this assumption is not accurate, with substantial variation in carbon content between tree species, as well as between tissue types [37].

The study results show a non-linear relationship between diameter and height, which suggests that a simple regression (linear model) might not accurately represent the data. These involve using non-linear equations (e.g., power functions, exponential functions) or applying transformations to the data to linearize the relationship. Among the transformation methods, log–log models were most often reported in many studies of different ecosystems [4,26,39].

Several studies in the literature recommend that biomass equations based on both diameter (D) and height (H) are more accurate than equations based only on D [4,40,41]. Also, the precision and the accuracy of allometric equations increased with the level of specificity of equations as found by Paul et al. [42]. This study included diameter, height, age, and root-to-shoot ratio for the root biomass model as specific independent variables. The results revealed that the best model for leaves included D, H, and age; D and age for stem biomass, and D, H, age, and root–shoot ratio for root biomass. Therefore, the fit model for total biomass included all the mentioned variables with the highest biomass variation (R² = 0.95). On the other hand, the accuracy of biomass estimation largely depends on the appropriate selection of allometric models [26,43]. In the study, both models 3 and 9 performed well in predicting leaf biomass, with high R-squared adjusted values of 0.95. However, model 1 showed a lower AIC score than model 9, suggesting that it may capture the relationship between predictors and biomass slightly better. Model 3, on the other hand, shows a potential for heteroskedasticity, which means that the error variances may not be consistent across the data. This could have an impact on the reliability of the conclusions drawn from the model. Our findings agree with those of Mokany et al. [35]. They emphasize the need for reliable root–shoot ratios across various vegetation types to enhance the accuracy of root biomass estimates, particularly for purposes such as National Greenhouse Gas Inventories and carbon accounting and for studies of ecosystem dynamics.

Henry et al. [14] highlighted the limited consideration of root biomass in current carbon (C) inventories under an arid climate (only 1.3% of equations). They reported the challenges in measuring root biomass as the high cost and time required for the direct measurement of root biomass and the difficulty of extracting the entire root [14]. In this study, the roots of 5- and 6-year-old argan plants were found to have deeper roots and develop further into the soil compared to the above-ground parts. This limited the extraction of these root samples. This suggests that we should consider alternative methods for estimating root biomass for argan, such as fractal geometry, minirhizotrons, and ground-penetrating radar. The importance of accurate root biomass data is emphasized, as they can contribute to improving carbon inventories and enhancing our understanding of ecosystem dynamics.

In summary, this study formulated biomass allometric equations for each component of young argan plants, including the leaf (Equation (4)), stem (Equation (5)), root (Equation (6)), and total biomass (Equation (7)). The total biomass is calculated by summing the biomass of each component.

$${Biomass}_{Leaf}=e^{-7.21}\times {\left(D^{2}H\right)}^{0.6}\times {age}^{3.2}\times 1.28$$

(4)

$${Biomass}_{Stem}=e^{(-8.15+\left(2.20\times D\right)+\left(1.24\times age\right)-(0.35\times \mathrm{D}\times \mathrm{a}\mathrm{g}\mathrm{e}\left)\right)}\times 1.41$$

(5)

$${Biomass}_{Root}=e^{-5}\times D^{1.48}\times H^{0.4}\times {age}^{1.38}\times {Roottoshootratio}^{0.31}\times 1.26$$

(6)

$${Biomass}_{TotalBiomass}={e^{-4.2}\times D}^{1.36}\times H^{0.57}\times {age}^{1.67}\times {Ratioshoottoroot}^{-0.3}\times 1.23$$

(7)

The study demonstrates that carbon biomass storage increases with argan plant age, ranging from 0.01 to 0.82 t CO₂ ha⁻¹. This highlights the significance of conserving older argan trees to improve carbon sequestration and inform conservation strategies. The total biomass of argan plants in the orchards studied was between 0.006 ± 0.002 and 0.47 ± 0.06 tonnes of dry biomass (DB) per hectare. The findings of the current study differ from those of the Belghazi [16] study in terms of reported biomass values. Belghazi [16] found that the total dry aboveground biomass of a young argan coppice aged 5 years old was 1.62 t ha⁻¹ for a density of 75 coppice ha⁻¹, corresponding to 21.6 kg per coppice [16]. This value is approximately 21 times higher than the current study’s value (1 kg per plant). The observed difference could be attributed to the disparity in stand characteristics. While Belghazi [16] studied coppice derived from well-established root systems, our study focused on plants grown from nursery seedlings subsequently transplanted into the field. In coppicing practice, trees are trimmed close to the ground, stimulating vigorous new growth from the well-established root system. Variations in site and plant density, competition for water availability, and nutrient limitations may also affect growth.

Between 2021 and 2023, the average annual carbon sequestration within the studied age range of argan plants was 0.20 t CO₂ per hectare per year, representing the establishment phase of growth. The low rate observed in our findings could be attributed to the species-specific growth phase examined, in contrast to previous studies integrating the exponential growth phase. Environmental conditions, including soil properties, genetics, and arid and semi-arid climates with prolonged dry seasons, particularly those experienced in Morocco during the study period, could account for these differences. The observed carbon sequestration observed is lower than the reported values for some broader agroforestry systems. These systems have been found to have CO₂ removal rates ranging from 0.8 to 15.6 t CO₂ ha⁻¹ year⁻¹ during the first 20 years of growth [44]. Further research is required to investigate the long-term carbon sequestration potential of argan trees as they mature.

5. Conclusions

Allometric models were developed to estimate the biomass of different components including leaves, stems, roots, and total biomass of young argan plants (age ≤ 6 years). Additionally, the total carbon dioxide (CO₂) storage during this establishment growth phase was calculated for the different components. In this study, we found that the performance of allometric equations varied among plants biomass components and the independent variable also varied. The highest performance of the allometric models was found in total biomass estimates with high explained variance (R² = 0.95). Allometric equations provide biomass estimates based on diameter, height, age, and root-to-shoot ratio. This research has raised many questions in need of further investigation. Further work is needed to determine whether locally specific allometric equations should be developed to account for seasonal dynamics in estimating leaf biomass and to identify areas where fractal geometry can be used to estimate root biomass. This contribution can enhance the accuracy of biomass estimation models, leading to improved carbon inventories and a better understanding of ecosystem dynamics. The implementation of the new concept of Arganiculture through the recently established argan orchards in various regions of the ABR in Morocco presents an opportunity for research concerning argan plants. Sustained data collection and the monitoring of tree establishment, especially during the accelerated or exponential growth phase, will be crucial. This continued monitoring will aid in developing equations specific to various growth phases, encompassing exponential, linear, and deceleration phases. Such an approach will be essential to the comprehensive modelling and analysis of tree growth dynamics.