Assessment of a Cocoa-Based Agroforestry System in the Southwest of Colombia

Abstract

Cocoa-based agroforests play an important role in farmer livelihood and the global environment; however, despite these facts, their low yields and tree aging put at risk their fate. This project investigated the carbon storage potential, productivity, and economics of different agroforestry arrangements of cocoa (Theobroma cacao) with Melina (Gmelina arborea) trees, in the southwest of Colombia. We established the experiment under a Randomized Complete Blocks design with seven treatments and three repetitions. Different allometric models were tested. Allometric models were made for G. arborea trees with dbh, ranging between 30.24 and 50.11 cm. The total carbon accumulation fluctuated between 49.2 (Treatment 4) and 88.5 t ha⁻¹ (Treatment 2), soil organic matter (SOM) ranged between 9 and 17%, bulk density decreased from 0.83 to 0.77 g cm⁻³. Cocoa yield ranged between 311 kg ha⁻¹ year⁻¹ (Treatment 7, traditional farm) and 922 kg ha⁻¹ year⁻¹ (Treatment 6). Treatment 6 showed the best performance with a net present value (NPV) of COP 1,446,467 (US $337.6), an internal rate of return (IRR) of 42%, and a cost-benefit ratio (B/C) of 1.67%. The benefits of AFS were also evidenced in some of the physical and chemical soil properties. Despite local marginality, these cocoa agroforest arrangements are a viable alternative to improve the traditional (local) cocoa systems because cacao agroforest arrangements increased cacao yield and carbon storage becoming a suitable alternative to improve traditional systems.

1. Introduction

Food security and climate change represent one of the most worrisome threats to the global environment and humanity due to the impacts caused on human health, biodiversity, food security, economy, natural resources, and infrastructure [1]. These troubles will significantly threaten human fate because of their social, environmental, and economic impacts and the high cost of implementing adaptation and mitigation measures [2]. Therefore, the 2030 agenda for ‘Sustainable Development members’ calls attention to protecting the planet from degradation and taking urgent action to tackle climate change concerns [3].

Fortunately, many of these hazards can be reduced by increasing resilience and resource-efficient use in agricultural production systems [4], which will improve the local farmers’ adaptive capacity. Similarly, the FAO proposed a ‘climate-smart agriculture’ (CSA) approach, a tool to improve agricultural productivity and reduce yield variability over time under adverse climatic scenarios [4,5].

GHGs could be mitigated in two ways: by reducing anthropogenic CO₂ emissions or by creating and improving carbon sequestration sinks [6]. Agroforestry systems (AFS) and the mixture of crops and trees are a C sink and an alternative to mitigate the effect of the agricultural production systems [7] because they integrate agricultural landscapes with rural communities [8]. AFS, the art and science of farming with trees [9,10], is a multifunctional land-use system that offers environmental services in agricultural landscapes [9,11]. For instance, cacao agroforests preserve the natural soil biota, control soil erosion, and provide sustained land use land while maintaining suitable yields [12,13,14].

These systems can sequester and store atmospheric carbon, in agricultural lands at a low cost [7,8]. Growing windbreaks, shelterbelts, silvopastoral systems, forest farms, riparian buffers, woodlots, promoting natural regeneration of vegetation, and the conservation of forests make an enormous contribution to the local carbon budgets [11,12,13,14,15,16,17,18].

Trees in the AFS also provide numerous goods and environmental services that benefit farmers, landscapes, and infrastructure and reduce the susceptibility to extreme climatic events, making it a tool for Smart agriculture approaches [18,19,20,21,22,23]. Likewise, Agroforestry is considered a sustainable and efficient land management system, the AFS can contribute to the implementation of 9 out of the 17 SDGs, and special attention is paid to food security, climate change adaptation and mitigation, and biodiversity [24].

Environmentally sustainable practices are one of the highest priorities for agricultural systems in the tropics [25,26]. An overview of the main technologies currently used by cocoa growers, in Colombia, shows that cocoa growth under traditional production systems [27,28], with low technology, old cacao trees, and high shading. These conditions trigger fungal diseases such as frosty pod rot (Moniliophthora roreri) and Witch’s broom (Moniliophthora perniciosa) [29], which reduce substantially cocoa yields. In this scenario, traditional farms average a yield of 300 kg ha/year [27,30]. The outcome of various researchers conclude that these systems are not viable for cocoa farmers [16]; however, other researchers identify important social and economic co-benefits of environmentally-friendly cocoa production regarding reduced pesticide use, resource conservation, long-term productivity, soil health, and human welfare [31].

On the other hand, cocoa farming, however, is associated with numerous environmental, social, and economic concerns, such as deforestation, child labor, and farmers’ poverty [31], that lead to public and consumer pressure [32] and a growing claim for sustainably-produced cocoa [33]. Thus, cocoa traders and chocolate companies have started addressing farm-level sustainability through supply chain mechanisms [34].

Past research on cocoa sustainability has mostly focused only on child labor in the value cocoa chain [35], environmental impacts, and the relationship between environmentally-friendly farming practices and profitability [36].

Full-sun cocoa farming is currently the most widespread cocoa cultivation system in the world [37]; however, its negative effects including biodiversity loss, soil fertility depletion, and soil quality degradation, have incredibly received low attention. Some ecofriendly purposes must be studied to revert the ecological effects of full-sun cocoa systems.

T. cacao-G. arborea association has been little studied on the pacific coast of Colombia despite its good performance; thus, a better understanding of its economic and environmental effects is required [30], to offer different strategies to cocoa farmers’ decision makers about the new cocoa production systems in the country.

The potential of AFS to store aboveground carbon is estimated to be 1.9 × 10⁹ Mg C year⁻¹ intemperate, and 2.1 × 10⁹ Mg C year⁻¹ in tropical biomes [38]. Carbon accumulation in monoculture of trees and crops shows 40% and 84% less than AFS, demonstrating that AFS is an important carbon sink in agricultural lands [39,40,41].

This research is focused on answering what are the carbon storage potential and profitability of different cocoa-based agroforestry arrangements compared to traditional cocoa systems? Therefore, the purpose of this research is to assess cocoa-agroforestry arrangements’ potential to increase the yield and storage in atmospheric carbon compared to traditional cocoa systems. For that, understanding the agroforestry arrangements’ performance was important for adoption purposes taking into account the ‘view of the farmer’ which facilitates the implementation of improved agroforest arrangements [42].

2. Materials and Methods

2.1. Study Area

The research was carried out in Tumaco, Nariño, southwest of Colombia, located at 01°39′12′′ north latitude and 78°41′49′′ west longitude (Figure 1). The experimental zone, located in a Tropical Rain Forest (bh-T) [43] had an average temperature of 27 °C, relative humidity of 80%, precipitation of 2800 mm/year, and a solar brightness of 1008 h/year [44].

The agroforestry system was 10 years old, established under an experimental plot of four ha, with a Complete Randomized Blocks Design (CRBD), and encompassing three blocks and seven treatments. Each trial unit had 1600 m².

Table 1. Treatments, spacing, and density of cacao and Melina trees in the experimental design.

Treatments	Cacao		Melina
	Spacing (m2)	Trees/ha	Spacing (m2)	Trees/ha
1	3 × 3	1111	3 × 3	1111
2	4 × 4	625	4 × 4	625
3	3 × 4	833	8 × 6	208
4	3 × 4	833	12 × 6	139
5	3 × 4	833	16 × 6	104
6	3 × 4	833	3 × 3 × 7.5	440
7 *	7 × 7	200	12 × 12	69

* Traditional cocoa production system (control).

gives more details about treatments. The G. arborea trees have a dbh range between 30.24 and 54.11 cm, and a height range between 57.03 cm and 27.61 m, respectively.

2.2. Tree Sampling

The tree sample size was 70 trees (35 of G. Melina and 35 of T. cocoa), five for treatment chosen randomly to replicate the whole range of diameters and height in the treatments. Tree biomass was attained according to McDicken, and Picard et al. approach [45,46].

We cut Melina trees (five for treatment) at ground level and immediately: (i) separated four fractions of aboveground biomass (i.e., stem, branches, twigs, and leaves); (ii) weighted each fraction (total fresh weight) using a hanging field-scale (Golden Lark model, precision 200 g), and (iii) collected a sample of 500 g from each fraction of aboveground biomass and stored each sample in a paper bag, which was subsequently weighed on a precision balance (Kern 440-55N, precision 0.2 g, Ebingen, Germany).

In the lab, the samples were dried at a temperature of 64 °C until they reached a constant weight. the moisture content of the sample was determined with Formula (1). These values were extrapolated to the biomass of different components of the cut trees; then, using the 0.47 conversion factor [47] biomass-carbon carbon stock was attained.

$$Biomass=\frac{Totalfreshweight\times Dryweight}{Freshweight}\times 100$$

(1)

2.3. Data Processing

A total of 17 models were evaluated; eight equations were proposed by different authors (

Table 2. Allometric equations used to estimate the biomass potential of AFS.

Number	Author	Equation
1	Berkhout	bm = a + b × dbh
2	Kopezky	bm = a + b × dbh2
3	Hohenadl-Krenn	bm = a + b × dbh + c × dbh2
4	Husch	Ln bm = a + b × ln dbh
5	Spurr	bm = a + b × dbh2 × ht
6	Stoate	bm = a + b × dbh2 + c × dbh2 × ht + d × ht
7	Meyer	bm = a + b × dbh2 + c × dbh2 × ht + d × dbh2 × h
8	Schumacher-Hall	Log bm = a + b × ln dbh + c × ln × ht
9	Brenack	Log bm = a + b × dbh + c × 1/dbh
10	This study	Sqrt (bm) = a + b × dbh
11	This study	bm = a + b ln(dbh) + ln(ht)
12	This study	Sqrt (bm) = a + b × dbh + c × ht
13	This study	bm = a × exp(b × dbh)
14	This study	bm = a × dbh^b
15	This study	bm = a + b ln(dbh))

Source: Loetsch et al. [50]. bm = biomass (kg/tree) or C (kg/tree); dbh = diameter at the breast height (1.30 m), ht = total height (m); a, b, c, d = model parameters; ln = logarithm base e = 2.718282.

) and nine by the study authors. Some of these regression models included transformed data to estimate biomass based on trunk dbh and height. Although dbh is currently used for most local or regional biomass estimations, some researchers have suggested that both dbh and height should be included for larger-scale applications [48,49]. As such, we included height in some models for estimating biomass in these open-grown trees.

Before and after evaluating the best-fit model to the G. arborea biomass data, the homoscedasticity (constant variability of errors), normality errors, linear independence, and linearity of the residuals were tested. Homoscedasticity was accomplished by eliminating three observations (outliers) and applying the Breusch–Pagan test for constant variance. Normality was attained by using the QQ-plots and the normal curve, in this, some deviated points were observed in the tails, but they did not affect normality. Linear independence was found with Pearson’s correlation coefficient, which was not significant between explanatory variables. Finally, linearity was in some cases met using the exact valor of lambda [51] or log transforming response variables. A correction factor prevented us from bias in biomass prediction when log-transformed variables are used [52,53] (Equation (2)).

$$CF=\exp \left(\frac{SE{E}^2}{2}\right) or \exp \left(\frac{variance}{2}\right)$$

(2)

where CF is the correction factor, SEE the standard error of regression estimate, and variance is the square of the root-mean-square error (RMSE2) in logarithmic form. Finally, the validation process consisted of two steps. First, the database was split into two parts, one for training, which corresponded to 80% of the data, and the other for testing, which retained the remaining 20%. Second, the final competing models were evaluated with the variance inflation factor (VIF), the R2, and the mean squared prediction error (MSPE) [54,55,56]. After selecting the best-fit equation, graphic analysis of the student residuals was performed to test for normality and heteroscedasticity in the errors.

On the other hand, cocoa aboveground biomass was calculated by using a regression equation [57] which is based on the tree collar diameter at 30 cm as given in Equation (3).

$$LogAGB=-1.625+2.626\ast log\left(D30\right)$$

(3)

where AGB = Aboveground biomass; D30 = tree diameter at 30 cm aboveground.

Cocoa belowground biomass was attained with Equation (4) [58].

$$BGB=\exp [-1.0587+0.8836\ast Ln\left(AB\right)$$

(4)

where BGB = root biomass (t ha⁻¹); Ln = natural logarithm; exp: power base e.

AB = Total aboveground biomass (t ha⁻¹) of cocoa

Concerning cocoa yield, in all treatments, it was measured monthly.

2.4. Data Analysis

Tree carbon storage and cocoa yield were compared with the One-way ANOVA procedure and the adjusted Tukey test to detect differences among treatments. Data processing was carried out with SAS 9.3 and R 3.5.3. (R Core Team, Vienna, Austria) software [59].

2.5. Economic Analysis

Production cost and cocoa yield from each treatment was monthly registered, while G. arborea trees were valued in situ at USD 15.79. The economic analysis was performed on a hectare basis over the 10-year period using the Net Present Value (NPV) (5), the Internal Rate of Return (IRR) (6), and the Benefit-Cost Ratio (BCR) (7) indexes.

$$NPV={\sum }_{t=1}^n\frac{C{F}_t}{{\left(1+r\right)}^t}-Co$$

(5)

$$\mathrm{IRR}=0=NPV={\sum }_{t=1}^n\frac{C{F}_t}{{\left(1+r\right)}^t}-Co$$

(6)

$$BCR=\frac{{{\displaystyle \sum }}^{}PV benefits}{{{\displaystyle \sum }}^{}PV costs}$$

(7)

where:

CF_t = net cash inflow-outflows during period t

r = internal rate of return that could be earned in alternative investments

t = time period cash flow is received

n = number of individual cash flows

Co = Total initial investment cost

PV = Present value

3. Results

3.1. Carbon Storage Potential of Agroforestry Arrangements

The agroforestry system with cocoa showed statistical differences (Pr < 0.0001) for aboveground C stored by the agroforestry system (T. cocoa and G. arborea). The highest C for the stock arrangements was treatment 7 (14.02 t Cha⁻¹ year⁻¹), while for the improved arrangements, it was treatment 2 (11.32 t Cha⁻¹ year⁻¹) (Figure 2C). The outcomes of the other treatments ranged between 8.73 and 6.29 tCha⁻¹ year⁻¹; accordingly, the total carbon accounted (below- and aboveground) by the agroforestry systems in 10 years was between 140.226 and 62.85 tCha⁻¹ (Figure 2D), which is equivalent to a 14.02 to 6.29 tCha⁻¹ year⁻¹.

G. arborea aboveground carbon had statistical differences (p < 0.0001) among treatments, treatment 2 displayed the highest amount of biomass stored with 5 t Cha⁻¹ (Figure 2A). T. cacao aboveground biomass had statistical differences (p < 0.0001) among treatments too. Treatment 7 showed the highest potential (6.7 t Cha⁻¹) (Figure 2B). The difference in carbon stored by traditional cocoa agroforest compared to improved arrangements was around 20%.

3.2. Biomass Allometric Equations

Comparing different allometric models using data from destructively sampled G. arborea trees, 15 models fitted the data rationally well, fulfilling almost all information criteria (

Table 3. Performance of the different competing allometric models in the information criteria indexes.

Model	R2	AIC	BIC	PRESS	Cp	VIF	FI
1	0.93	399.7	404	560.3	14.4	1.0	3.9
2	0.93	401.6	406.4	55.8	16.5	1.0	59.1
3	0.93	400	405	48.2	5.8	14.5	33.8
4	0.91	399.8	404.5	153.6	2.00	1.0	65.8
5	0.93	70.8	66.00	134. 8	16.4	139.6	59.8
6	0.94	405.5	410.2	0.30	2.80	144.8	19.4
7	0.94	401.6	407.9	0.30	15.2	66.1	3.8
8	0.91	70.8	66.00	155.5	18.7	13.7	67.5
9	0.91	68.8	62.5	150.1	1.80	144.8	65.5
10	0.92	118.0	125.9	143.1	2.80	1.0	62.6
11	0.92	403.5	411.4	134.8	17.4	124.5	60.6
12	0.92	114.6	119.3	147.7	4.80	13.7	63.3
13	0.93	402.9	412.4	155.5	2.60	1.0	7.4
14	0.93	402.8	413.9	134.9	5.60	1.0	33.24
15	0.93	399.8	404.5	160	16.4	1.0	68.7

R² = Determination coefficient; AIC = Akaike information criteria; BIC = Bayesian information criteria; PRESS = predicted residual sum of squares; VIF = Variance inflation factor; FI = Furnival index.

).

According to the results in Table 3, models 1, 2, 4, 10, 13, 14, and 15 were selected. These had the highest determination coefficient, VIF less than 10, lowest Akaike information criteria (AIC); Bayesian information criteria (BIC); predicted residual sum of squares (PRESS); Mallows’ Cp (Cp); Variance inflation factor (VIF) and Furnival index (FI). These competing models were tested to determine their accuracy using mean square prediction error (MSPE) (

Table 4. Competing allometric models selected to make biomass estimates for G. arborea.

Model Number	Model 1	R2	α	β	MSPE	Rank
1	Berkouth	0.93	−534.339	33.282	5.74	1
14	This study 3	0.93	1.8048	1.6469	5.78	2
4	Husch	0.91	0.3982	1.6982	5.82	3
10	This study 1	0.92	4.64771	0.58219	5.84	4
2	Kopezky	0.93	141.54096	0.39794	5.89	5
15	This study 4	0.93	−4153.61	1346.99	6.11	6
13	This study 2	0.93	164	0.0386	6.21	7

¹ 35 trees for model training and 1 tree drawn at random (testing) without replacement to evaluate the precision of each model repeated in 8 different trees. α, and β are regression coefficients, R² = Adjusted determination coefficient, MSPE = mean square prediction error.

). The best predictor model was Berkouth with MSPE = 5.74 which was very close to the ‘This study 3’ model.

3.3. Cocoa Yield

The variance analysis showed significant statistical differences (p > 0.0001) in cocoa yield by the treatments. Treatments 2, 3, 4, 5, 6 and 1 showed the highest yields (922, 845, 838, 837, 831, 710 kg ha⁻¹) (Figure 3A); treatment 1 presented the lowest. When the improved cocoa arrangements were compared to traditional cocoa farms (treatment 7), the improved arrangements showed significant differences. The traditional cocoa farm had the lowest yield, with an average of 310.67 kg ha⁻¹ year⁻¹.

There was also a positive effect of all AFS in reducing soil bulk density (Figure 3B) where there were no significant differences in the treatments within the blocks, but between the three blocks studied, there was a reduction. This reduction was equivalent to an average of 23%. These results show that the AFS is an alternative for improving soil health.

In the soil organic matter (SOM), there were no significant differences in the treatments within the blocks but between the three blocks studied there was an increase (approx. 17%) in the amount of organic matter transferred by the AFS to the soil (Figure 3C).

3.4. Economic Analysis

The economic analysis shows that all treatments had positive values in the indicators analyzed (

Table 5. Metrics of the financial analysis to estimate the profitability of the different agroforestry arrangements in San Luis Robles—Tumaco, Nariño.

Treatments	NPV1	IRR (%)	BCR
1	1,737,024	26	1.14
2	1,262,004	25	1.16
3	1,308,798	30	1.22
4	1,302,763	29	1.20
5	1,287,711	29	1.18
6	1,446,457	42	1.67
7	651,650	13	1.02

NPV¹ = Net Present Value (Colombian pesos -$ COP); IRR = Internal Rate of Return; BCR = Benefit-Cost Ratio.

). Compared to all improved cocoa arrangements, treatment 6 offers the best profitability with an NPV of 1446.45 (Colombian pesos—$ COP), an IRR of 42%, and a BCR of 1.67. The lowest performance treatment was treatment 2 with an NPV of 1262, an IRR of 25%, and a BCR of 1.16. Relating these values with those obtained by the cocoa traditional farm (treatment 7), the traditional farm displayed even lower values in these indices (NPV 651.65, IRR 13%, and a BCR of 1.02).

4. Discussions

4.1. Carbon Stored by the AFS

The carbon capture and storage potential depend on the agroforestry framework’s structure and functions dictated by various socio-economic and environmental factors [60]. In this study, total biomass (aboveground and belowground) in all treatments was lower than the control (traditional coca farm). The conceivable explanation behind this could be the effect of microclimatic interactions in cocoa-based agroforestry systems, the spacing [61], the age/diameter, and the miscellaneous structure of traditional farms. It is reported that radiant energy and rainfall interception by foliage and the temperature and humidity of the air surrounding the foliage [62] impact plant growth. This study detected that treatments with fewer woody trees and cocoa (traditional farm) but with multiple understory species growing with them stored more biomass. In the same way, the traditional cocoa agroforest was older than all modern cocoa arrangements, which affected the carbon storage budget. Despite cocoa’s high-density planting (HDP) being reported to reach higher cocoa yield than traditional ones (less than 700 trees/ha) [63], its effects on carbon storage are limited [64].

Many authors report the potential of C storage by G. arborea. For example, total biomass C stocks (above- and belowground) increased five-fold from the monoculture to the multi-shade tree system (from 11 to 57 Mg ha⁻¹), this increase was associated with a six-fold increase in aboveground biomass, but only a 3.5-fold increase in root biomass, indicating a clear shift in C allocation to aboveground tree organs with increasing shade for both cacao and shade trees [65].

G arborea plantation stored 41.6 t C ha⁻¹ at one year and three months old, in Costa Rica [66]; 22.9 t C ha⁻¹ at six years, 145.4 t C ha⁻¹ at nine years old in Madhya Pradesh, India [67], 8.31 t ha⁻¹ at 3 years old in Mexico [61], 15.54 t ha⁻¹ at four-year-old, in Mexico [68], 24.39 t ha⁻¹ at six years old in Colombia and [69], 41.6 t ha⁻¹ all five years old [70]. The C storage potential from these outcomes ranges from 2.77 to 40 t C ha⁻¹, reflecting the effect of environment, site index, and spacing on the C stored by G. arborea. Therefore, the range from 16.2 to 20.9 t ha⁻¹ yr⁻¹ [71] does not encompass the total variability of the G. melina in different scenarios.

T. cacao carbon storage potential in AFS seems to be in the range of agroforestry systems. For instance, a 13-year-old gmelina-cacao agroforestry system stored 185 Mg C/ha in the Philippines [72], which is lower than a pure gmelina plantation (294 Mg/ha). This could be due to the spacing because it favored the development of cacao trees. However, we found that in the opposite case, the trees of treatment 1, despite having the highest planting density (1111 trees ha⁻¹), reported the lowest C storage with a potential of 2.36 t tCha⁻¹ year⁻¹. One reason is that possibly the high humidity and the low luminosity in the tropical forest increased by the planting density caused more longitudinal growth than that in diameter, generating more foliage than wood. The average C storage potential ranging from 1.7 to 3.3 t tCha⁻¹ year⁻¹ [73,74] is lower than in this study.

Cocoa planted in very shady environments leads to lower rates of CO₂ assimilation and lower production of fruits and biomass. Regarding water availability, there are already reports that cocoa plants adjust their physiology [74]. Therefore, light and water are one of the factors that can favor or stress cocoa plants, becoming an important factor in plant growth and photosynthetic rate [75].

The high carbon stored in this study could partly be explained by the fast-growth tree rate and the high stand density in some of the AFS. Furthermore, site conditions in the study area support optimum growth for G. arborea and T. cacao. Therefore, it appears that the high nutrient requirement of G. arborea [76] is adequately met by the soils of the study area. This is to be expected since they were planted on humid tropical rainforest soils where biomass production is higher, and it is associated with soils with pH > 6 and C:N ratio > 20 [71]. Thus, soil organic matter is an important indicator of agricultural productivity and environmental resilience and is vital for soil structure stabilization, improvement of water-holding capacity, and retention of crucial plant nutrients [1].

The introduction of trees improves the potential of agricultural lands to store soil organic carbon [9,77,78,79,80]. Numerous authors report greater stocks of carbon in agroforestry than in field crops [9,81].

The values for bulk density found in this study corroborate the positive effects of AFS on soils. These values represent an improvement in the soil quality over the first 20 cm, which is very important to understory plants [22].

4.2. Allometric Models

We tested and proposed linear regression models of the square root, logarithm, and power of the biomass using coefficients extracted from tropical AFS biomass data. Our optimal models have only dbh as the independent variable, which met all statistical parameters [54]. Tree height was left out because of its effect on multicollinearity [54]. The models explain more than 90% of the sample’s variance with MSPE lower than 7%. These results are within the range of those reported by similar studies in AFS [11,81]. The response variable without transformation got the best accuracy in biomass prediction. However, the power regression function (formula as: y = a × exp(b × dbh)) had a prediction accuracy very close to untransformed data.

Logarithmic allometric models are used in tree biomass studies [79]; in this research, log-transformed model fitted the data well but with lower R2. The advantage of these models is that they can be derived by linear regression and be generalized more easily than linear or weighted regression models [79]. Their disadvantage is that the sum of component estimation usually does not equal estimates from real data and has to be adjusted when the response variable is log-transformed. In this case, the correction factor was 1.032. In some cases, logarithmic transformation of the dependent variables stabilizes the variance and fits well with the model meeting the information indexes’ requirements [80,81].

The initial observation was that all the models generated in this study met accuracy criteria, having low AIC, BIC, PRESS, IF, IV, and very high R2 (Table 3). It indicates the independent variable (dbh or dbh-height) explained a very well high proportion of the variation in C.

Generic models met most of the information criteria. Unfortunately, when they were tested for variance inflation (VIF) and R2 indexes, some failed. High VIF values greater than 10 suggest that the predictor variables considered in a regression model are highly correlated with themselves and are synonymous with multicollinearity [80].

The allometric models showed a similar prediction of the total aboveground biomass with some models [81] but disagreed with others [41,82], which over- or underestimated the total aboveground biomass for trees with higher dbh. These outcomes call attention to reviewing the background of each model before using it. The two winner models performed the best in the validation process (Table 4), but some warning must be taken when using them. In this regard, before using any allometric model, it must be ensured that the data are within the validity range of the selected models [41].

From this call, it can be inferred that the derived allometric models can be correctly and efficiently used to estimate the aboveground biomass and carbon stocks in AFS. To sum up, there is an attractive opportunity for farmers to benefit financially from traditional and AFS with G. arborea if the cocoa growers can access the carbon markets because these arrangements had a high potential to produce environmental services.

4.3. Cocoa Yield in the Agroforestry Arrangements

The agroforestry arrangements evaluated showed variability in cocoa yield. The high planting densities (lower spacing) increased humidity triggering cocoa diseases and demanding high labor to control them [23,27]. The low yields of the traditional farm (treatment 7) indicate that traditional cocoa farms are not profitable if their only objective is cocoa yield [23,27]. However, if evaluated as a system, including all good and environmental services such as biodiversity, the results may differ. In this sense, some cacao growers state that the institutional trend to increase cacao planting densities goes against the traditional farmers’ view because the low cocoa trees’ density (400 trees ha⁻¹) allows them growth miscellaneous crops for their livelihood [23]. However, with some new practices, they can increase their yield to 1000 kg ha⁻¹ keeping these traditional cocoa arrangements [83,84].

In the traditional system, the energy investment is less than commercial ones; for every 1 megajoule invested, 23 are produced (1:23 ratio) [27]. Therefore, the energy balance is highly efficient. On average, cacao yields were, 41% higher in monocultures, but the revenues derived from traditional cocoa agroforest economically overcompensated for this difference. Indeed, the return on labor across the years was roughly twice higher in the agroforestry systems than in the monocultures [84].

When analyzing yield in each of the treatments, the same trend can be observed with the traditional farm reporting the lowest values. However, in the dry season, which occurred in the municipality between July to October, there was a slight separation of the treatments, suggesting that the shading produced a differential effect.

For good performance and yield of cocoa-based systems, the companion trees should provide a shade below 50%; the most recommended is 30% [85] because shade greater than 60% causes yield limitations [86,87]. However, cacao has been traditionally grown under shade regardless of yield [86]. In an experiment in Ghana, strong reductions in yield were observed due to shading. Cacao trees growing in full sunlight had a higher yield than the shading ones [87]. Conversely, scientists and environmentalists alike are beginning to realize this switch’s error for the ecology of cocoa plantations [88]. Canopy cover-up to 39% raised yields at the field level compared to cacao grown in full sun, but increasing shade above this level can limit yields [89,90]. Whereas in Cameroon, increasing canopy cover-up to 47% enhanced yield but greater than 60% reduced cocoa yield [91].

Therefore, growing in sunlight will require more intensive management, including increased fertilizer inputs [85]. Shading may not be required in all cacao-farm regions, its applicability is dependent on local climate conditions. That is why the control of both the growth and density of cacao trees, the increases in aeration, light perception, and fertilization [88,92] are necessary to raise the yield.

4.4. Economic Assessment of the Agroforestry Arrangements

The low profitability of the traditional cocoa agroforests agrees with most studies [93]. They indicate that traditional cocoa-based AFS with few forest species, and few investments generate low incomes. However, lower yields, in some cases, can be offset by cacao’s premium prices [94]. This is an important finding because traditional/indigenous production systems make a high contribution to the environment and rural welfare, more economic research is needed. In other scenarios, the revenues derived from agroforestry by-crops, economically overcompensate due to self-consumption of companion crops, such as bananas, fruits, herbs, and peach palm, among others [94,95]. There is a bias, when assessing cacao production systems because most studies focus on cacao yields without quantitatively evaluating the economic returns from companion crops [86]. Other drawbacks of the cacao farms’ competitiveness are a lack of access to the market and low density of trees (400 per ha). Therefore, despite their potential to increase farmers’ revenues, crop products have been mainly used for self-consumption [96].

Results show that cacao yields were, on average, 41% higher in improved cacao agroforestry, but the revenues from agroforestry companion crops have great potential. The explanation about high IRR in treatment 6 could be the result of the optimum performance of G. arborea trees under these spacing and alley arrangements and that G. arborea is a sunlight-demanding, drought-resistant tree, which has fairly good tolerance to moist soils [97]. Under these conditions on the Colombian pacific coast, G. arborea trees reached dbh and heights higher than 50 cm and 11 m, respectively, which were sold at $70.000 COP, (USD 17.5). Indeed, the best economic performance was attained with intermediate diversity (three to seven species) and a density of 100 to 400 companion plants ha⁻¹) [98]. The same trend was reported in another study where G. arborea agroforest was 2–3 times more profitable in terms of net present value compared to sole G. arborea or mango or pigeon pea [99], these tendencies are very close to the results in this study. When comparing the cost of all improved cocoa arrangements they had no significant differences; however, when compared to traditional systems the differences were outstanding. Traditional agroforestry budgets are very low (1 million COP, USD 250, approximately), especially for labor, which allows farmers to develop miscellaneous activities and the use of on-farm inputs. Sustainable production systems such as agroforestry and organically managed systems are expected to yield less cacao but by-crops and premium prices, respectively, might economically compensate for the lower yields [84].

The IRR of 41% was high compared to the banks’ discount rate but there is no information about the IRR for other agricultural systems in the region.

These findings provide a roadmap for optimizing crop diversity and density to adjust the economic balance between sales and self-consumption in cocoa AFS.

Finally, if agroforestry is to be used in carbon capture and storage schemes such as the clean development mechanisms, better information is required to determine above- and belowground carbon stocks and soil carbon in agroforestry systems landscapes [100]. Thus, there is a need for biomass estimation, which is sensitive to a specific arrangement, objectives, spacing, companion plants, and management practices. The AFS assessed in this study could be a good alternative for the Colombian government to full fill its commitments to COP 21 and the Sustainable Development Goals– SDG [100], or the 2030 agenda in SDG 13 (climate action) [101].

Further research is needed to investigate the impact of different ways of integrating miscellaneous trees with cocoa on wider environmental, social and economic sustainability aspects, that are driving increasing interest in the SDGs, climate change, and food security [102,103,104]. Likewise, it is needed to design the strategies for adopting [105] these results in the region.

5. Conclusions

The carbon stock in the different agroforestry arrangements was statistically different. The lowest accumulation happened in treatment 4 and the highest in treatment 2. To estimate the biomass produced in the different agroforestry arrangements, two allometric models were developed for G. arborea based on dbh. Cocoa yield showed significant statistical differences in the different arrangements. The proposed agroforestry arrangements had positive effects on soil bulk density (Da) and organic matter, the first was reduced and the second had a significant increase. All agroforestry arrangements had positive financial benefits. Overall, treatment 6 presented the best performance in all financial indexes.