Artificial neural network (ANN) in forecasting of poverty line and economic-energetic efficiencies into the maize-based agroecosystems

ABSTRACT

In Mexico, corn is cultivated in small agroecosystems by rural farmers on communal lands. These farmers are economically vulnerable, and low yields from their plots affect both their economic and food security. A Feed-Forward Back Propagation Artificial Neural Network (ANN) aids in estimating the variables with the greatest impact on the agroecosystem related to Economic Efficiency (EC ha⁻¹), Energy Efficiency (ENE ha⁻¹), and the ‘Poverty Coverage Line’ (PCOVER). With an R = 0.86, the ANN has identified that the variables with the most significant impact on EC ha⁻¹ are the ‘cultivated area’, the ‘total energy consumed per hectare’, and the ‘presentation of products in the market’. For ENE ha⁻¹ and PCOVER, the key variables are the ‘cultivated area’, the ‘planting rate’, and the ‘total energy consumed per hectare’. The ANN demonstrates its utility by predicting that the cultivated acreage and the total energy invested by the farmer in their activities are the primary factors contributing to the poverty line in the agricultural sector of a rural community in Mexico. The variables feeding into this ANN encompass the fundamental energy and economic investments in other crops, making it adaptable and replicable in various agricultural contexts.

KEYWORDS:

• Agroecosystem
• artificial neural network
• artificial intelligence
• economic- energetic efficiencies

Introduction

In Mexico, small-scale dry corn cultivation (Zea mays L.) is predominantly practiced by low-income families for self-consumption and/or as a source of income from their agricultural activities (Boltvinik 2012; Borrego and Román 2019). However, the low adoption of agricultural practices and the impact of climatic conditions in dryland maize growing regions strongly affect grain production and food security for these families (Ureta et al. 2020). This context of maize cultivation is often associated with the highest poverty rates in Mexico and coincides with areas with the highest proportion of communal lands known as ‘ejidos’, which lack organized connections between agroecosystems (AES) and local or regional markets (Ramírez et al. 2013).

The low yield of dry corn production has been addressed in scientific literature proposing approaches and strategies to improve grain production and farmer´s economic income. For instance, Singh et al. (2016) and Chhagan et al. (2019) demonstrated that integrated nutrient management, combining chemical fertilizers and organic manures (Dominguez-Hernandez et al. 2020), along with crop rotation, diversification of dryland maize-wheat crops (Sharma et al. 2017), and proper tillage and intercropping (Pradhan et al. 2016; Piao et al. 2019), are viable and environmentally friendly options for soil conservation and profitable production yields, while reducing crop costs and human energy (Haarhoff et al. 2020). However, all these factors pose a complex problem that cannot be solved by common sense or farmer experience alone. In this context, the main challenges of agricultural sustainability have required studies based on disruptive information and communication technologies to improve agricultural production systems (Sharma et al. 2020). To address this problem, Artificial Intelligence based on Artificial Neural Networks (ANN) (Aslam et al. 2019) and Fuzzy Logic (Meza-Palacios et al. 2020; Ugbaje et al., 2019) have been implemented to assist farmers in tasks such as fertilizer selection, disease and pest diagnosis, nutrient dosing, and to improve crop productivity (Dutta et al. 2020). Artificial Neural Networks (ANNs) are systems composed of multiple processing units or elements that perform simultaneous calculations. The operation of these networks is determined by the network structure, connection weights, and the processing carried out in the elements or nodes (Davim 2012). ANNs have been implemented to assess poverty prediction (Huang 2021). Convolutional ANNs that utilize satellite images for poverty prediction have also been used (Yan 2021; Okaidat et al. 2021).

In other studies, Pino‐Mejías et al. (2018) present ANN models and linear regression to predict the likelihood of low-income households falling into poverty to secure social housing. Papada & Kaliampakos (2022) propose a model that measures certain human behaviors through subjective indicators to predict objective energy poverty at a level ranging from 56% to 58%. The work of Nabavi-Pelesaraei et al. (2021) models the energy consumption of agricultural products using an adaptive neuro-fuzzy inference system. Other studies have been presented to evaluate the energy consumption of workers in their activities as a way to measure sustainability (Del Pozo Rodriguez et al. 2014). These approaches are always necessary to manage human, economic, and material resources in various tasks in the industrial and agricultural fields. For example, the pioneering work of Odum (1995) proposed a methodology for assessing worker energy expenditure which minimizes differences in resource consumption between work processes (Del Pozo Rodriguez et al. 2014). Other studies have proposed the use of ANNs in the massive analysis of data collected in agricultural activity to solve production performance problems, which can often be fuzzy or redundant and cannot be treated by traditional statistical analysis methods (Nabavi-Pelesaraei et al. 2016; Khanali et al. 2017; Elbeltagi et al. 2020). In contrast to traditional methods, ANNs allow many complicated tasks to be performed easily without formalizing the knowledge (Ahmad et al. 2009; Noor et al. 2010).

The decision-making process for farmers is a complex task due to the combination of multiple factors involved in agricultural crop production that make solutions difficult to obtain supported by their experience or with traditional tools or conventional programming. Studies of this nonlinear nature, in addition to combining different types of variables, are accompanied by uncertainty, which makes it impossible for traditional techniques to process nonlinear information.

To make the decision-making process easier, this article presents a decision support tool based on an ANN that effectively predicts the value of related indices to poverty line coverage (PCOVER), energy efficiency (ENE), and economic efficiency (ECE). This ANN facilitates the analysis of the impact that agricultural practices, management of human and material resources available to the farmer, degree of schooling, experience, growing season, and form of commercialization have on the PCOVER, ENE, and ECE indices, considered by the AES of small maize producers in a study region in Mexico with a high degree of marginalization (approximately 1.183 in relation to CONAPO’s marginalization index) (FIRA et al. 2019; CONAPO 2020).

In that sense, this decision support tool is especially useful for evaluating the impact of the farmer’s activity related to the investment of their financial and energetic resources in the activities of tillage, maintenance, harvesting, and marketing of their agricultural products. This research supports the hypothesis that the results of an artificial neural network can help determine the best decisions to maximize both energy indices and poverty level through participatory tools, biophysical indicators, and sensitivity analysis applied to the most influential input variables in agriculture. The goal is to maximize economic indices and minimize energy indices, which in turn will have an impact on the poverty line.

This paper contributes with a Decision Support System developed using an Artificial Neural Network (ANN) that estimates indices related to poverty threshold coverage (PCOVER), energy efficiency (ENE) and economic efficiency (ECE). To do so, it evaluates the impact of the farmer’s activities, in particular his investment of financial and energy resources in tasks such as cultivation, maintenance, harvesting and marketing of his agricultural products.

Methodology

Figure 1 describes the ANN architecture with 18 input variables to the system. Then, two hidden layers are used. In each ANN, the first hidden layer uses 14 neurons to adjust the connection weights and biases of the network, while the second hidden layer or output layer has three output variables also influenced by their weights and biases. The system also provides a sensitivity analysis to evaluate the impact that the input variables have on the output variable.

Figure 1. Artificial neural network (ANN) architecture.

The three output variables defined as indicators are: efficiency in the use of economic resources, which is calculated as the total annual income per hectare from corn marketing minus the total corn production costs per hectare for the i-th activity performed during the corn production process. The efficiency in the use of energy resources is the total sum of energy expended by the worker per hectare in corn production, divided by the total sum of energy expended per hectare in the i-th corn production activity per year.

Finally, poverty line coverage is an indicator of material welfare deprivation, which is generally associated with the lack of the most basic opportunities and capabilities for human and social development (Sengul and Tuncer 2005) see Table SA in Appendix A The study variables were provided by three experts between 15 and 25 years old in the cultivation of corn in the study region. The value of the input variables was collected between February and June 2021 in 5 communities’ representative of marginalized communities in the municipality of Tantoyuca-Veracruz-Mexico, through 147 surveys applied to farmers with crop extension of less than or equal to 3 ha: Crucero Palmito, Los Ajos, Julio Juarez, Mezquite, and San Sebastian. As indicated in Table 1, most variables are used in a binary, categorical, discrete, and continuous manner. For example, variable X_6 (type of seed) used four categories: (1) commercial maize seed, (2) white-creole maize, (3) yellow-creole maize, and (4) purple-creole maize. Variable X_11 (fertilization) used binary values: (0) fertilization applied in AES, and (1) fertilization not applied in AES.

Table 1. Variables of the model.

Variable	Name	Type	Levels
X1	Community	Categorical	Community name
X2	Schooling	Discrete	Age
X3	Experience	Discrete	Working years
X4	Farm area	Continuous	Production area
X5	Sowing rate	Continuous	Number of seeds sown
X6	Type of seed	Categorical	(1) commercial maize seed (2) white-creole maize (3) yellow-creole maize (4) purple-creole maize.
X7	Crop density	Continuous	Quantity of plants per square meter (plants·m^−2).
X8	Soil tillage practices	Binary	(1) mechanical process (2) traditional process
X9	Chemical weed control	Binary	(1) chemical control applied (2) chemical control not applied.
X10	Pest management	Binary	(1) pest program included (2) pest program not included
X11	Fertilization	Binary	(1) fertilization applied in AES (2) fertilization not applied in AES
X12	Maize selling prices	Continuous	Sale price per kilogram of maize.
X13	Man-hours	Continuous	Man-hours worked in MJ/ha^−1
X14	Man-hours in MJ ha^−1	Continuous	Man-hours worked in MJ/ha^−1
X15	Total MJ ha^−1	Continuous	MJ expended to produce one ha^−1 of maize
X16	Maize marketplace	Categorical	(1) Local market (2) external market (3) Tantoyuca city market (0) none of the above.
X17	Product presentations on the market	Binary	(0) kernels (1) ear of maize
X18	Planting season	Categorical	(1) Seasonal (2) Tonalmil (3) the previous two.
Y1 (Output)	ECE	Continuous	Economic efficiencies
Y2 (Output)	ENE	Continuous	Energy efficiencies
Y3 (Output)	PCOVER	Continuous	Poverty line coverage

The output variable ‘PCOVER’ (Poverty Line Coverage) was calculated based on the costs of the basic food basket and other essential services, such as education, housing, and health in Mexico, as reported by Boltvinik (2012) and Estévez et al. (2016). This information was used to feed the model proposed by Boltvinik (2003) to estimate the costs of both household basic goods (BFG) and individual basic goods (BIG) variables, as described by García M (2002), covering the national requirements for marginal areas in Mexico (COPLAMAR and Del 2003). This requirement includes all basic consumption goods in a household. The costs required for the minimum level of welfare in an adult male were used as the reference unit applied for each family member. Values of 0.81, 0.58, 0.54, 0.43, and 0.43 were taken for an adult female, a small boy, a small girl, a male baby, and a female offspring, respectively. This unit refers to the proportion of the minimum wage that applies in a given community. Higher values are consistent with higher proportions of the minimum wage earned by workers in a given region, while lower values imply lower minimum wages, which impact the poverty level in the same community.

The Matlab® software was used to develop a feed-forward artificial neural network (ANN) model using backpropagation algorithms. The feed-forward backpropagation network used in this study is organized in interconnected layers, which propagate in a single direction from one layer to another until they reach the output layer and the output neurons. The activation function used in the ANN model is the hyperbolic tangent sigmoid transfer function (tansig). The tansig function is commonly used for pattern recognition problems and is excellent for neural networks where speed is more important than the exact shape of the transfer function (Dorofki et al. 2012).

The Levenberg-Marquardt algorithm was used as a learning rule, implemented through the ‘learngdm’ adaptive learning process. The performance function for the mean square error (MSE) was defined in two hidden layers. The data were normalized and linearly scaled between [−1 and 1] using the ‘mapminmax’ function in Matlab®. This produced a more homogeneous data set, avoiding data redundancy, allowing easier and faster learning of the network, and protecting data integrity. Karsoliya (2012) explains that if data in a problem are linearly separable, then there is no need to use two or more hidden layers as the activation function can be implemented in the input layer to solve the problem. However, in the case of problems that deal with arbitrary decision boundaries to arbitrary accuracy with rational activation functions, two or three hidden layers are required.

In order to obtain the best performance of the ANN, the number of neurons in the hidden layers should be the same. If more unnecessary neurons are present in the network, then ‘overfitting’ may occur. In this problem, good accuracy was achieved using a hidden layer with 14 neurons.

In training, validation and testing, the sample data was divided into the following percentages: training target ratio = 0.7, validation target ratio = 0.15, and test target ratio = 0.15. Table 2 shows the number of data used to program the neural network.

Table 2. Number of data used for training, validation, and testing.

Network	Data
	Sample size	Training	Validation	Test
ECE	147	103	22	22
ENER	147	103	22	22
PCOVER	147	103	22	22

The training parameters were as follows: epochs = 1000, goal = 0, min_grad = 1e-07, max_fail = 6 and mu = 0.001. After getting a training model, its performance was validated to make sure that the model can generalize the input-output relationships.

Results and discussion

The best results of the ANN are presented in Table 3. During the training phase, various configurations were tested with different numbers of neurons in the hidden layer. Training commenced with the default parameters considered by the MATLAB toolbox and then progressively increased the number of neurons in Layer 1 until the best performance was achieved. The Mean Squared Error (MSE), obtained from the performance graph, represents the best validation performance achieved at a given epoch.

Table 3. Best training, validation, and test results.

Network	Neurons in the hidden layer	R-Training	R-Validation	R-Test	MSE
	10	0.81076	0.66031	0.58055	0.87442
ECE, ENER, PCOVER	11	0.86934	0.63301	0.18937	1.2211
	12	0.83066	0.51384	0.45463	1.4516
	13	0.80528	0.69529	0.72058	1.3222
	14	0.81621	0.86435	0.84518	0.53366

Figure 2 shows the results of the best model validation performance; it can be seen that the validation line (green line) and the test line (red line) have the same graphical pattern, showing an initial rise until reaching the final stabilization, which ensures the reliability of the developed ANN model. The performance of the mean square error is observed in Figure 2; the best validation performance shows an MSE equal to 0.53366. The results of the developed ANN show correlation coefficients higher than 80% (R ≥ 0.8) (Figure 3), so the developed ANN model is reliable to predict.

Figure 2. ANN model performance.

Figure 3. Linear regression models from the developed ANN.

The optimal number of layers was obtained with an ANN containing 14 neurons. Figure 3 shows the validation model with correlation coefficients for training, validation, and test of R = 0.816, R = 0.864 and R = 0.845 respectively. These values are higher than those obtained with the initial 10 neurons (R = 0.53 and R = 0.55) which ensures the quality of the ANN model.

To determine the relative contribution (RC) of the input variables to each output, a sensitivity analysis was performed. Garson’s algorithm was used to identify the most influential input variables for each output variable. This algorithm calculates the importance coefficient based on the product of the connection weights between the input layer neurons, the hidden layer neurons, and the output layer neurons of the neural network (Maozhun and Ji 2017).

(1) $RC=\frac{\frac{{\sum }_{j=1}^n{W}_{ij}{V}_{jk}}{{\sum }_{k=1}^n{W}_{ij}}}{{\sum }_{i=1}^I{\sum }_{j=1}^n\frac{W_{ij}{V}_{jk}}{{\sum }_{i=1}^n{W}_{ij}}}$(1)

Where, i, j, k, respectively, refer to an input layer, hidden layer, and output layer neurons; $W_{ij}$is the connection weights between input layer and hidden layer neuron, $V_{jk}$ is the connection weights between hidden layer and output layer neurons, n is the total number of input layer neurons, m is the total number of output layer neurons. Figures (4–6) show the 18 input variables and their impact on the model’s output variables.

Figure 4. Sensitivity analysis for the output variable ECE/ha.

Figure 5. Sensitivity analysis for the output variable ENE/ha.

Figure 6. Sensitivity analysis for the output variable PCOVER.

After identifying the variables with the greatest impact for each output variable, a sensitivity analysis was performed for each of these, from only the input variables with the greatest impact on them. The purpose of selecting only the input variables with the greatest impact, is to clean the original graph of 18 variables, and to make more visible their influence on the study variable.

Maximizing and minimizing the ECE by sensitivity analysis

In Table 5, as compared to Table 4, the communities of Crucero Palmito and Mezquite show a slight improvement in economic efficiency (ECE). However, the ECE did not increase in the communities of Los Ajos, Julio Juárez, and San Sebastián (Figure 7). This behaviour can be explained by the fact that as the total megajoules (MJ) and farm area decrease, the ECE increases, as the economic resources used in maize production on the AES are minimized. Our results partially agree with Linares and Labandeira (2010), who argue that such an increase in ENE is a consequence of the rise in total energy demand, which occurs only when producers are able to save resources.

Figure 7. Displays a comparison between observed values (Table 3) -vs- Modified values (Table 4) in ECE/ha.

Table 4. Major impact variables that maximizes the efficiencies on the use of the human resources.

Community	Input variables			Output variables
	Farm area (ha)	Total MJ ha^−1	Product presentation††	ECE^† ha^−1	ENE^† ha^−1	PCOVER^†
Crucero Palmito	3	635.66	0	0.70274	0.61589	−0.03363
Los Ajos	2	682.25	0	4.27350	3.09869	0.23699
Julio Juárez	0.5	288.04	1	5.64784	1.03408	0.01854
Mezquite	1	5177.87	0	1.40845	0.76533	0.01418
San Sebastián	1.5	808.14	0	3.34225	1.75159	0.10280

^†Economic efficiency (ECE); Energy efficiency (ENE); Poverty line coverage (PCOVER).

^††(0) kernels (1) ear of maize.

Table 5. Modified impact variables to maximize the economic efficiencies on the use of resources.

Community	Input variables			Output variables
	Farm area (ha)	Total MJ ha^−1	Product presentation^††	ECE^† ha^−1	ENE^† ha^−1	PCOVER^†
Crucero Palmito	1	5	0	0.9841	0.5032	0.44799
Los Ajos	1	5	0	2.7952	2.4981	−0.04489
Julio Juárez	0.25	5	1	4.6763	1.2304	−0.04581
Mezquite	0.5	5	0	1.4091	0.8902	−0.02607
San Sebastián	1	5	0	1.2245	0.8345	0.03981

^†Economic efficiency (ECE); Energy efficiency (ENE); Poverty line coverage (PCOVER).

^††(0) kernels (1) ear of maize.

In Table 6, compared to Table 5, it is observed that to obtain a low ECE in at least three out of five communities, it was necessary to increase the proposed quantity of the original impact variables. The only community in which an opposite effect was expected was Julio Juarez, which showed a high ECE. It can also be explained that as the total megajoules (MJ) consumed – a large amount of workforce – increases, the product presentation on the market reduces the ECE, as producers require a greater quantity of resources for maize production. These results contrast with those reported by Linares and Labandeira (2010). However, they agree with Valdés et al. (2009), who explain that the energy balance is significantly affected by the external agricultural inputs required to maintain the AES.

Table 6. Modified impact variables to minimize the economic efficiencies on the use of resources.

Community	Input variables			Output variables
	Farm area (ha)	Total MJ ha^−1	Product presentation^††	ECE^† ha^−1	ENE^† ha^−1	PCOVER^†
Crucero Palmito	3	10000	0	0.53440	0.29561	0.46933
Los Ajos	2	10000	0	0.79309	0.41534	−0.04552
Julio Juárez	0.5	10000	1	10.11760	2.22880	−0.04567
Mezquite	1	10000	0	1.04430	0.41980	−0.04166
San Sebastián	1.5	10000	0	0.87591	0.38522	−0.03021

^†Economic efficiency (ECE); Energy efficiency (ENE); Poverty line coverage (PCOVER).

^††(0) kernels (1) ear of maize.

Maximizing and minimizing the ENE by sensitivity analysis

In Table 7, compared to Table 6, it can be seen that in order to achieve high energetic efficiencies (ENE) in at least three out of the five communities, it was necessary to increase the sowing rate of the original impact variables. Low energetic efficiencies were observed in the communities of Julio Juárez and Los Ajos (Figure 8). This result is supported by the fact that as the total megajoules (MJ) and the sowing rate (kg ha⁻¹) increase, the ENE also increases. This is probably because as productivity is raised, more energy is needed to support the AES production, and consequently, this indicator increases in magnitude.

Figure 8. Displays a comparison between observed values (Table 6) and modified values (Table 7) for energy efficiency (Ene ha⁻¹) at a sowing rate of 50 kg ha⁻¹.

Table 7. Major impact variables to maximize the efficiencies on the use of energy.

Community	Input variables			Output variables
	Farm area (ha)	Sowing rate (kg ha^−1)	Total MJ ha^−1	ECE^† ha^−1	ENE^† ha^−1	PCOVER^†
Crucero Palmito	3	14	635.66	0.70274	0.61590	−0.03364
Los Ajos	2	14	682.25	4.27350	3.09869	0.23699
Julio Juárez	0.5	7	288.04	5.64784	1.03408	0.01854
Mezquite	1	14	5177.87	1.40845	0.76533	0.01418
San Sebastián	1.5	19	808.14	3.34225	1.75159	0.10280

^†Economic efficiency (ECE); Energy efficiency (ENE); Poverty line coverage (PCOVER).

Our results are consistent with those reported by Tobasura et al. (2012), who argue that there is a direct relationship between financial and energetic productivity. The authors also state that as production increases, energetic productivity rises and the efficiency of energy use also increases. For practical applications in this study, increases in farm area were not included, because this variable represents the maximum area in which the maize seed is sown in the studied AES, and therefore, this variable remains constant. This finding is consistent with Linares and Labandeira (2010), who attribute every improvement of ENE to increases in the use of resources.

In order to obtain a low ENE the values of the original variables were diminished Sowing rate (kg ha⁻¹) and Total MJ ha⁻¹for the five sampled communities. The previous demonstrates that the ANN was able to generate reliable predictions. Such behavior may be attributed to reduction of total used MJ and the sowing rate (kg ha⁻¹). Therefore, the ENE also decreases, and consequently, this index will remain at low levels because the energy requirements are minimized in the AES (Table 9 compared to Table 8). These results are in agreement with those reported by Linares and Labandeira (2010).

Table 9. Modified impact variables to minimize the economic efficiencies on the use of energetic resources.

Community	Input variables			Output variables
	Farm area (ha)	Sowing rate (kg ha^−1)	Total MJ ha^−1	ECE^† ha^−1	ENE^† ha^−1	PCOVER^†
Crucero Palmito	1	7	5	0.6911	0.3433	0.3350
Los Ajos	1	6	4	1.4120	0.8913	−0.0455
Julio Juárez	0.25	4.5	3	4.3535	0.9980	−0.0458
Mezquite	0.5	7	2	1.7537	1.0122	−0.0406
San Sebastián	2	9.5	5	1.0044	0.6574	−0.0338

^†Economic efficiency (ECE); Energy efficiency (ENE); Poverty line coverage (PCOVER).

Table 8. Modified impact variables to maximize the economic efficiencies on the use of energetic resources.

Community	Input variables			Output variables
	Farm area (ha)	Sowing rate (kg ha^−1)	Total MJ ha^−1	ECE^† ha^−1	ENE^† -1	PCOVER^†
Crucero Palmito	3	50	15000	2.4046	1.7016	−0.6161
Los Ajos	2	50	15000	0.5332	0.3457	0.1967
Julio Juárez	0.5	50	15000	0.4188	0.3431	−0.0441
Mezquite	1	50	15000	1.1917	1.2175	0.2204
San Sebastián	1.5	50	15000	3.7403	2.6504	0.4397

†^{Economic efficiency (ECE); Energy efficiency (ENE); Poverty line coverage (PCOVER).}.

These results show that as the cultivated hectares decrease, and the amount of M.J ha⁻¹ as labor decreases, the economic efficiency (ECE) decreases as can be seen in the communities Los Ajos, Julio Juárez and San Sebastián. That is, the smaller the cultivated area, the lower the energy expended in the form of man-hours in the plantations, and consequently the energy efficiency (ENE) decreases due to the lower harvested product.

These findings coincide with those reported by Pérez and Flores (2003) who emphasize that corn production in a traditional system is not energy efficient, i.e. it consumes more energy than it produces. However, these findings should be considered with reservations, since, in agricultural cultivation, of smaller or larger scale, the factors that intervene in crop yield are diverse, which can be climatic and those related to agricultural practices.

Maximizing and minimizing PCOVER by means of sensitivity analysis

According to Boltvinik (2012), the holistic perception of poverty has important implications for the quality of life in households. However, the author concludes that this approach has received little study in Mexico and worldwide. In order to achieve this purpose, the relationships between income and basic necessities that have not been satisfied, along with an exceeded working time index, should be considered.

In this study, to maximize PCOVER efficiency, crop density (plants m⁻²) was increased, while maize selling prices were diminished, and pest management and fertilization values remained constant. This allowed us to identify three out of five municipalities included within the poverty line (Crucero Palmito, Los Ajos, and San Sebastián). The predicted values were similar to those observed, and the error rate was insignificant (Tables 10 and 11). This result coincides with that observed by Purroy-Vásquez et al. (2015) in Veracruz, Mexico, who concluded that the AES with the lowest cultivated areas and low productivity derived from the use of maize-livestock combined systems showed the least coverage of the poverty line and the highest practices of self-consumption.

Table 10. Major impact variables to maximize the percentage of poverty line coverage.

Community	Input variables				Output variables
	Crop density (plants m^−2)	Pest management	Fertilization	Maize selling Prices ($Mx)	ECE^† ha^−1	ENE^† ha^−1	PCOVER^†
Crucero Palmito	1	1	2	5	0.7027	0.6159	−0.0336
Los Ajos	0.64	1	2	5	4.2735	3.0987	0.2361
Julio Juárez	1.2	2	2	8.5	5.6478	1.0341	0.0185
Mezquite	0.8	1	2	5	1.4085	0.7653	0.0142
San Sebastián	1	1	2	5	3.3423	1.7516	0.1028

^†Economic efficiency (ECE); Energy efficiency (ENE); Poverty line coverage (PCOVER).

Table 11. Modified impact variables to maximize the percentage of poverty line coverage.

Community	Input variables				Output variables
	Crop density (plants m^−2)	Pest management	Fertilization	Maize selling prices ($Mx)	ECE^† ha^−1	ENE^† ha^−1	PCOVER^†
Crucero Palmito	3	2	1	1	0.9439	0.7577	0.6180
Los Ajos	1.5	2	1	1	0.9631	0.3845	0.1694
Julio Juárez	2	2	1	2	1.3904	0.7630	−0.0433
Mezquite	3	2	1	2	3.7952	0.9600	−0.0146
San Sebastián	4	2	1	2	4.2977	1.3781	0.2351

^†Economic efficiency (ECE); Energy efficiency (ENE); Poverty line coverage (PCOVER).

On the contrary, in order to minimize the PCOVER index, low values for crop density (plants m⁻²) were tested. Additionally, different values for pest management, fertilization, and maize selling prices variables were tested to keep as many municipalities as possible above the poverty line. This allowed us to include three out of five communities (Los Ajos, Julio Juárez, and Mezquite). However, for practical applications, the Mezquite community was excluded from the poverty line due to its proximity to zero absolute value (Tables 12 compared to 10). According to Purroy-Vásquez et al. (2015), AES that combine productive activities and consider their own environmental conditions can achieve a higher degree of welfare.

Table 12. Modified impact variables to minimize the percentage of poverty line coverage.

Community	Input variables				Output variables
	Crop density (plants m^−2)	Pest management	Fertilization	Maize sale prices ($Mx)	ECE^† ha^−1	ENE^† ha^−1	PCOVER^†
Crucero Palmito	0.6	1	2	2	0.4187	0.2715	0.6109
Los Ajos	0.5	2	1	2	1.6752	0.3170	−0.0289
Julio Juárez	1	2	1	4	1.6752	0.5966	−0.0457
Mezquite	0.4	1	2	3	1.7634	0.7085	0.0082
San Sebastián	0.5	2	2	3	4.5487	1.6009	0.1419

^†Economic efficiency (ECE); Energy efficiency (ENE); Poverty line coverage (PCOVER).

The analysis of the ECE, ENE, and PCOVER rate highlights the importance of studying the ENE as a principle to reduce labor energy needs and achieve competitive costs in small-scale agricultural AES. The study of this index, supported by the ANN presented here, is an approach to simulate scenarios of how human resources should be integrated into agricultural activities to reduce energy expenditure. The main benefits of the ANN are the reduction of energy resources employed, represented by the farmer’s man-hours invested in the farm to achieve a given level of energy service, i.e. optimized energy efficiency, over the depletion of energy resources -available man-hours of work- and improve energy security, monetary savings, and environmental impact related to energy use (Linares and Labandeira 2010). Therefore, the factors with the greatest impact in this work, such as energy investment, farm production area, corn market, pest management, fertilization, and corn sales prices, also had the greatest influence in the studies of the authors cited above. Thus, the proposed ANN model has proven to be reliable to study more robust agroecosystems, covering their critical deficiencies, as pointed out by (Noor et al. 2010) in the use of artificial neural networks.

Conclusions and implications

Related studies to this research have assessed the extent of poverty, energy efficiency, and economic efficiency without analyzing the impact of agricultural variables and their relationship with these indices. This article proposes a decision support tool that effectively predicts poverty line coverage, energy efficiency, and economic efficiency of low-scale maize farmer agroecosystems.

The tool utilizes an ANN, in which biophysical indicators are analyzed, and the most influential variables in these indices are examined to maximize the economic indices and minimize the energy indices, with a special focus on poverty line orientation and impact in marginalized small-scale farming communities in the region.

The scenarios evaluated by ANN show that the best impact values on the ECE, ENE, and PCOVER indices are achieved when constant agricultural practices are maintained, and these are combined with the efficient management of man-hours related to crop extension. We also observed that the presentation of corn in the market, whether in grain or on the cob, has no major importance in the ECE index when the area of cultivation is reduced, and the energy of the worker used in man-hours for the agricultural activity is reduced. The interpretation of the results may be a limiting factor that discourages the usefulness of this study approach for the analysis of the economic investment and labor force of the farmer in their crop. The user of this tool can be a non-specialist who does not require professional expertise but rather seeks to understand how technological and human resources can be integrated in a crop, so that the results of this tool can help them determine the integrated management of their resources to improve the profitability of the crop.

The technical implication of this tool to be used in other agroecosystems is related to the factors that can impact crop yield, for example, climate and those that explain the vegetative development of the crop. In this sense, future work for this ‘decision support tool’ would be to include variables that are not necessarily related to energy value or economic investment.

In this research, the ANN generated predictions with success rates exceeding 80%. Nevertheless, the model could potentially incorporate new variables for study, not necessarily limited to agricultural factors, such as climate-related variables or other socioeconomic indicators like education, access to healthcare services, among others. Appendix A.

Acknowledgments

We would like to thank the Instituto Tecnológico Superior de Zongolica for their invaluable support to carry out this research.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Appendix

Table A1. Classification and description of these input/output variables.

Variable and type variable	Description
Community (linguistic variable)	Describe the community’s name in which questionnaires was applied within Tantoyuca, Veracruz region.
Schooling (discrete variable)	It is the schooling level of the farmer. The value taken by this variable was (1) for primary school, (2) for secondary school, (3) for high school, and (4) to bachelor´s degree.
Experience (continuous variable)	Describe the working years of the farmers in their AES.
Farm area (continuous variable)	Production area in the farm measured in hectares.
Sowing rate (continuous variable)	Quantity of seeds (kg·ha-1) used to sow the farm area.
Type of seed (discrete variable)	Type of seed used to sow the farm area. The value taken by this variable was (1) for commercial maize seed, (2) for white-creole maize, (3) for yellow-creole maize, and (4) for purple-creole maize.
Crop density (discrete variable)	Quantity of plants per square meter (plants·m-2).
Soil tillage practices (binary variable)	Refer to methods of soil preparation before to sow. There are two principal methods employed by the farmers, taking values of (1) for mechanical process and (2) for traditional process.
Chemical weed control (binary variable)	Denote the application of a chemical control of weeds. The value taken by this variable was (1) when the chemical control is applied and (2) when the chemical control is not applied.
Pests management (binary variable)	Imply a pest management program into the AES. The value taken by this variable was (1) whether the farmer include a pest program and (2) when the program is not involved.
Fertilization (binary variable)	Application or not of a fertilization program into the AES. There are two possible values taken by this variable: (1) whether the fertilization program is applied in the AES or (2) whether the farmer has not applied any fertilization program.
Maize selling prices (continuous variable)	Refer to the sale price per kilogram of maize.
Man-hours (continuous variable)	Number of man-hours worked per hectare.
Man-hours in Mega Joules per hectare [MJ·ha-1] (continuous variable)	Number of man-hours worked per hectare, expressed as Mega Joules required to produce one hectare of maize.
Total Mega Joules per hectare [MJ·ha-1] (continuos variable)	Amount of energy expended in Mega Joules to produce one hectare of maize, calculated via man-hours in mega joules variable.
Maize marketplace (discrete variable)	Indicate the place where the maize production can be sold: (1) Local market (within each community), (2) external market (outside of the community), (3) Tantoyuca city market (county seat), and (0) none of the above.
Product presentations on the market	Maize commercial presentation on the market: (0) kernels, (1) ear of maize
(discrete variable) Planting season (discrete variable)	It is the part of the year during the local weather conditions allow the normal plant growth, which includes (1) Seasonal, (2) Tonalmil, and (3) the previous two.
ECE [Economic efficiencies] (output variable)	Result between the total sum of the annual incoming per hectare from the maize commercialization, and the total sum of the costs from maize production per hectare for the i-th activity done during the productive process of maize.
ENE [Energy efficiencies] (output variable)	To calculate this variable was used the total sum of the generated energy per hectare into the maize production, divided by the total sum of the energy expended per hectare in the i-th maize productive activity by year.
PCOVER [Poverty line coverage] (output variable)	It is understood as a deprivation of material welfare, which is generally associated with to a lack of opportunities and capabilities most basic to human and social development (Sengul and Tuncer 2005)