Net annual income per hectare (ha) of the SAES (Inetha)

The net annual income per hectare of the SAES was determined, using the total income per ha (Ingtoha) and the total production costs per ha (Ctpha) of the i-th activity carried out in maize production. Later, the difference between these was calculated to obtain the net annual income per ha, which was divided by 365 to determine the daily value with the aim of comparing it with the official minimum wage for the region according to the National Commission on Minimum Wages (Comisión Nacional de los Salarios Mínimos, ^{CONASAMI, 2016}). All the values obtained were expressed in Mexican pesos.

Net annual energetic income per ha of the SAES (Inet∆ha)

To determine the Inet∆ha the total energy production per ha (pro∆ha) was calculated for the i-th activity carried out in the productive process of maize and the total energy applied (fertilizer and man-hours) per ha (inv∆ha), in Mega Joules (MJ), for the i-th activity carried out in the productive process of maize. For this purpose, the production and total investment per ha in each SAES was determined, converting it into energy values with the conversion factors to then apply the subtraction (^{Mora-Delgado et al., 2007} and ^{Pimentel, 1993}).

Economic efficiency per hectare (Eeha)

The indices of economic efficiency allow identifying the yield of the resources used in the productive process. It was calculated by dividing the sum of the total gross annual income per hectare (Ingtoha) generated by the sale of maize, by the sum of the total production cost per hectare (Ctpha) for the i-th activity carried out in the productive process of maize (^{Purroy-Vásquez et al., 2016}).

Efficiency in the use of energy per hectare (EΔha)

The efficiency in the use of energy per hectare (EΔha) determines the level of management of energetic resources within the productive processes in the SAES. For its calculation, the sum of the total energy production per hectare (PtΔha) generated in the maize productive activity (grain production in MJ), was divided by the sum of the energy invested (fertilizer and man-hours in MJ) per hectare (invΔha) in the i-th productive activity of maize in a period of one year (^{Purroy-Vásquez et al., 2016}).

Productivity

It is understood as the relation between the production obtained by a system of production or services and the resources used to obtain it. The determination of economic and energetic productivity of the systems is suggested through indicators, as described next:

Indicators of economic productivity (Ipreag)

Economic productivity allows us to determine the productive behavior of the SAES (Table 1) in pesos ($) in relation to units of work ($ Man-hours ^-1) and energy ($ MJ^-1).

Indicators of energetic productivity (IprΔagr)

Energetic productivity allows defining the productive behavior of the SAES (Table 2) in Mega Joules (MJ). The methodology proposed by ^{Denoia et al. (2006)} was used for its determination, calculating the energetic productivity per unit of work (MJ Man-hours ^-1) and the monetary (MJ $^-1).

Auto-consumption

For auto-consumption (Ac), the definition by ^{Leite (2004)} was used, which mentions that the study of auto-consumption is limited exclusively to the production of foods; that is, the part of agricultural and livestock production destined to feeding the family members and animals, deducting from this production the parts relative to commercialization, donation or loss. In its calculation, the total of the product and byproducts obtained from the SAES are quantified, and from this amount the total of the product destined to commercialization was subtracted, and the result was converted into percentage (^{Gallardo-López et al., 2002}; ^{Purroy-Vásquez et al., 2016}).

Percentage of coverage of the minimum welfare line

To determine the proportion of coverage of the minimum welfare line (Pcober), first the cost of the Normative Basket of Essential Necessities (Canasta Normativa de Satisfactores Esenciales, CNSE) was calculated through the linear equation developed by ^{Marín (2002)} and adjusted by ^{Boltvinik and Marín (2003)} for the calculation of the cost of the variables family goods (BF) and individual goods (BI) (both by their initials in Spanish), based on the requirements of the General Coordination of the National Plan for Depressed Zones (Coordinación General del Plan Nacional De Zonas Deprimidas, COPLAMAR), where all the essential necessities required by a household are considered. For the calculation, the costs equivalent to those of an adult male are considered as unit of reference; thus, for an adult female it is 0.81; a boy, 0.58; a girl, 0.54; a male baby, 0.43; and a female baby, 0.43.

where CNSE: Cost of the Normative Basket of Essential Necessities; ae: Sum of units of an equivalent adult; p: number of people in the household. *The constant values are updated until June 2016.

Then the calculation was about to what proportion the net annual income generated in agriculture and livestock activities in the SAES allows each family to reach or surpass the minimum welfare line.

The net agricultural and livestock income (Inetoagr) was calculated by totalizing the gross income, generated from agricultural and livestock activities carried out in the SAES, including the Ac and, next, the total costs of agricultural and livestock activities was subtracted (^{Purroy-Vásquez et al., 2016}).

Statistical analysis

To determine the types of SAES, the following variables were analyzed: net economic income, net energetic income, economic efficiency, energetic efficiency, indicators of economic productivity, and indicators of energetic productivity. Multivariate grouping techniques were applied. First a tree diagram or dendrogram was made, using agglomerative hierarchical grouping (^{Chalate-Molina et al., 2010}; ^{Purroy-Vásquez et al., 2016}), using Euclidian distances and the algorithm of complex linking. To characterize these groups the k-mean technique was applied, and then variance analysis and means tests (Tukey, p<0.05) were performed to understand the statistical difference between groups.

Later the multivariate technique of canonic correlation was used, with the aim of understanding which of the indicators of energetic economic efficiency and of productivity of the SAES contribute to surpass the minimum welfare line (MWL). The independent variables or of efficiencies were: surface, energetic efficiency, economic efficiency, energetic productivity per money invested, economic productivity per energy invested, work productivity per energy invested, and work productivity per money invested. The dependent or social variables were: proportion of coverage of the minimum welfare line and of auto-consumption. For all the analyses, the statistical software Statistica^® version 6 (^{Stat-Soft Inc, 2003}) and Microsoft Office Excel 2007^® were used.

Types of SAES

Resulting from the conglomerate analysis, three groups of SAES were identified, which, according to their characteristics of technological level and maize productivity, were named: Improved Traditional (TM=2.04 %), Traditional (T=27.21 %) and Subsistence Traditional (TS=70.80 %). Based on this classification, significant differences were found (P<0.05) in the variables analyzed (Inetha, Inet∆ha, Eeha, E∆ha, Ipreag and Ac), except in the percentage of coverage of the minimum welfare line (Figure 1). The distance at which the cut was made to define the groups was of 9000.

Figure 1 Conglomerate analysis diagram based on the k-media method and dendrogram of the types of SAES. 

Description of SAES groups

Three SAES were identified, which were classified as Improved Traditional (TM), Traditional (T), and Subsistence Traditional (TS) (all by initials in Spanish). In the TM the age of producers in these SAES is 78±3.74. All 100 % of the producers sow in the Tonalmil period (Huasteco name), which covers the months of November to December, harvesting in April. The surface of the TM SAES is 1.67±0.37 ha, with a production of 7.4±1.7 t ha^-1 of maize; this production is attributed to the use of improved maize seeds, the use of agrichemicals, and a population density of 74000±600 plants ha^-1, which are obtained with sowing carried out at a distance of 50 cm between furrows, 27 cm between plants and 3.8 to 4 plants per linear meter, in accordance with what was reported by ^{Rincón-Sánchez et al. (2014)}, who mention that the density of plants with hybrid maize must be 60 000 to 80 000 plants ha^-1, obtaining a grain production that exceeds the national average of 2.4 t ha^-1 of maize for summer-spring rains (^{SIAP-SAGARPA, 2017}). This agrees with what is reported in the literature, where it is indicated that by applying adequate technological packages it is possible to increase the productivity of agroecosystems (^{Damián et al., 2007}; ^{Sanclemente et al., 2012}; ^{Uzcanga et al., 2015}). This productivity impacts directly the values of Inetha, Inet∆ha and Eeha (Table 3), in addition to having an influence on the efficient use of energy per ha (E∆ha), the economic productivity per MJ invested (Pe∆), the economic productivity per work invested (Pet), the energetic productivity per money invested (P∆$), and the energetic productivity per work invested (P∆t). These results agree with those reported by ^{Tobasura et al. (2012)}, which indicate that there is a direct relation between energetic and economic productivity, where it is confirmed that with a higher production the energetic productivity increases.

In the SAES (TM), 100 % of the producers use 50.85±8.79 % of the production for their consumption and therefore achieve certain degree of security. These results differ from those reported by ^{Romero et al. (2016)}, who indicate that with a higher maize productivity, less percentage is destined to auto-consumption. For the case of the study region the percentage destined to auto-consumption is due to the cultural rooting that these communities have for maize, as ^{Martínez et al. (2006)} indicate in a study about characterization of the diversity and participative selection of maize prospects in Chiapas, Mexico.

The traditional group (T) is constituted by 27.21 % of the SAES studied. The age of the producers that manage these SAES is 57.15±14.88 years. Of the total, 95.19 % sows during the period of November-December, harvesting in April. They have a surface of 1.26±0.55 ha, with a production of 2.25±0.74 t ha^-1 of maize; this production is similar to the national average. The use of some agricultural practices is observed, such as weed control, low fertilization, low population density of 41 000±300 plants ha^-1 that are obtained with sowing carried out at a distance of 80 cm between furrows, 30 cm between plants and 3.3 plants per linear meter, in addition to the use of native seeds. The results found in these SAES are similar to those reported by various authors (^{García et al., 2013}; ^{Damián et al., 2015}; ^{Turiján et al., 2012}), who agree that by not applying a technological package in maize sowing, the crop’s yield is low.

In relation to the behavior of the variables: net economic income per ha (Inetha), net energetic income per ha (Inet∆ha), economic efficiency per ha (Eeha), efficient use of energy per ha (E∆ha), economic productivity per MJ invested (Pe∆), economic productivity per work invested (Pet), energetic productivity per money invested (P∆$), energetic productivity per work invested (P∆t), has mean values (Table 3), which is a result of the low yield of native maize grains compared to what is obtained with improved varieties and with the application of adequate technological packages.

The subsistence traditional group (TS) is constituted by 70.75 % of the SAES studied. The age of the producers who manage these SAES is 57.79±13.49 years. Of them, 87.50 % sow in the period of November to December, harvesting in April (Tonalmil); the rest sow twice a year (Rainfed and Tonalmil). They have a surface of 1.01±0.39 ha, with a production of 0.919±0.397 t ha^-1 of maize; the population density and the distances between planting are the same as the traditional; however, 58.80 % less production is obtained per ha. The use of some agricultural practices was identified, such as manual weed control, without pest control or use of fertilizer and with the use of native maize seeds, which is obtained from the sowing from the past cycle. This low production of rainfed maize is also reported by ^{Damián et al. (2014)} and ^{De Ita et al. (2016)}, who indicate that this productive condition is because small-scale producers do not have access to technological packages that adapt to the agroclimate and cultural conditions of the region where they are located; in addition, something to take into account is that native maize is of low yield (between 0.66 and 1.673 t ha^-1) in plant densities between 26 000 and 36 000 plants ha^-1 and under conditions of low or very low technology (^{Luna and Gaytán, 2001}; ^{Ayala-Garay et al., 2013}).

Concerning the behavior of all the variables in the SAES (TS) analyzed in Table 3, it was found that these have very low levels, which agrees with what was exposed before about the low productivity in maize grains, considering that, according to ^{Risoud and Chopinet (1999}), the energetic efficiency of a farm is the relation between the energy produced and the sum of all the energy used directly and indirectly, which depends on the productivity in maize grains. The values of economic efficiency and efficient use of energy were 1.37±0.90 and 0.74±0.31, respectively; these values are similar to those reported by ^{Guevara et al. (2015)} in mono-culture maize systems.

Variables that determine the proportion of coverage (Pcober) of the minimum welfare line (MWL) and auto-consumption

The TM group obtains net annual income per ha of $39 412.17±11 685.64 ha^-1, which is equivalent to a net daily income per ha of $ 107.98±32.01día^-1, when compared to the minimum wage that is $ 92.32 day^-1 for 2016. Based on this information we can determine that these producers have an income 14.50 % higher than the official minimum wage (^{CONASAMI, 2016}). All 100 % of the TM producers (2 % of the total producers surveyed) obtained, through maize production, income that allow them to surpass the minimum welfare line in 40±21 %.

The canonic correlation showed that there is a significant correlation between the two groups of social or dependent canonic variables, and the independent ones, explaining 75 % of the variability. The canonic weights of the first canonic correlation point out that all the variables have high correlation, except the auto-consumption variable for this group (Figure 2).

Figure 2 Association pattern of the first canonic correlation of the relation of the proportion of coverage of the minimum welfare line and the percentage of auto-consumption of the rural family, with the indicators of financial energetic efficiency and of productivity of the SAES (TM). U1: Association of independent variables. V1: Association of dependent variables. 

Figure 2 shows that to the extent that the variables (U₁): economic efficiency per ha, efficient use of energy per ha, economic productivity per invested energy, economic productivity per man-hours invested have higher values, the producer has more capacity to reach the percentage of coverage of the minimum welfare line, which is completely logical since the producer’s purchasing power increases and, therefore, the producer can manage to purchase some essential products.

The traditional SAES (T) generate net annual income per ha of $7883.84±3904.89 ha^-1, which is equivalent to a net daily income per ha of $21.60±10.70 day^-1, which when compared to the minimum wage of $92.32 day^-1 for 2016 (^{CONASAMI, 2016}), it was determined that these producers earn 76.60 % below the official minimum wage.

Through maize production, T producers attain incomes that allow them to reach the minimum welfare line in only 8 ± 6 %. This indicates that with the maize production a large number of producers cannot generate incomes that allow them to satisfy their needs, remaining in dietary poverty, as ^{González et al. (2015)} indicate in a study carried out in indigenous communities of Chilchota, Michoacán.

The canonic correlation showed that there is a significant correlation between the two groups of social or dependent canonic variables and the independent, explaining 69 % of the variability. The canonic weights of the first canonic correlation signal that the variables: economic efficiency per ha (Eeha), efficient use of energy per ha (E∆ha), economic productivity per MJ invested (Pe∆), economic productivity per work invested (Pet), energetic productivity per money invested (P∆$), energetic productivity per work invested (P∆t) has high correlation, except the variable coverage of minimum welfare line (Figure 3), which agrees with the previous data, since 100 % of the peasant families of the producers that manage these SAES barely manage to cover the minimum welfare line. In relation to the variables of economic efficiency and efficient use of energy, their behavior indicates that as these variables increase from a higher productivity, auto-consumption increases (+Ac), which indicates the positive value of this variable, while the percentage of the product that is destined to the sale decreases (^{Rayón, 2014}; ^{Zagoya, 2015}).

Figure 3 Association pattern of the first canonic correlation of the relation of the proportion of coverage of the minimum welfare line and the percentage of auto-consumption of the rural family, with the indicators of financial energetic efficiency and of productivity of the SAES (T). U1: Association of independent variables. V1: Association of dependent variables. 

The subsistence traditional SAES (TS) generate net annual incomes per ha of $2410.05±823.59 ha^-1, which is equivalent to a net daily income per ha of $6.60±2.26 day^-1, when comparing it to the minimum wage, which is of $92.32 day^-1; for 2016, we can determine that these producers earn 92.85 % below the official minimum wage (^{CONASAMI, 2016}).

Through maize production, the TS producers achieve incomes that allow them to reach the minimum welfare line in only 5 ± 1 %; this indicates that a large part of the producers do not manage to generate incomes to satisfy their needs with maize production, remaining in dietary poverty (^{González et al., 2015}).

The canonic correlation showed that there is a significant correlation between the two groups of social or dependent canonic variables and the independent ones, explaining 84 % of the variability. The canonic weights of the first canonic correlation point out that all the variables have a high correlation (Figure 4); in addition, 100 % of the peasant families of the producers that manage these SEAS do not manage to cover the minimum welfare line, destining most of the production to the sale to satisfy their basic needs. These results differ from what was reported by ^{Zagoya (2015)}, who indicates that the main destination of the production is auto-consumption and, in lower proportion, commercialization.

Figure 4 Association pattern of the first canonic correlation of the relation of the proportion of coverage of the minimum welfare line and the percentage of auto-consumption of the rural family, with the indicators of financial energetic efficiency and of productivity of the SAES (TS). U1: Association of independent variables. V1: Association of dependent variables.