Economic efficiency per hectare (Eeha)

The indexes of economic efficiency allow identifying the yield from resources used in the productive process. It was calculated by dividing the sum of the total annual gross income per hectare (Ingtoha) generated in each one of the agricultural/ livestock activities, by the sum of the total production cost per hectare (Ctpha) per activity.

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 the energetic resources within the productive processes in agroecosystems. For its calculation, the sum of the total energy production generated per hectare (PtΔha) was divided by the i-th agricultural/livestock activity, by the sum of the energy invested per hectare (invΔha) in the i-th activity during a period of one year.

Productivity

It is understood as the relationship between the production obtained by a system of production or services and the resources used to obtain it. The determination of the financial and energetic productivity of the systems through indicators was suggested.

Economic productivity indicators (Ipreag)

Economic productivity allows us to determine the productive behavior of the agroecosystem (Table 2) in pesos ($) with regards to work units ($ Man hours^-1) and energy ($ MJ^-1).

Table 2 Variables used to calculate the indicators of economic productivity of agroecosystems. 

Indicators of energetic productivity (IprΔagr)

Energetic productivity allows us to determine the productive behavior of the agroecosystem (Table 3) in megajoules (MJ). For its determination, the methodology proposed by ^{Denoia et al. (2006)} used when calculating the energetic productivity per unit of work (MJ Man hours ^-1) and monetary (MJ $^-1).

Table 3 Variables used to develop the index of energetic productivity of the agroecosystems. 

Index of agricultural/livestock biodiversity

To obtain the index of agricultural/livestock biodiversity, the Shannon diversity index was calculated (^{Shannon and Weaver, 1963}). This model takes into account the number of agricultural sub-systems and the distribution of the surface to obtain the agricultural/livestock biodiversity. When the index is high there is greater diversity and high uncertainty (^{Gallardo et al., 2002}; ^{Salgado-Mora et al., 2007}; ^{Cirujeda et al., 2008}).

where: ρ _i : n _i /N; H’: diversity; n: surface assigned to each agricultural/livestock sub-system; N: total surface of the agroecosystem.

Auto-consumption

For auto-consumption (Ac), the ^{Leite (2004)} definition was used, which states that the study of auto-consumption is limited exclusively to food production; this is the part of the agricultural/ livestock production destined to feed the members of the family and the animals, deducing from this production the parts related to commercialization, donation or loss. In its calculation the total of the product was quantified and the amount that the producer used for family consumption was subtracted from the sub-products obtained in the AES; then, the percentage it represented was calculated (^{Gallardo et al., 2002}).

Percentage of coverage of the line of minimum welfare (Pcober)

In order to determine the proportion of coverage of the line of minimum welfare (Pcober), the cost of the Normative Basket of Essential Satisfiers (Canasta Normativa de Satisfactores Esenciales, CNSE) was first calculated through the linear equation adjusted by ^{Boltvinik and Marín (2003)} from the table elaborated by ^{Marín (2002)} for the calculation of the cost of the variables family goods (FG) and individual goods (IG), based on the requirements of the General Coordination of the National Plan for Depressed Zones (Coordinación General del Plan Nacional de Zonas Deprimidas, COPLAMAR) in which all the essential satisfiers required by a household are considered, the costs equivalent to those of an adult male which counts as the unit are the following: adult woman 0.81, boy 0.58, girl 0.54, male baby 0.43 and female baby 0.43.

where: CNSE: Cost of the Normative Basket of Essential Satisfiers, ae: sum of equivalent adult units, p: number of people in the household. ^*The constant values are updated up to June 2007.

Later, we calculated in what proportion the net annual income generated through the agricultural and livestock activities in the agroecosystem allows each family to reach or exceed the line of minimum welfare.

The net agricultural/livestock income (Inetoagr) was calculated by adding up the gross income generated from the agricultural/livestock activities carried out in the agroecosystems, including the Ac, and next the total costs of the agricultural/livestock activities were subtracted.

Statistical analysis

The multivariate technique of canonical correlation was used, with the aim of understanding which of the indicators of economic energetic efficiency and of productivity of the agroecosystems contribute to exceeding the line of minimum welfare (LMW). The independent variables or of efficiency were: zone, surface, biodiversity index, 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 line of minimum welfare and of auto-consumption. For this purpose, the statistical software Statistica^® version 6 (^{Stat-Soft Inc, 2003}) and Microsoft Office Excel 2007^® were used.

Auto-consumption in the agroecosystems

The plots in the irrigation zones have a surface of 6.90±9.9 ha, slightly higher than those located in the hill zones, with an area of 5.81±9.3 ha. Auto-consumption (Ac) is observed primarily in the agroecosystems where the activities of cattle breeding and maize sowing are carried out, directing part of the production to Ac and selling the excess (milk, cheese and maize), result that coincides with what was reported by ^{Perales et al. (2005)} where maize is a source of food, as well as of income, cultural identity and social condition, and part of a network of food security for the peasant rural family. In the AES devoted to sugar cane and fruit tree production the Ac is not made evident due to the characteristics of these products. In the case of the maize component, in the irrigation zone, 15 % of the production was used for Ac (human and animal), while in the hill zone 16 %. The peasant family obtains milk and meat (standing animals) from the bovine component, but only milk in liquid or transformed form (cheese) participate in the Ac, with values of 4 % in the irrigation zone and 5 % of the milk production in the hill zone. Of the milk, 6 % is used in the form of cheese for the rural family’s diet in the irrigation zone, and 8 % in the hill zone; these values are similar to those reported by ^{Jiménez et al. (2008)}, who estimated that 81 % of the producers carry out auto-consumption and represent 4 % of the daily production volume.

According to ^{Brunett et al. (2005)}, a large part of milk production is sold to “boteros” or “lecheros”, who are in charge of selling it in the communities adjacent to the agroecosystems; in other cases, milk production is absorbed by “queseros”, who collect it and transform it into fresh cheese. The surplus production in agroecosystems is destined to Ac, whether in liquid form or as cheese. ^{Quintos and Quispe (2004)} report that generally in small-scale production units, an important part of the products (milk, meat, manure or animals) are destined to the sale, and the surplus to Ac; the rural family tries to improve the nutritional state of its members through this practice.

Relation of the efficient use of energy, economic efficiency, by zone and by productive activity with the proportion of coverage of the line of minimum welfare

Of the 81 producers surveyed in the municipality of Paso de Ovejas, 50 own plots located in Irrigation District 035 La Antigua, of which 84 % have cultivating sugar cane as main activity, which requires large quantities of water. In that sense, ^{Parra (1989)} reported that the climate factor that limits most the sugar cane production in the state of Veracruz is the distribution of rain precipitation, since the temperature of the state does not affect the development of the crop. As can be seen in Table 4, it presented the highest values of efficient use of energy, results that are similar to those reported by ^{Markos (2007)} with sugar cane as a crop of high energy production. The efficiency of these is high, in relation to the efficiency shown by other production systems, such as those with fruit trees, which is close to one (^{Gliessman, 2001}). Sugar cane has a low productivity and, therefore, the producer obtains moderate income from this activity in the AES; this crop contributes with e0.61±0.42 of the proportion of coverage of the line of minimum welfare as a result of the incentives that the sugar plant offers sugar cane producers; however, because of the low profitability of the crop the producers obtain moderate income that does not allow them to exceed at 100 % the line of minimum welfare. ^{Bahena and Tornero (2009)} report similar results in a diagnosis of the family production units under small-scale irrigation in the sub-basin of the Yautepec River, in Morelos, México.

Table 4 Rate in the efficient use of energy, economic efficiency, by zone and by productive activity, with the proportion of coverage of the line of minimum welfare. 

The second crop of greatest importance from the point of view of the efficient use of energy in the irrigation zone was maize (Table 4); this low energetic balance is because the production system under irrigation presents an excessive use of inputs and machinery. According to ^{Alemán and Brito (2003)}, in maize production there are considerable energetic expenses when a “green revolution” type model is followed. The economic efficiency of maize under irrigation was 1.48±2.56 as a result of a relatively higher yield than in the hill zone; that of rainfed areas presented values of efficient use of energy of 1.28±0.89, that is, 1.48 under what was obtained in the irrigation zone and economic efficiency of 0.61±0.42, as response to the low yields. ^{Ramírez et al. (2009)} report that those obtained under rainfed conditions are quite low due to the use of materials of low potential, deficiencies in the plant’s nutrition, and lack of sufficient moisture. In the AES, where the totality of the surface is subject to very erratic rainy seasons, it is frequent to find that between 40 % and 50 % of the surface sown is lost totally or partially.

In relation to cattle production, this productive system presented a low efficiency in the use of energy both in the hill zone 0.93±1.83 as under irrigation 0.81±2.31, because double-purpose cattle breeding is carried out with feeding based on grazing plus maize residues, or only grazing, which does not allow an adequate transformation of inputs into products (milk or meat). When characterizing the animal genetic resource in the design of sustainable cattle production systems in the tropics, ^{Magaña et al. (2009)} indicate that the ideal situation is for the cow to convert efficiently the energy from food into sellable products, such as milk and kilograms of calf, which can be achieved with changes in the dietary management. ^{Bacab-Pérez and SolorioSánchez (2011)} report milk production in doublepurpose cattle managed in forest-grazing systems in Tepalcatepec, Michoacán, where the cows received 8 kg animal^-1 day^-1 of concentrate meal during lactating in the traditional system, and only 1.5 kg animal^-1 day^-1 in the forest-grazing systems; however, milk production in the forest-grazing ranches was 9.0 and 9.2 kg animal^-1 day^-1, and in the traditional ones 10.4 kg animal^-1 day^-1.

In both zones livestock production was the product system that reflected highest economic efficiency, with index values of 3.91±4.73 for the irrigation zone and for the hill zone. In most of the production units there is not a high expenditure in production as a result of the low technology applied in the sanitary management and in the diet with the use of fibrous resources as the main component in the diet, result that agrees with what was reported in several studies in double-purpose production systems (^{Corro et al. 1996}; ^{Herrera et al.. 2008} and ^{Orantes et al.. 2014}). In a study about the productive response of double-purpose cows under grazing of sorghum shoots (Sorghum bicolor) and supplemented with a liquid diet based on cují (Acacia macracantha) and phosphate urea, ^{Espinoza et al. (2009)} report that as far as the producer performs a small investment, the production of the herd is increased favorably. Double-purpose livestock production is the activity that has greatest incidence on the proportion of coverage of the line of minimum welfare in the hill zone 0.33±0.51, considering that, in most cases, in the rural zones of México livestock production has the function of family savings, which transforms quickly into money and allows facing contingencies in the household and the production unit, which agrees with what was reported by ^{Reyes and Gijón (2007)} in a study about rural development, international migration and market scarcity in México.

Regarding the zones, it is evident that there is a greater efficiency in the use of energy and economic efficiency in the irrigation zone (Table 4) as a result of using fertilization, improved seeds, and of applying irrigation, thus avoiding hydric stress in the plants; on the contrary, in the hill zone with erratic climatic conditions, the use of Creole seeds and grasses of medium to low quality (in most of the cases), it is not possible to obtain an adequate productivity. These results agree with what was reported by ^{Vilaboa (2012)}, which indicate that there are social, economic, productive and social limitations that restrict the development of the locality of Angostillo, with it being representative of the hill zone in the municipality of Paso de Ovejas.

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

Of the producers, 74.08 % do not attain income through the agricultural and livestock activities in the AES to allow them to overcome the welfare line. These results are well above those reported by ^{CONEVAL (2014)}, which indicates that the percentage of population with income lower than the line of welfare went from 52.6 % to 58 % from 2012 to 2014 for the state of Veracruz.

The canonical correlation between the two groups of social or dependent canonical variables and the independent ones showed that there is a significant correlation, explaining 83 % of the variability. The canonical weights of the first correlation point out that economic efficiency, economic productivity per man hours, and the agricultural/livestock biodiversity index have a low correlation (Figure 1).

Figure 1 Pattern of association of the first canonical correlation of the rate of the proportion of coverage of the poverty line and the percentage of auto-consumption of the rural family, with the indicators of financial energetic efficiency and of productivity in the agroecosystems. U₁=Association of independent variables. V₁= Association of dependent variables. 

Figure 1 shows that to the degree that the variables (U₁): efficient use of energy, energetic productivity per money invested, economic productivity per energy invested, zone and surface, increases, the percentage of coverage of the line of minimum welfare also increases; this is entirely logical, since the purchasing power of the producer is also increased and, therefore, the producer manages to reach or overcome the line of minimum welfare. This can be observed in the hill zone, where a moderate use of the energetic efficiency in the maize AES is maintained, although, when complemented with the economic efficiency of cattle breeding, this conjugation of ecological and productive resources allows families to cover the line of minimum welfare. On the contrary, when these independent variables (U₁) decrease, autoconsumption in the AES increases (Figure 1), as a result of a reduction in the capacity to generate adequate income through agricultural/livestock activities in the AES.