Geographical framework of the investigation

Calpan is located between parallels 19° 03’ and 19° 09’ North latitude and meridians 98° 23’ and 98° 35’ West longitude. It has an altitude above sea level of between 2 200 and 3 200 m and has an area of 67 km² (^{INEGI, 2015}). The orography of the municipality is determined by its location with respect to the Sierra Nevada and the Neo-Volcanic axis, where the soil type is: Arenosol 38%; Phaeozem 26%; Cambisol 8%; Andosol 8%; Fluviso 7% and Leptosol 13%. In terms of hydrology, the municipality is located in the western high part of the Atoyac River basin, has intermittent and permanent streams from the foothills of the Iztaccihuatl (^{INEGI, 2010}).

Most of the work areas are dedicated to rainfed agriculture. Maize represents the most important crop in the municipality, with a planted area of 2 256 ha, by 2015, 73% of the total area devoted to agriculture, obtaining yields of 2 701 kg ha^-1 (^{SIAP, 2016}).

Design and application of the questionnaire

To design the questionnaire, it was based on questions referring to the two conditions (general and concrete) that influence the management of maize.

Calculation of the sample

To determine the sample size, the simple random sampling formula was used (^{Cochran, 1982}):

Where: n= sample size; N= 546 total families benefited from (PROAGRO Productivo) in the municipality; d= 0.14 (precision); Z_α/2= 1.95 (reliability 95%); S_n²= 0.25

Simple random sampling was applied with proportional distribution of the municipal sample according to the number of producers in the communities (334 San Andres Calpan, 146 San Lucas Atzala, 62 San Mateo Ozolco and 5 Pueblo Nuevo). The sample size was 110 families and were distributed as follows for San Andres Calpan 42, San Lucas Atzala 36, San Mateo Ozolco 27 and Pueblo Nuevo 5.

Radical Innovations Appropriation Index (IAIR)

To assess the use of radical innovations, the radical innovations appropriation index (IAIR) was calculated. To this end: a) the recommendations of the INIFAP (Table 1) were compared with the practices applied by the farmer; b) a nominal value was assigned to the management of 100 points and it was weighted according to the impact each component has on productivity: sowing date (10), variety (20), density of plants (15), fertilization dose (25), fertilizer application date (5), type (6) and herbicide dose (4), type (6) and insecticide dose (4) and disease control (5); and c) each weighted value was divided into two: the first quotient was for the use of the recommendation and the second for its proper management. The value of the IAIR varied between 0-100 units and for its calculation the following mathematical expression was used:

Where: IAIR= rate of appropriation of radical innovations; k= number of components of the technological package recommended by INIFAP; p_i= weighting granted to the ith recommendation component; Σp_i = 100; i= 1, 2, k; SPA_i = agricultural production system for the i-th recommendation component; i= 1, 2, k; PTA_i = agricultural technology package for the i-th recommendation component; i= 1, 2, k; (SPA_i/PTA_i)= proportion of technology used that can take values of zero, for the non-appropriation of the technology recommended by the INIFAP; one, for the appropriate use of technology and 0.5 for the inappropriate use of the technological component.

Degree of employment of progressive innovations (GEIP)

To evaluate the use of progressive innovations, the GEIP was calculated which measures, on a scale from 0 to 100, the proportion in which the producers used the following agroecological practices or inputs: creole seed, association and rotation of crops, conservation techniques of soils and application of manure, giving each of them a value of 20 units. In this way, the nominal value of the GEIP was 100. The GEIP was obtained by applying equation 3 (^{Damián and Toledo, 2016}).

Where: GEIP= degree of employment of progressive innovations; k= 5: number of technologies considered for the study; V_i= weight given to the i-th peasant technology depending on its use or not; The value was zero if the producer did not use the technology or 20 if he used it.

Typology of producers

The producers were grouped according to the value of units of the IAIR and the GEIP: low (0-33.3) medium (33.34-66.66) and high (greater than 66.66). The typology made it possible to identify general and specific characteristics and thus have a more integrated knowledge of the different producers.

Evaluation of radical and progressive innovations

The management of seasonal maize in the municipality is based on the interaction and application of radical and progressive innovations. When evaluating the IAIR, only producers of low and medium appropriation were found (Table 2).

The low use of these radical innovations is explained because they prioritize the edapho-climatic factors and elude, that the general and concrete conditions of maize management are different among the producers (^{Damián and Toledo, 2016}). The results show that there is no relationship between the degree of application of radical innovations and performance (r= -0.086, p= 0.369). Even the producers of low appropriation obtained higher unit yields than the average ones, finding significant differences between the yields, even though they applied 14.8 more units of the technological package.

This coincides with that reported by ^{Damián et al. (2007)}; ^{Osorio et al. (2012)}, that when evaluating the use of technology appropriation, it was found that farmers adopted the technology, but this did not have a positive effect on the increase of maize yields.

For its part, Table 3 mentions that the GEIP average is higher (60.1) than the IAIR (40.2). Likewise, it is evident that in the use of progressive innovations there is a direct relationship between the GEIP and yields (r= 0.263, p= 0.011), with significant differences between yields of the types of producers. The highest yields are due to the fact that progressive innovations promote agroecological interactions which improve the productivity of the scarce resources used to manage maize (^{Mendoza, 2004}, ^{Altieri and Nicholls, 2012}).

Variables related to the appropriation of radical innovations and yields

In Tables 4 and 5 it was observed that in Calpan the variables that had a positive correlation with the IAIR were the level of schooling and the income of the producer (r= 0.235 p= 0.014; r= 0.259 p= 0.013, respectively).

The greater schooling is related to a greater receptivity to the advice provided by the agrochemical merchants in the municipality. ^{Morales et al. (2012)}, indicate that the level of education is positively associated with the use of radical innovations.

Regarding income, this greater appropriation is due to the fact that radical innovations have a high cost and can only be accessed by higher income producers. In this regard, ^{Bernardino (2013)}, indicates that level of income positively influences the use of radical innovations.

Variables related to the appropriation of progressive innovations and yields

According to the figures shown in Tables 6 and 7, the variables that correlated positively with the GEIP were the number of members per family (r= 0.229, p= 0.016) and the age of the producer (r= 0.273, p= 0.019).

The first case is due to the fact that in the municipality of Calpan a traditional smallholder agriculture is practiced, where certain agricultural activities (cultivation work), requires a greater amount of labor force. ^{Magdaleno et al. (2014)}, confirm that a greater number of children represents a greater labor force to carry out agricultural activities, contributing with their work force in various tasks in the field.

Regarding income, this greater appropriation is due to the fact that radical innovations have a high cost and can only be accessed by higher income producers. In this regard, ^{Bernardino (2013)}, indicates that level of income positively influences the use of radical innovations.

For its part, the positive relationship between the age of the producer and GEIP can explain why producers over 63 years of age maintain management habits that have been nourished by knowledge, experience, knowledge and peasant practices, which were taught by their ancestors, which allows them to achieve higher yields (Table 7).

Authors such as ^{Koohafkan (2010)}; ^{Toledo (2013)}, point out that the peasant knowledge used in the management of applied resources in agricultural production is a fundamental characteristic of the elderly population and is based on experience and practice, conditions that maximize the synergies between resources.

In this study, the higher productivity of older maize farmers (>63) is due to the fact that they managed the maize in the following way.

They selected the creole seed immediately after the harvest considering: the ears of greater size and quality, that the ear was thin, selecting the part of the middle of the ear from which they obtain the grains that they will use in the next planting. The farmers select the maize seed from the barn after the harvest, considering the size of the ear, size of ear and shape of the seed.

They carried out the sowing in the months of March-April, probably this influenced in a greater use of light hours what derived in a greater yield. ^{Cirilo (2015)}, mentions that early plantings present the maximum production potential, since they take advantage of solar radiation levels.

They used an average of 2 196 kg ha^-1 of manure, which is an essential component of maize management since it improves the structure of the soil and thereby increases the water retention capacity and the availability of nutrients for plants (^{López et al., 2001}).

They associated the cultivation of maize with legumes beans (Phaseolus vulgaris L.) and fava bean (Vicia faba L.) in 92%, while younger producers associated maize-legumes on average 45%. The associations boost soil productivity, since they limit the problems of pests and diseases; as well as legumes capture nitrogen one of the essential nutrients for the development of plants (^{Damian and Toledo, 2016}).

They carried out crop rotation, a technique that allows them to break the biological cycle of pests and improve soil properties. Among the main rotations found among these producers is the bean and leguminous bean which, as already mentioned, is essential for the capture of atmospheric nitrogen.

They carried out soil and water conservation practices, terraces and boards, which allowed them to preserve these inputs, as well as nutrients and their recycling, which are essential to improve the productive capacities of agricultural land. In addition, these practices guarantee greater biodiversity of plants, which regulates the proliferation of pests and diseases.

They planted a higher density of plants (70 513), which is probably associated with the use of higher quality creole seed, manure and the third labor that only they applied. ^{Krall et al. (1997)}, state that high yields are associated by a greater number of plants, which together make efficient use of water and nutrients.

The complementarities and interactions that occur between progressive innovations are those that trigger the highest yields. As indicated by ^{Vallejo et al. (2011)}, farmers have learned to grow their grain in small plots located at different altitudes and in different microenvironments, to rotate their crops to break disease cycles and maintain healthy soils, planting a wide variety of crops, carry out tillage practices and select seeds that tolerate particular micro niches.