Introduction

Rainfed maize is the most important crop in Mexico with an area of increased plantings of 56% of the agricultural area, and average 2.26 t ha^-1. Jalisco is the State with the largest area planted 565,486 ha and an average yield of 5.37 t ha^-1 (SIAP, 2012); in this State the region Cienega stands with an area of close to 25% seed and grain yield by 7.33 t ha^-1. Another important area is the Altos de Jalisco, particularly the close relationship that has maize to livestock production, particularly family dairy (^{Flores et al, 2007}). Productivity in rainfed maize in the region Cienega, Jalisco, characterized by a system ofmonocroping with high use ofinputs, particularly fertilizer, improved seeds and pesticides to control pests and weeds, with two variants important in the management of waste, one is the extraction of these at about 90% and another is the inclusion of 100% ofwaste (^{Flores et al, 2011}); instead the Altos de Jalisco also has high availability of manure, typical input maize in this region (^{Flores et al, 2009}).

The yield ofmaize in Jalisco during the last 10 years has shown a sustained increase in the order of 285 kg/ha/year (^{Flores et al, 2011}), but the low efficiency ofmanagement practices by applying inputs in maize make it a high economic cost cult and important source of diffuse pollution caused deterioration of soil and surface water (^{Flores-López et al, 2012}).

In this context, agriculture is an activity consisting of four site-scale components: climate, soil, and crop and farmer management technology on these three components. Of particular importance is the dependence of agriculture on climate, because of its high sensitivity to global climate change and climate variability, because is essential to understand the interactions between climate change and agricultural production for the stable development of society (^{Hui et al, 2013}). However, this same activity with industry and urbanization, emit greenhouse gases contributing significantly to global warming and climate change, global temperature increase of 0.74 °C from 1906-2005 (^{IPCC, 2007}).

This is the reason that a recurring theme is the effect of research aimed at understanding the effect of management practices on crop grain yield and its long term effect on the economy (^{Chavas et al, 2009}) in the processes related to the dynamics ofsoil organic matter (^{Aurbacher et al, 2013}), the soil water dynamics (Huszar et al, 1999), reduced crop cycle (^{Gohari et al, 2013}), among others.

According to the ^{IPCC (2013)}, the emissions of CO2 by human activities are considered the main cause of climate change, in 2011 the CO2 emissions were around 390 ppm with an average annual increase of the last 15 years in the order of1.35 ppm; according to the patterns ofrepresentative concentration (PCR) acting on the radiative forces (FR), four possible scenarios for future changes occur: PCR with FR of 2.6, 4.5, 6 and 8.5 W/m². According to this scenario, the simulation models show that, the surface temperature on overall average will be about 0.3 to 1.7 °C for the PCR2.6, from 1.1 to 2.6 °C for the PCR4.5, 1.4 to 3.5 °C for PCR6.0 and 2.6 to 4.8 °C for PCR8.5. With regard to the water cycle, the ^{IPCC (2013)} reports a significant contrast between dry and wet rainfall regions, but also between the dry and wet seasons, except for some regions, but with increase in extreme rainfall events.

Climate change has an ambivalent impact on agriculture, so that while increasing mean temperatures and atmospheric CO2 content, the result is an increase in yields (^{Farina et al., 2011}), but also smaller amount of precipitation during summer and increased precipitation variability and patterns of rainfall and evapotranspiration and larger amounts of vapour in the atmosphere with serious implications for the global hydrological cycle (^{Gohari et al., 2013};^{Aurbacher et al., 2013}).

In Mexico, there is a tendency in some agricultural areas to increase the temperature perceptibly from 1990 to date is shown (^{Ruiz et al, 2011}; ^{Zarazúa et al., 2011}) and a slight decrease in annual precipitation in producing areas (^{Ruiz et al, 2011}). The consequence ofthese changes is expected to be reflected in increases in potential evapotranspiration, with a water balance less favourable, reducing the growing season in tropical and subtropical areas, but with equal or higher accumulation of heat units and growing season equal to or larger in the high valley (^{Hatfield et al, 2011}), with a reduction in the ability of the land to produce maize, lower profitability, but in general, the reduction of the production potential of the crops will be associated with greater dynamism in the presence of pests, diseases and weeds (FAO, 2007).

In this context, the agricultural systems have a particular response with the management practices used on the site, so we need to identify their long-term impact and how to direct them to the mitigation/adaptation to climate change and the contribution they have to maintain for agricultural productivity (^{Lal et al, 2011}). With this consideration the management of the agricultural system it is likely that the response of crops like maize in Jalisco, can be damped, which can lead to mitigation-adaptation of the great ecological, economic and social problems that are expected for this crop.

The inherent complexity of agricultural systems makes it difficult to make decisions on crop management, a problem exacerbated in recent years with climate change. One option for solving this problem is the use of simulation models to predict process-based cultivation results, which provide explanations of the dynamic behaviour of the system to changes in the environment, genotype and management, justifying its application in projecting the impacts ofclimate change and adaptation in agricultural production. One of these simulation models (MS) is the EPIC which originally was constructed to quantify the effects of erosion on soil productivity (^{Williams, 1990}).

Today it has become a tool to describe high degree of certainty the yield of crops with complex rotations and tillage operations in more than 100 crops, with routines to evaluate the management of the effects of fertilization, the increase in CO₂ and temperature in the atmosphere, with its implications on the use of rainwater or irrigation, plant growth, nutrient cycling N and P fertilizers or chemical form, the dynamics of crop residues, and density changes soil tillage, erosion and leaching (^{Kiniry et al., 1995}; ^{Hilger et al, 2000}; ^{Wang et al., 2006}; ^{Gaiser et al., 2010}), which makes it a suitable model to evaluate the consequences of increased CO₂ and temperature on the global climate of the earth, as predicted by the ^{IPCC (2013)}.

Adaptation to specific locations, requires only computer and information acquisition a few cycles of crop growth to calibrate the model in the appropriate environment (^{Hodges, 1987}), where the main obstacle to its use is the availability of information for calibration and validation (^{Angulo et al, 2013}).

The MS operating parameters basically develop individual simulation processes studied experimentally in field or laboratory tests. The process of assessment and collection of such parameters is known as parameterization; these parameters are involved in multiple processes which cannot be studied independently in separate experiments; this process is known as model calibration (Witt, 1978). Within the parameters required to operate the model there are some that have more effect on their behaviour or yield; identification of these parameters is known as sensitivity analysis (Witt, 1978; ^{Ferrer et al., 2000}). In maize, the parameters that have been most sensitive model EPIC are the leaf area index, harvest index, crop cycle expressed by accumulated degree days from planting to maturity development (^{Kiniry et al., 1995}).

Once the calibration and sensitivity analysis of MS have been done, it is necessary to resort to the validation process to identify and correct various aspects of the model that can distort and distract from the fact the predictions made, achieving adequate growth simulation, development or yield, defining an adjustment to what happens on the field. The aim ofthis study was to calibrate and validate the model EPIC on rainfed maize to assess the effect of climate change and management practices on grain yield ofrice in the region, Cienega and Altos Sur of Jalisco.

Materials and methods

Model calibration EPIC. Model calibration in rainfed maize used the experimental data of maize described in Table 1.

Table 1 Relationship management producers of maize, used in model calibration EPIC. 

Model validation EPIC. Model validation used the experimental data of maize described in Table 2.

Table 2 Relationship management maize producers used in the model validation EPIC. 

Climate and soil. Climate information from weather stations listed in Table 3 were used. The simulation of long-term maize yield climate model generator EPIC was used with the parameters obtained from the stations shown in the Table 3. Regarding the soil, the database with information from laboratory analyses of soil profiles in the study area generated by INEGI was used. For experimental site used the analysis of the surface horizon (Ap) was used.

Table 3 Weather stations used in the calibration and validation of EPIC and characteristics of climate and soil. 

Assessing the effect of management practices for rainfed maize screened every five years, with the following considerations:

Yield evaluation model EPIC.

Statistical evaluation of model yield EPIC, used the following tests:

Where: n is the number of samples, Pi and Oi are the predicted and observed values, and O is the mean ofthe observed data. With close to zero the root mean square error (MSRE), the more accurate is the model. The model efficiency (E) is between 0 and 1; an efficiency of 1 corresponds to a perfect match between the model estimates and observed data values; with E equal to zero indicates thatthe model predictions are as accurate as the mean ofthe observed data, while a lower efficiency than zero (-0 < E < 0) occurs when the observed mean is a better predictorthan the model. The index ofagreement (d) represents the ratio of the mean square error and potential error, so that a value of d equal to 1 represents a perfect match between the measurement and the model prediction. The coefficient of determination (r²) and the slope and intercept compares the predicted with the observed value. Test "t" was used for comparison between management practices.

Results and discussion

Calibration and validation of the model EPIC

The Table 4 shows the results ofstatistical tests for calibration and validation of the simulation model yield EPIC. The MSRE has over 1.25 t h^-1 in the prediction for the calibration and validation ofthe model, particularly with the middle and high yields, a situation that affects the efficiency (E) of the model with values of0.7 and 0.68, respectively. With respect to the index of agreement (d), the simulations show high coherence values between simulated and measured yields.

Table 4 Results of statistical tests of the model EPIC in the calibration and validation. 

In Figure 1a and b diagrams shown with maize yields estimated versus observed for model calibration and validation EPIC with its linear regression. The coefficient of determination (r²) has values of 0.82 and 0.78, respectively, and a slope higher than unity and lower intercept than zero, indicating a tendency to underestimate and overestimate high yields slightly lower yields.

Figure 1 Relationship between grain yield observed for maize grain yield estimated: a) calibration; b) Model validation EPIC. 

The results of the calibration and validation of the model EPIC obtained in this study are similar to those observed by ^{Gaiser et al. (2010)} , the calibration and validation of this model to simulate maize production in the humid tropics of West Africa and the semi-arid region of Brazil. However, these authors emphasize the importance of harvest index for genotypes oflandrace maize and improved yield and materials are influenced by the physicochemical characteristics of the soil. Given the results presented in model validation, EPIC calibration presents a good yield for use in simulating maize yields to assess the impact of proposed climate change.

Modelling the effect ofyield practices and climate change on maize yield

The EPIC calibrated and validated model, the PCR2.6 climate change scenario was used with the management practices shown in the Table 4, and assess the impact of climate change on maize production system in the rainfed regions Altos-Sur and Cienega of Jalisco. The Figure 2 shows the yield trend for the next 100 years shown with the estimated five years to practices evaluated in the region Altos-Sur of Jalisco handling yield. The average yield between PRC1 and PRC2 and PRC3 practices, was 7.7, 9.8 and 9.1 t ha^-1, respectively, with significant differences between PRC2 and PRC1 against PRC3, but no significant differences between PRC2 and PRC3.

Figure 2 Trend of grain yield in rainfed maize estimated five years in the region Altos-Sur Jalisco, for the next 100 years. 

It is remarkable the difference in yield management practices with PRC2 and PRC1 PRC3, particularly after 2080, where the maize falls steeply PRC1 management. At this point, the temperature is expected to reach at least 0.8 °C increase in temperature and 83 pm CO₂ in the atmosphere, under the most conservative climate change scenario with 2.6 W/m¹ radiative force (^{IPCC, 2013}). The PRC1 scenario involved the use of an intermediate-early genotype under IAF and the use ofmanure and chemical fertilizer two, with the most critical result for maize yield.

Although, the interaction ofmanagement practices ofmaize is complex with climate change scenarios, the explanation of the collapse of handling PRC1 and PRC2 less impact in 2080 and 3 following scenarios could occur by the increase ofCO₂ in the atmosphere, in that increased use of plant water are reported for the reduction ofevapotranspiration (^{Hatfield et al., 2011}) but also the increase in temperature increases the length ofthe growing season, availability and mineralization of nitrogen and changes in the availability of moisture (^{Izaurralde et al., 2011}; ^{Ruiz et al., 2011}), an increase in the soil temperature increases in the mineralization of the OM (Lin and Zhang, 2012).

For PRC1 practice it has low LAI (2.7), which favours evaporation with a consequent reduction in water availability for cultivation and ET reduced by increased CO2. The same situation is observed in PRC3 PRC2 and practices, but with less intensity. After 2080, the practice seems PRC3 cushion the impact of climate change, so it is necessary to further analyse the behaviour of this system of management of maize. Although the IAF is identified as a limiting factor in yield under climate change, it is necessary to examine other factors associated with the response of maize , such as planting date, crop cycle, soil erosion, dynamic soil organic matter could dampen these effects.

Grain yield obtained for handling scenarios region Cienega shown in Figure 3. The average yields for practical PRC4, 6, 7, 8, 9 and 10 were 7.1, 6.4, 6.1, 6.6, 6.5 and 6.1 t ha^-1, respectively, with no significant differences between scenarios. The trend in the yield of this figure shows that after 2075 the yield begins to decline, for the same reasons that occur in the yield of the region Altos-Sur.

Figure 3 Trend of grain yield in maize under temporary management practices in six periods of five years for the region, Cienega of Jalisco in Mexico. 

Although the yields from tríese practices were no statistically significant differences, we had two groups of practices with a significant contrast: the management of crop residues. In scenarios PRC4 and PRC6 not harvest residues are left, but in the PRC7, 8, 9 and 10 scenarios, crop residues incorporated into the soil with two steps of drag, which results in that the content of organic matter (OM) of soil is taken at levels up to 4.6%. In Figure 4a and b trend maize yield for the region Ciénega is shown with management practices grouped tillage with crop residue incorporation without residue incorporation. In this figure the trend of management practices with residue incorporation remains the most stable practices without residue incorporation, profit attributable to the increase in soil organic matter yield (Causarano et al., 2008).

Figure 4 Trend of grain yield in rainfed maize: a) incorporation of crop residues; b) without crop residues, estimated every five years for the region Cienega of Jalisco in Mexico. 

The highest content of OM in the soil has features that reduce the impact of climate change (^{Izaurralde et al., 2006}), along with other benefits such as soil conservation, saving energy, time and labour, reduced machinery costs, moisture retention, reduced soil compaction (^{Figueroa et al., 1992}). Part of the solution to the problem is a modification to the management practices of the PRC scenarios 7 to 10, as is the adaptation of technologies genotypes used shorter the cycle, incorporation of conservation tillage and planting density to generate IAF higher than 5, but it is also necessary to evaluate other factors that may reduce the effect of climate change, to identify practices that maintain stable yield subsequent to 2070.

Conclusions

The indices used for the calibration and validation of the model EPIC were used for estimating the yield ofmaize in the long term, in the Altos-Sur and Cienega regions of Jalisco. The modelling of maize yield in the region Altos-Sur of Jalisco, the PRC1 practice shows significant differences with respects to yield practices and PRC3 PRC2, but the practice PRC1 showed that after 2080, the yield tends to decline, a result attributed to the low density of plants expressed with IAF lower than 2.7; however, the PRC3 practice dampens the effects of climate change. For the region Cienega, no significant difference was shown in maize yield in the long term, but tend to decrease after 2075 yield.

Two contrasting groups of practices were present, where in one the crop residues are included in the soil, obtaining more organic matter, a condition that gives greater stability in maize yield until 2070, at which point it begins to decay the yield. Further research is needed to evaluate interactions with other management factors such as planting date, crop cycle, soil erosion dynamics of organic matter in the soil, which could dampen yield in the long term after 2070.