Revista Mexicana Ciencias Agrícolas   volume 12   number 3   April 01 - May 15, 2021

DOI: https://doi.org/10.29312/remexca.v12i3.2482

Article

Statistical model for predicting corn grain yield

Fernando Reyes-González1

Arturo Galvis-Spinola1§

Juan José Almaraz-Suárez1

Teresa Marcela Hernández-Mendoza2

1Postgraduate in Edaphology-Postgraduate College-Montecillo Campus. Mexico-Texcoco Highway km 36.5, Montecillo, Texcoco, State of Mexico, Mexico. CP. 56230. (frg-58@hotmail.com; jalmaraz@colpos.mx). 2Department of Irrigation-Chapingo Autonomous University. Highway México-Texcoco km 38.5, Chapingo, Texcoco, State of Mexico, Mexico. CP. 56230. (teresa-hdz2004@yahoo.com).

§Corresponding author: galvispinola@gmail.com.

Abstract

The growth of the world population leads to the demand for food, and these must be obtained through the efficient use of resources, this could be achieved by planning and prioritizing the factors that involved in production processes. Simulation models are a tool with which it can visualize scenarios and quantify the inputs to use. In this work, with data on maximum maize yields (RG) from 1943 to 2017 obtained from global field experiments and predominantly data from the United States of America (80%), a statistical model was generated to estimate grain yield in maize (RGE) and to support the decision-making of those involved in the grain maize production process. The most important variables to express the model were: population density (DP), potassium dose (K), irrigation sheet (LR), nitrogen dose (N) and phosphorus dose (P) and were used to generate the model with the stepwise multiple regression method and expressed as: RGE= 3.158205 + 0.693319 (DP) - 0.022246 (K) + 0.005990 (LR)+ 0.010687 (N) + 0.013794 (P), had an R2= 0.73 and a standard error of 0.964 Mg ha-1. DP was the variable that explained in greater proportion the value of RGE, with the analysis of RG data the increase in the planting rate over time was observed to achieve a higher DP and increase the RG, which generated the demand for inputs.

Keywords: Zea mays L., nitrogen, population density.

Reception date: January 2021

Acceptance date: March 2021

Introduction

The highest rate of yield increase in maize hybrids from 1950 to 1999 in east Nebraska, for dry conditions was 0.05 Mg ha-1 year-1 in soils with high water retention capacity, followed by irrigation with 0.028 Mg ha-1 year -1 (Mason et al., 2008). Yield trends from 1987 to 2015 indicated a comparable increase according to latitudes (108, 97 and 117 kg ha-1 year-1 for 35-40°, 40-45° and 45-50° north latitude, respectively) and there was an improvement in high environments (AR) and extremely high yield (MAR) at the average maximum rate of 50 kg ha-1 year-1 (Assefa et al., 2017).

Optimizing agrotechnical elements reduces harmful climate effects (Sárvári and Pepó, 2014). The contribution to factors yields (transgenic resistance to insects, strobilurin fungicide, P-sulfur phosphorus fertilization, S-zinc Zn and nitrogen fertilization N) was greater when applied as part of a complete supplement of inputs than when added individually (Ruffo et al., 2015). Technology and management were the most limiting factors, followed by precipitation and soil in maicera regions of China (Zhao et al., 2018). The challenge is to untangle the interaction of factors that can be manipulated by farmers to increase yields (Van Loon et al., 2019).

Reduced yield in the long rainy season in 2000 and 2001 was attributed to poor precipitation distribution (Shisanya et al., 2009). Precipitation was the limiting factor for water-limited yield potential to reach potential level in four maicera regions in China (Liu et al., 2017). In dry maize by correlation, seasonal precipitation explained to grain yield by 66% (Limón-Ortega et al., 2016).

The effect of moisture stored in the soil and available to the plant plus adequate fertility and a high level of management indicated that the potential to produce maize is determined by such soil capacities (Leeper et al., 1974). Soil texture should be an important criterion on which to make recommendations of the static dose of N to optimize yield and prevent the accumulation of residual nitrate in the soil (Alotaibi et al., 2018).

Problems persist, such as specifying the dose of fertilizer to be applied to increase the efficiency of the use of nutrition and the profitability of production, without deterioration of natural resources (Bugarín-Montoya et al., 2002) and those related to the relative content of nutriments in a crop are connected with problems related to fertilization techniques (Alcántar-González et al., 2016). The consumption of N necessary for a maximum growth rate depends in part on the growth rate when it is not limited by the lack of water or nutrients; the percentage of N in widely different crops seem to be determined not so much by the species but by the total weight of dry matter per unit area (Greenwood, 1983).

Maize requires between 20 to 25 kg N ha-1 for each ton of grain produced (Melgar and Torres-Duggan, 2004). The design of an integrated crop and N management system is an alternative approach to maximizing the use of solar radiation and favorable temperature periods, to achieve high yield and new efficiency in the use of N (Guo et al., 2016). The residual effect of the broadcast application of P in maize and caupi (Vigna unguiculata L.) production, as a measurement of soil yield and P, was greater than high applied doses (Smyth and Cravo, 1990).

The balanced application of N, P and S resulted in an increase in yields compared to treatments with unbalanced or no application, the maximum absorption of nutrients was related to higher yields (Ciampitti et al., 2010). The concentrations in the cob leaf of N-P-S-copper (Cu) and Fe explained the variation in grain yield by more than 50% and 40%, respectively (Kovács and Vyn, 2017). K represents the cation that is absorbed in greater quantity by plants, grasses are known as accumulators of K (Alcántar-González et al., 2016). Under drought stress, the spraying of K and iron (Fe) could reduce such stress in maize (Zare et al., 2014). Foliar application of 1-3% and 0.1-0.2% K and Zn respectively, was more beneficial under limited irrigation conditions and in vegetative stage resulted in better growth and higher yield (Amanullah et al., 2016).

When the number of plants per area goes beyond optimal there are detrimental consequences for the ontogenia of the cob, and it results in infertility (Sangoi, 2000). Increasing plant density can improve biomass and yield and also increases competition for resources between plants, in high density, changes in the structure and functions of the individual and population plant affect the morphogenesis of plants, the accumulation of carbohydrates in the stem, bark tissue and mechanical resistance of the stem, the structure and functioning of the root and are more susceptible to acame (Jun et al., 2017).

Organic farmers can improve the suppression of weeds in maize by interspersing with hedge crops and optimizing yields by sowing maize at a lower rate than is typically used with hedging cultivation (Youngerman et al., 2018).

The availability of precocious hybrids with lower height, fewer leaves, vertical leaves, smaller styles and synchrony between male and female flowering has improved resistance to high densities without showing excessive infertility and has allowed it to intercept and use solar radiation more efficiently, contributing to the potential increase in yield (Sangoi, 2000).

Utilizing genetic diversity has been a pillar of production improvements prior to high-throughput DNA sequencing; related bioinformatics and genetic technologies can be used to detect hidden genetic variability and understand the functions of genes (Phillips, 2010). The cultivation of new genetic materials is important to increase yield potential and meet the growing demand for food (Tao et al., 2015).

A model can be a conceptual, numerical, or graphical representation of an object, system, process, activity, or thought; highlights the characteristics that the modeler considers important of the phenomenon in question (García, 2008), can integrate climatic, soil and genetic variables into the diagnosis of N fertilization of crops (García, 2005), the information generated is the basis for improving the synchronization of pesticide applications, fertilization, irrigation and harvesting (Verdugo-Vásquez et al., 2016). The APSIM-Maize model calibrated in the Northern China Plain (PNC) explained >63% variations in maize yield (Wang et al., 2014).

The yield gap determined with the MCWLA-Maize model decreased by approximately 2% per year in the main corn regions in China (Tao et al., 2015). In different locations and regardless of the reporting method, estimate data in V7 predicted the yield (R2 >0.7) and can be used to predict yields in drought-free conditions in New York (Tagarakis and Ketterings, 2017).

The objective of this work was to discern between different environmental and management conditions, those variables that most influence the RG. Based on this, create a mathematical model to determine the RGE, applicable under different production conditions.

The working hypotheses were: the RG is a function of environmental and agronomic management conditions, climate variables have a more significant influence on the RG, compared to those that make up agronomic management and the RG is a consequence of the incidence of multiple variables, for this the multiple regression model makes it possible to more appropriately determine the RGE for different environmental and management conditions.

Materials and methods

The database of maximum maize grain yields (RG) was generated with information sought in 2019 in the databases: Science Direct and ASCESS DL with the keywords ‘high yield’ ‘corn’ ‘maize’ from the period 1943 to 1946 and from 1948 to 2017, about ten representative RG values were selected per year, studies covering more than a year of research represented RG of more than one year. Within the RG recorded in the literature by essays, no one from Mexico was considered because there were higher records in the rest of the world.

From each study, the location, year(s) studied, genetic material, agronomic management, properties and characteristics of the soil were captured, in addition of climatic conditions and response from experimentation. The RG was adjusted to 13.5% grain moisture and expressed in Mg ha-1. Because of the diversity of the trials, the variables it is reported were not always the same. The classification of variables was: study, other variables reported, and site. The dependent variable studied was the RG, as the main maize product, and which depends on various factors.

The data analysis was: identification and classification of the independent variables of each experiment; general trend of RG; over the years by linear regression (RL), trend of RG over the years by the water regime reported, by RL; trend of RG over the years for each independent variable identified interchangeably of the reported water regime, by RL, trend of RG; over theyears for each independent variable identified, according to the reported water regime, by RL, filtration of independent variables for the creation of the model in the following order: irrigation sheet, doses of N, dose of P, dose of K and population density, selection and ordering of independent variables for analysis using the stepwise multiple regression method, generation of equations: general, by water regime and according to soil texture, by tillage system and by irrigation system and validation of the model: observed RG vs RG estimated by RL.

The factor analysis methodology was carried out using a ‘stepwise’ calculation program, which includes or eliminates predictor variables based on the impact that this causes in the statistic used to assess the significance of the relationship (De la Casa, 1992), the statistical analyses was carried out with the R program (R Core Team, 2017).

Results and discussion

Spatial and temporal distribution of data

The studies analyzed represented eighty different locations and 80% were located in the United States of America (Table 1), the rest was located in Romania, Lebanon, Canada, Spain, Slovenia, France, China and Argentina, a representativeness of different production environments and management schemes was achieved. Over the years, population density, the use of fertilizers and improved varieties in production systems increased, in order to achieve the highest yields. Future research could continue to focus on improving yield and reducing low-yield and medium-yield environments with improved technologies for growing and using hybrids (Assefa et al., 2017).

Table 1. Summary of grain yield data (RG) for the period (1943-2017).1

Corn grain yield trends 1943-2017

The RG averaged 10.679 Mg ha-1, the maximum value was 19.779 Mg ha-1 in 2012 and the minimum of 1.996 Mg ha-1 and was recorded in 1959; throughout the years of study the data showed an uptrend (p< 0.01, R2= 0.74, n= 732) (Figure 1), which verified the constant improvement in production systems to achieve greater RG. Assefa et al. (2017) found a comparable increase in average maize yield at latitudes (rates of 108, 97 and 117 kg ha-1 year-1 for latitudes 35° to 40°, 40 to 45° and 45 to 50° north latitude, respectively).

Figure 1. Relationship between study years and RG (1p< 0.01).

Water regime

The RG averaged 12.395 Mg ha-1 and 10.602 Mg ha-1 for the production of ‘irrigation’ and ‘dry’ respectively, while the maximum RG reached were 19 779 Mg ha-1 in irrigation and 13 834 Mg ha-1 for dry, in both cases of RG and under both water irrigation regimes (p< 0.01, R2= 0.7, n= 331) and dry (p< 0.01, R2= 0.59, n= 23) an uptrend was observed; through the years (Figure 2). The rate of increase in yield was 0.05 Mg ha-1 year -1 for dry conditions in soils with high water retention capacity and 0.028 Mg ha-1 year-1 for cultivation under irrigation (Mason et al., 2008). In 2009 maize yields ranged from 9.05 Mg ha-1 for the dry regime to 15.5 Mg ha-1 for full irrigation, and in 2010 they were 11.7 Mg ha-1 and 15.5 Mg ha-1, respectively (Djaman et al., 2013).

Figure 2. Relationship between study years and RG in different water regimes 2(p< 0.01).

Analysis over time of the identified study variables

With the analysis of the dispersion of the effect in the RG for each independent quantitative variable, levels were delimited to be able to visualize the trend through the study period (Table 2).

Table 2. Levels of quantitative variables studied.

LR= irrigation sheet; N= nitrogen dose; P= phosphorus dose; K= potassium dose; DP= population density.

Irrigation sheet

The response in the RG to irrigation was greater for rates greater than 900 mm (p< 0.01, R2= 0.74, n= 18) and 450-699 mm (p< 0.01, R2= 0.73, n= 26). In four irrigation regimens, there was a linear increase in real crop evapotranspiration (ETr) with increasing amounts of irrigation (R2≥ 0.97) (Djaman et al., 2013). In sandy soil and dry conditions, irrigation significantly increased yields and was the most important factor compared to tillage and rotation (Huynh et al., 2019).

Nitrogen dose

The response in the RG to the doses of N was greater for doses greater than 500 kg N ha-1 (p< 0.01, R2= 0.73, n= 51) and 400-500 kg N ha-1 (p< 0.01, R2= 0.90, n= 31). Grain yield with a management proposal ranged from 16.1-19.1 Mg ha-1 over four years for China Loess Plateau and reached 98 to 108% of potential yield; the optimal dose of N ranged from 207 to 222 kg ha-1 with a ratio of 65 to 80 kg of grain per kg of N applied (Guo et al., 2016). When the application of N increased from 0 to 60 kg ha-1, the yield increased 7.3% (Limón-Ortega et al., 2016).

Water regimen and nitrogen dose

With this combination there was greater response in the RG for irrigation +400-500 kg N ha-1 (p< 0.01, R2= 0.92, n= 23) and irrigation+dose greater than 500 kg N ha-1 (p< 0.01, R2= 0.58, n= 42). The grain yield with a Lay Flat® hose system was 10 500 kg ha-1, with an extraction of N by the grain of 165 kg ha-1 and an extraction of N by the dry matter of 109 kg ha-1 (Sifuentes-Ibarra et al., 2015).  

Phosphorus dosage

The largest response in RG over the years to applied P was for 275-325 kg P ha-1 (p< 0.01, R2= 0.45, n= 23) and 150-199 kg P ha-1 (p< 0.01, R2= 0.84, n= 78). There was no response in yields beyond a dose of 22 kg P ha-1, in equal amounts of applied P, the absence of a yield difference between the application methods (in band and broadcast) indicated that the band placement of 22 kg P ha-1 would be the best method of application of P to maintain long-term crop production, under the manual tillage practices used in the study region (Smyth and Cravo, 1990).

Water regime and phosphorus dose

By combining these two factors, increased response was observed in the RG for irrigation + 150-199 kg P ha-1 (p< 0.05, R2= 0.62, n= 59) and irrigation +100-149 kg P ha-1 (p< 0.01, R2= 0.77, n= 30).

Potassium dose

The response in the RG was greater at 250-300 kg K ha-1 (p< 0.01, R2= 0.92, n= 34) and at 145-199 kg K ha-1 (p< 0.01, R2= 0.72, n= 57). The effects of K chloride (KCl) in the summer of 2005 at two different locations in Sulaimani: Kanypanka and Bazyan, (dose of 0, 75, 150, 225, 300 kg K ha-1) were that increased KCl application increased grain yield by 30.17% and 55.45% for Kanypanka and Bazyan, respectively; K fertilizer response increased from 8.27 to 41.56% in Kanypanka, and in Bazyan it was 3 to 34.25% and the efficiency of fertilizer use ranged from 61.63 to 85.53% for Kanypanka and from 26.6 to 54.83% for Bazyan (Mam-Rasul, 2010).

Water regime and potassium dose

In this combination, a greater response was observed in the RG for irrigation+145-199 kg K ha-1 (p< 0.01, R2= 0.73, n= 19) and irrigation +250-300 kg K ha-1 (p< 0.01, R2= 0.94, n= 20). In dry maize, yields were reduced by up to 13% in the absence of K in one year (Subedi and Ma, 2009). In drought stress, the application of K compared to control caused increased grain yield, the weight of 1 000 grains and the number of grains per cob at 16.5, 9 and 5.5%, respectively (Zare et al., 2014). The plots K-treated performed better than the control in terms of better growth, higher yield, and improvement in yield components; by increasing the dose of K applied up to 90 kg of K ha-1 in two equal fractions, it improved maize growth and productivity in semi-arid climates (Amanullah et al., 2016).

Population density

The response in the RG was higher for densities greater than 7.5 plants m-2 (p< 0.01, R2= 0.2, n= 74) and for 5.5-7.5 plants m-2 (p< 0.01, R2= 0.29, n= 126). In the maize-soy rotation, increasing population narrowed the yield gap (high technology vs standard technology TE) when all other inputs were applied at the supplementary level to TE (Ruffo et al., 2015). The increase in density had a negative effecton the biomass of the coverage crop, in two places, the yield in low density (3.71 plants m-2) did not differ from the standard (7.41 plants m-2) (Youngerman et al., 2018).

Water regime and population density

The largest response in the RG was obtained in irrigation + densities greater than 7.5 plants m-2 (p< 0.01, R2= 0.21, n= 47) and irrigation+5.5-7.5 plants m-2 (p< 0.01, R2= 0.11, n= 101). Under dry conditions, yields were reduced by 8-13% with low plant density (PPD) (60 000 plants ha-1) in all years, and the increase from PPD to 90 000 plants ha-1 did not improve yield (Subedi and Ma, 2009). In arid environments, yield at all densities was low (2 448 kg ha-1), yield variation was high in semi-arid environments, the polynomial regression (p< 0.001, n= 951) had its maximum point with 140 000 plants ha-1 and yield of 9 000 kg ha-1, in sub-humid environments the yield had a positive response to density, the yield increased both for conventional tillage and no-tillage systems as the population increased, in systems with a high contribution of N (R2= 0.19, p< 0.001, n= 2 018) the response to the population to applied N was weaker than in medium contribution systems (R2= 0.49, p< 0.001, n= 680) (Haarhoff et al., 2018).

Crop

The materials used in the studies were hybrids of seed-producing companies and crossbreeds tested by research centres, the generality of the data indicated the predominance of yellow corn, on those of sweet and white type, due to missing data no analysis was performed; however, it is known that the introduction of new crops contributes significantly to the increase in maize yield (Qian and Zhao, 2017).

Tillage system

There was response over time and an uptrend in the RG obtained in conventional tillage (p< 0.01, R2= 0.69, n= 397) and zero tillage (p< 0.01, R2= 0.56, n= 14). Huynh et al. (2019), found a negative influence of zero tillage that was noted after 3 years, leading to significantly lower yield compared to conventional tillage; however, the authors note that the results are likely due to the specific characteristics of the soil and the site where their study was conducted.

Water regime and tillage system

In this interaction there was a significant response over time and an uptrend in the RG obtained in irrigation + tillage conventional (p< 0.01, R2= 0.7, n= 164) and dry + tillage conventional (p< 0.01, R2= 0.87, n= 11). The loss of N due to runoff and deep filtration, denitrification caused by higher soil water content and a low rate of N mineralization caused by lower soil temperatures under zero tillage potentially contributed to the observed decrease in grain yield under this system (Anapalli et al., 2018).

Irrigation system

When analyzing the response in the RG to the system used it was found that the drip irrigation (p< 0.01, R2= 0.74, n= 57) was superior to the other systems over time.

Cultivation system

There was a higher response in the RG for monoculture (p< 0.01, R2= 0.50, n= 92) and rotation (p< 0.01, R2= 0.73, n= 157). The most favorable rotation of maize was with winter wheat, with the addition of NPK from 60-120, 60-70 and 90-110 kg ha-1 respectively and density of 75 000-90 000 plants ha-1, yields ranged from 2 to 11 t ha-1 in extensive systems and from 10 to 15 t ha-1 in intensive, respectively (Sárvári and Pepó 2014). Crop rotation significantly increases and maintains yield as much as the use of conventional tillage and irrigation (Huynh et al., 2019).  

Water regime and cultivation system

The effect on the RG was greater for irrigation + monoculture (p< 0.01, R2= 0.51, n= 68) and irrigation + rotation (p< 0.01, R2= 0.81, n= 30).

Soil

According to was reported in the studies consulted, the highest RG was achieved in soils with sandy loam texture (p< 0.01, R2= 0.62, n= 73) and loam (p< 0.01, R2= 81, n= 61). The effect of the interaction between soil quality and fallow on maize yield was negative, this suggested the influence of the quality of leaf litter and the immobilization of N in soils (Braimoh and Vlek, 2006). The optimal economic dose of fertilizer N (DOEN) was higher in the soil Gleysol (Sg) (173 kg ha-1) and lower in the soil Podzol (Sp) (123 kg ha-1) with a grain yield in Sp of almost 60% lower than expected in other textural groups of the soil, DOEN in clay and loam soils was 144 and 164 kg ha-1 with an estimated grain yield of 12.7 and 12 Mg ha-1, respectively, the content of residual soil nitrate (NRS) was higher in Sg and Sp soils, and the NRS estimated by the DOEN was lower than that observed in the Sp soil, which indicates possible losses of N in this soil (Alotaibi et al., 2018).

Water regime and soil

It was observed that the higher values of RG were found in irrigation + sandy loam soil (p< 0.01, R2= 0.69, n= 48) and irrigation + loam soil (p< 0.01, R2= 0.96, n= 13).

Proposed models

The variables used in model generation were irrigation sheet, nitrogen dose, phosphorus dose, potassium dose and population density, with which five model proposals were generated using stepwise multiple regression method (Table 3).

Table 3. Obtained models and their parameters for maize yield prediction (RG3E).

RGE= estimated grain yield; n= number of observations; EE= standard error; DP= population density (plants m-2); K= potassium dose (kg ha-1); LR= irrigation sheet (mm); P= phosphorus dose (kg ha-1); N= nitrogen dose (kg ha-1); p< 0.01 value.

According to the first analysis by joining the five identified variables of the studies, which pointed to population density as the most significant variable in the stepwise procedure, the combinations revolved around this variable, and were considered as a demanding input (water and fertilizers), model 1 was chosen for the results report and its discussion because it considered the five variables of the study and because it presented the lowest value of the standard error.

Model 1

RGE is a function of the five variables identified and studied in this research, the statistical parameters of the model (p< 0.01, R2= 73, n= 45) indicated an error of 964 kg grain ha-1; in Figure 3 the RG and RGE were related through a linear regression, whose equation was highly significant (p< 0.01, R2= 73); likewise, the tendency to underestimate the values by the generated model was observed.

Figure 3. Relationship between observed and estimated data with model 1. The dotted line 3 indicates the 1:1 ratio between the observed value (RG) and the estimated value (RGE)

.

In this regard, De la Casa (1992) founds a multiple regression equation (R2= 0.8, EE= 407.1 kg ha-1), based on precipitation data, when using the stepwise method to predict maize yield in Argentina, accounted for three components, one technological or temporary, one rainfall, and one geographical, that equation achieved an average percentage error between 17 and 18% with respect to witness data. Monteiro et al. (2017) estimated by a model the yield of maize for the 2000-2001 to 2007-2008 in Brazil based on the technological level of production systems and meteorological conditions, there was a high correlation between estimated and observed yield (0.76 >R2 ≥0.92, p< 0.01) with model efficiency between 0.45 and 0.73, relative mean error (MAE) between -0.9 and 2.4, and absolute mean error (MAE) less than 70 kg ha-1 depending on the technological level.

Conclusions

The factors that influenced the obtaining of RGE in maize were population density, K dose, irrigation sheet, N dose and P dose and all of them belonged to the group of agronomic factors. According to the analysis of studies related to the production of maize grain yield and the diversity of environments in which they were developed, the influence of agronomic factors was significantly associated with the crop response, so only these variables were chosen to determine the RGE. The regression model (N= 45, R2= 0.73, EE.= 0.964 Mg ha-1) represented the effect of agronomic factors on the RG, while environmental variables did not have a significant impact on the crop response.

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