Biomathematics

Simulation of management strategies from the DSSAT model to increase the yields of a corn cultivar

0000-0002-6480-9971O. Rodríguez González^{1  *}  , 0000-0003-4494-660XR. Florido Bacallao¹  , 0000-0002-7159-7348Naivy Hernández Córdova¹  , 0000-0003-3285-6535F. Soto Carreño¹  , 0000-0001-6509-8932E.I. Jeréz Mompié¹  , 0000-0002-4923-812XDeborah González Viera¹  , 0000-0002-9324-4850R.J. Vázquez Montenegro² 

¹Instituto Nacional de Ciencias Agrícolas (INCA), carretera San José-Tapaste, km 3½, Gaveta Postal 1. San José de las Lajas, Mayabeque, Cuba. CP 32 700

²Instituto de Meteorología, Casa Blanca, Regla, La Habana, Cuba. CP 11 700

Abstract

Crop simulation models based on physiological processes are valuable tools for simulating crop production, estimating agronomic efficiency, and developing optimal management practices for sustainable agriculture. The objectives of this study were to calibrate the DSSAT model for the P-7928 corn cultivar and explore management strategies to improve crop production, which included sowing density, fertilization levels and edaphoclimatic conditions. The DSSAT model showed excellent performance. The simulated yields were related to those observed, and showed a Willmott index of 0.96. The square root of the mean square of the normalized error behaved with an acceptable value of 28% and R² of 0.985, which shows the good fit of model and shows that it can be used to simulate the crop yield and its physiological components under Cuba conditions. The simulations performed show higher yield, when combining the sowing of 7 plants m^-2 and a nitrogen fertilization of 150 kg ha^-1. The comparative study of the yields in different edaphoclimatic conditions shows the influence of the latter on the crop response.

Key words: calibration; crop simulation models; yield; corn

The crop simulation models based on physiological processes have been developed to assess the impact of climate change on food production and climate adaptation, as well as to develop strategies in the agricultural framework (^{Tatsumi 2016}). These models represent, in a simple and synthetic way, the most important physiological and ecological processes that govern growth through the use of mathematical equations (^{Guevara 2007}, ^{Gouache et al. 2015}, ^{Dias et al. 2016} and ^{Rodríguez et al. 2018}).

Modeling makes it possible to research the consequences of possible future scenarios and allows preparing for changes before they occur. The influence of climate change on agriculture represents a challenge in deciding policies based on quantitative models, which consider agriculture in its specific context (^{Hernández et al. 2017} and ^{Tian et al. 2020}).

The Agrotechnology Transfer Decision Support System (DSSAT) is a platform that includes 42 models and has been applied to simulate the effects of different management conditions on yield: sowing dates (^{Tofa et al. 2020} and ^{Shen et al. 2020}), irrigation levels, nitrogen fertilization (^{Marek et al. 2017} and ^{Abedinpour and Sarangi 2018}) and sowing density (^{Ren et al. 2020}).

DSSAT needs to be calibrated and validated in order to simulate the response of the crop to certain factors. In the calibration, the parameters in the model database are fitted: (i) through various simulation scenarios until an acceptable fit between simulated and observed values in field experiments is obtained, and also (ii) from experimental data of the literature for the region in which it will be validated. Validation is the procedure by which the performance of the model is evaluated, contrasting the simulated values of a certain variable with real data obtained in field experiments. The main objective when evaluating the performance of a crop simulation model is to assess its practical use as a research tool or support in making decisions about management and planning at the farm, regional or national level (^{Soto-Bravo and González- Lutz 2019}).

Corn (Zea mays L.) is a cereal of great economic importance in the world for human and animal intake, with a global production of 500 million tons. This crop covers an area of more than 120 million hectares and is cultivated in more than 70 countries, although it mainly predominates in the American continent (^{Mendoza 2017} and ^{Pérez-Madruga et al. 2019})

In Cuba, the corn covers an area between 77,000 and 100,000 hectares. The provinces from the central and eastern regions stand out in their production, with the largest extensions of sowing area. There are 47 commercial varieties in the country, four are traditional and the rest are cultivars from different national genetic improvement programs. Currently, the productivity of these cultivars does not exceed 1.44-2.35 t ha^-1 on average (^{ONEI 2017}).

Based on these conditions, the objective of this study was to calibrate the DSSAT model for the P-7928 corn cultivar and explore management strategies to improve crop production, which included sowing density, fertilization levels, and edaphoclimatic conditions.

Materials and Methods

To obtain the values of the genetic coefficients of the corn variety P-7928, data were taken from experiments carried out at the Instituto Nacional de Ciencias Agrícolas (23° 01 'north latitude and 82° 08' west longitude at 138 m o.s.l.). Three sowing dates were used, corresponding to November 2008 and June and July 2009.

A random block design with three replications was used. The sowing was carried out manually, with a sowing frame of 0.90 m x 0.30 m and a sowing density of 5 plants m^-2.

The agricultural labor was carried out as recommended in the Technical Instructions for Maize Cultivation (^{IIG 2012}). The water availability was ensured throughout the crop cycle. The control of pests and weeds was effectively carried out and fertilization was carried out by applying K₂O and P₂O₅ as basal dressing, at a rate of 60 kg ha^-1 of both, and 120 kg ha^-1 of nitrogen, divided during the crop cycle (sowing, 30 and 60 d after planting). The complete formula (9-13-17) and urea (46% N) were used as carriers, so that the plants developed without limitations.

Data collection. The duration in days of the phenological phases of the crop (dates of emergence, anthesis and physiological maturity) was evaluated in each experimental plot. Each phase was identified when more than 50% of the experimental plot showed the characteristics of these stages and the crop cycle was established by adding the duration of each one of them.

In each experimental plot, the agricultural yield and its components were determined: weight (g), length (cm) and diameter (cm) of the ears, number of rows and number of grains per ear and weight of 100 grains (g). An area of 1 m² was taken, with two repetitions in each replication and the values were expressed in t ha-¹, at 14% grain moisture.

Preparation of input files. Six input files were created to run the CERES-Maize model inserted in DSSAT v4.6: file X, file A, file T, soil file, climate file and genetic coefficients file (^{Alderman 2020}).

In files A and T the values of the physiological variables observed in the experiments were stored. Subsequently, they were compared with the values simulated by the model for calibration.

Data on field conditions, experimental treatments and simulation options were stored in file X. Crop production management data, separated into several sections, make up the majority of this file.

The soil in the area where the experiments were carried out is typical ferralitic, according to the Cuban soil classification (^{Hernández et al. 2015}) (table 1).

Table 1 Chemical properties of the soil from the experimental area 

Depth, cm	pH	OM, %	P, p.p.m.	Ca, cmol kg^-1	Mg, cmol kg^-1	K, cmol kg^-1	Na, cmol kg^-1
0-15	7.36	3.79	122.6	16.84	2.66	1.15	0.21

For the preparation of the climate file, the values of the meteorological variables (maximum and minimum temperatures, daily rainfalls and global radiation), corresponding to the months in which the experiments were carried out, were used. These data were obtained from Tapaste meteorological station, a few meters from the experimental area (table 2).

Table 2 Average monthly performance of the climatic variables in the years in which the experiments were carried out at INCA 

Months	2008				2009
	Temp. maximum, ºC	Temp. minimum, ºC	Precip., mm	Global radiation, J/m²	Temp. maximum, ºC	Temp. minimum, ºC	Precip., mm	Global radiation, J/m²
J	27.1	14.9	38.3	16.74	25.8	14	50.8	16.48
F	29	17.4	27.1	18.96	25.6	12.8	29.9	19.93
M	29.2	17.6	115.3	22.12	28	15.5	21.9	22.73
A	29.2	16.9	145.6	25.29	30.3	18.4	17.1	24.67
M	32.1	20.4	139.2	25.93	31.7	20.4	238.5	25.36
J	31.6	21.7	222.2	24.14	31.3	20.8	225.5	24.71
J	32.2	21.3	177.5	24.95	33	22.3	80.4	24.68
A	32.3	21.5	248.2	23.79	32.6	22.5	197.7	23.10
S	31.1	21.8	346.0	20.11	32.3	21.9	189.4	21.44
O	29.5	20.0	110.0	17.65	31.5	21.3	102.7	18.43
N	26.0	15.5	116.4	15.78	28.0	17.7	51.2	15.75
D	26.6	16.1	18.1	14.87	28	17.8	60.1	14.52

Crop simulation model calibration. To calibrate the CERES-Maize model for DSSAT, six genetic coefficients were obtained (P1, P2, P5, PHINT, G2 and G3). The P coefficients are considered phenological aspects of the crop, such as flowering and ripening. The G is related to the potential yield of a specific variety (^{Ahmed et al. 2016}) (table 3).

Table 3 Definition of the genetic coefficients of the corn crop 

P1	Thermal time from emergence to the end of young phase
P2	Thermal time from the end of the young phase to the spike initiation
P5	Thermal time from the beginning of grain filling to physiological maturity
PHINT	Phylochron interval: thermal time interval between successive appearances of the leaf tip, days degrees
G2	Scale for the partition of assimilates towards the panicle
G3	Grain fill rate during linear grain fill stage and under optimal conditions, mg/day

The genetic coefficients were calculated for each cultivar using the DSSAT GLUE (generalized probability uncertainty estimate) method. For the calibration of the crop simulation model, the data from the experiments of November 2008 and July 2009 were used. GLUE is a Bayesian estimation method to determine the probability distribution between the observed data and those estimated by the crop simulation model. The coefficients, whose values show the best fit, were copied into the DSSAT CUL file to apply them in the program routines and evaluate the model. This was validated with the data from the June 2009 experiment.

In addition, the square root of the mean square of the normalized error (RMSEn) and the d index (^{Willmott 1982}) were calculated, according to equations 1 and 2:

$RMSEn=100* \frac{\sqrt{\sum _{i=1}^n\frac{{(Si-Oi)}^2}{n}}}{\stackrel{-}{Ob}}$ (1)

$d=1-\frac{\sum _{i=1}^n{(Si-Oi)}^2}{\sum _{i=1}^n{(\left|Si-\stackrel{-}{Ob}\right|+\left|Oi-\stackrel{-}{Ob}\right|)}^2}$ (2)

Where:

$Si$ y $Oi$ :	simulated and observed values
n:	number of observations
( $\stackrel{-}{Ob}$ ):	mean of $Oi$ mean values

The RMSEn was used to provide a percentage measure of the relative difference between simulated and observed values for total plant weight. A simulation is considered excellent if the RMSEn is less than 10%, good if it is between 10 and 20%, reasonable if it is between 20 and 30%, and bad if it is higher than 30% (^{Raes et al. 2018}). ^{Willmott (1982)} states that the value corresponding to d must be close to 1.

Simulations. For the simulations, the file of the experiment carried out in June 2009 was taken and insert in the seasonal analysis tool, included in DSSAT. The sensitivity analysis of grain yield was evaluated in three different scenarios

1. By varying the fertilizer doses from 30 to 210 kg ha⁻¹ of nitrogen, with an interval of 30 kg ha⁻¹of nitrogen and sowing density of 5 plants m^-2

2. When evaluating the densities 5 plants m^-2, 7 plants m^-2, 8 plants m^-2, 10 plants m^-2, 15 plants m^-2 and 20 plants m^-2, three applications of nitrogen fertilization were made, each of 40 kg ha⁻¹ of nitrogen. One application was made at the time of sowing, and the rest was made monthly until adding 120 kg ha⁻¹ of nitrogen.

3. Record of the edaphoclimatic conditions of the localities Los Palacios in Pinar del Río and Tapaste in Mayabeque, and the soil and climate conditions for Los Palacios (tables 4 and 5, respectively).

Table 4 Chemical properties of Los Palacios soil used in the simulation 

Depth, cm	pH	OM, %	P, ppm	Ca, cmol kg^-1	Mg, cmol kg^-1	K, cmol kg^-1	Na, cmol kg^-1
0-15	5.16	2.34	27.94	6.68	3.04	0.12	0.19

Table 5 Average monthly performance of the climatic variables of Los Palacios used in the simulation 

Months	2009
	T. max, ºC	T min, ºC	Precipitations, mm
J	16.63	26.57	5.54
F	15.02	26.43	1.26
M	17.62	27.87	0.95
A	19.98	30.48	0.34
M	21.65	31.5	5.15
J	22.79	31.57	4.94
J	23.99	32.93	2.65
A	23.86	33.1	4.60
S	23.83	32.85	5.08
O	22.92	31.78	2.04
N	19.67	28.77	2.28
D	19.46	28.23	1.3

Results and Discussion

To calibrate the crop simulation model, the experiments planted in November 2008 and July 2009 were used. The GLUE Select Wizard option, version 4.6.1.0 was used and 10,000 iterations were performed. Genetic coefficients were obtained for cultivar P7928 (table 6).

Table 6 Genetic coefficients for the corn P-7928variety 

Genotype	P1	P2	P5	G2	G3	PHINT
P-7928	219.1	0.694	594.3	821.1	16.11	55.00

Table 7 shows the comparison of the observed and simulated values, in terms of days to anthesis, days to maturation and yield. The simulated yields were related to those observed, showing a d = 0.96. The RMSEn behaved with an acceptable value of 28% and R² of 0.985. This shows the good fit of the crop simulation model (figure 1) (^{Tovihoudji et al. 2019} and ^{Tofa et al. 2020}).

Table 7 Comparación de los valores observados y simulados 

Variables	Observed	Simulated
Days to anthesis, ddp	53	56
Days to physiological maturation, ddp	82	87
Yield, kg ha^-1	7257	7620
Number of grains per m^2	2452	3237
Weight of a grain, g	0.296	0.2354
Number of grains per ear	490	647.5
Total biomass at maturation, kg ha^-1	18026	14215
Harvest index	0.40	0.536

Figure 1 Result of the calibration of the crop simulation model for the yield variable 

It is of great importance to simulate corn crop production and develop optimal management strategies to achieve a sustainable agriculture (^{Jiang et al. 2019}). From the previous results (Figure 2) it is evident that with 30 kg ha^-1 and 60 kg ha^-1 of nitrogen fertilization, the yields are low. However, from 90 kg ha^-1 they are similar, and exceed 7 t ha^-1, which coincides with the crop technical instructions (^{IIG 2012}). These results agree with what was reported in researches by ^{Martín et al. (2009)}, who obtained a stable maximum yield from 69.07 kg ha^-1 of nitrogen.

Figure 2 Simulations with different doses of nitrogen fertilization 

Regarding the study of plantation densities, the results show that with a density of 7 plants m^-2 the highest yields can be obtained (figure 3). Although these results differ from those showed in the crop technical instructions, which recommends 5 plants m^-2 (^{IIG 2012}), they coincide with other researchers that propose a density of 7.5 plants m^-2 (^{Xu et al. 2017} and ^{Yan et al. 2017}).

Figure 3 Simulations with different planting densities 

Regarding the study of the yield performance in different edaphoclimatic conditions, in the localities Los Palacios, in Pinar del Río, and Tapaste, in Mayabeque, the simulated yields were 4694 kg ha^-1 and 7945 kg ha^-1, respectively. Higher yields were evidenced in Tapaste locality, which must be conditioned by the performance of edaphoclimatic conditions (figure 4).

Figure 4 Simulations in Tapaste and Los Palacios localities 

Los Palacios locality has a ferruginous nodular gley soil, characterized by poor internal drainage. The conditions of accumulation of water affect the corn yield because the roots cannot breathe well. On the other hand, Tapaste has a red ferralitic soil, which has good internal drainage and excellent physical properties for the development of crop.

Through simulations it was shown that the optimal option for this variety is to use a planting density of 7 plants m^-2 and carry out nitrogen fertilization with 120 kg ha^-1 in hydrated red ferralitic soils.

Conclusions

Obtaining the genetic coefficients of corn P7928 variety allowed establishing that the DSSAT model can be used to model the crop yield and its physiological components under Cuban conditions.

The simulation showed that from 90 kg ha^-1 of nitrogen fertilization, the yields exceed 7 t ha^-1. The highest yield is the one corresponding to the 150 kg ha^-1 dose.

Through the simulation it was shown that with a density of 7 plants m^-2 the highest yields can be obtained.

The study of the performance of yields in different edaphoclimatic conditions shows their influence on the crop response.

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Received: November 24, 2020; Accepted: April 15, 2021

^*Email:[e-mail]

Conflict of interest: The authors declare that there are no conflicts of interests among them

Author´s contribution: O. Rodríguez González: Original idea, analysis of the information writing the manuscript. R. Florido Bacallao: Analysis of the information, writing the manuscript. Naivy Hernández Córdova: Design and conducting the experiment, analysis of the information. F. Soto Carreño: Analysis of the information. E. I Jeréz Mompié: Analysis of the information. Deborah González Viera: Analysis of the information. R. J. Vázquez Montenegro: Analysis of the information.