The simulation of oat grain productivity does not contemplate the use of efficient models that involve important management with meteorological elements. The objective of the study is to propose a mathematical model capable of simulating the oat grain productivity through the management of nitrogen and growth regulator with variables related to the plant and to meteorological elements. In this study, two experiments were conducted in the years of 2013, 2014 and 2015: one to quantify biomass productivity and another to determine grain productivity and lodging at the management doses of nitrogen and growth regulator. The experimental design was a randomized block with four replications in a 4 × 3 factorial scheme for 0, 200, 400 and 600 mL · ha - 1 growth regulator doses and 30, 90 and 150 kg · ha - 1 nitrogen doses, respectively. During the crop cycles, the meteorological variables thermal sum, radiation and rainfall were quantified. The mathematical model proposed, which combines polynomial regression of the harvest index with multiple linear regression of the biological productivity, is efficient in the simulation of oat grains productivity with the use of growth regulator, nitrogen and meteorological elements. Thus, it adds to the conventional models of simulation and becomes an aid tool for making decisions regarding the management of oats culture.
Oat is a cereal of multiple purposes, mainly due to the great demand for its derivatives in food production [
Lodging is the phenomenon in which the plant loses its vertical position, bends and falls to the ground [
Although there are mathematical models for the estimation of grain productivity in cereals [
The field work was developed in the agricultural years of 2013, 2014 and 2015 in Augusto Pestana (28˚26'30'' South latitude and 54˚00'58'' West longitude), RS, Brazil. The soil of the experimental area is classified as typical dystroferric red latosol, and the climate, according to Köppen classification [
Two experiments were conducted in each cultivation year. One to quantify the rate of biomass production by the cuts made every 30 days until the harvest point and another to the harvest aiming at the estimation of grain productivity and lodging. In the two experiments, the experimental design was a randomized block with four replications in a 4 × 3 factorial scheme, in the sources of variation of growth regulator doses (0, 200, 400 and 600 mL∙ha−1) and N-fertilizer doses (30, 90 and 150 kg∙ha−1), respectively, totaling 96 experimental units. The growth regulator (Trinexapac-Ethyl) was sprayed at constant pressure of 30 lb∙pol−2 by compressed CO2 with flat fan tips at the stage of 1st and 2nd visible node of the stem.
The harvest of the experiments to estimate the grain productivity occurred manually by cutting the three central lines of each plot. The time of grain harvest was also defined as the last cut of the experiment directed to the analysis of biomass productivity (120 days), near the harvest point, with grain moisture around 15% [
where: I is the degree of inclination of the plants, ranging from 0 to 5, 0 (zero) indicating the absence of inclination and 5 indicating that all the plants are completely lodged; “A” is the area with lodged plants in the plot, which varies from 0 to 10, 0 (zero) corresponding to the absence of lodged plants and 10 to the plants lodged in the whole plot, regardless of their inclination. Thus, this equation weighs the incidence and severity of the plants lodging. In the experiments aiming at quantifying biomass productivity by cuts along the development of the plants, the harvest of plant material was performed close to the soil, from the collection of a linear meter of the three central lines of each plot, in the period of 30, 60, 90 and 120 days after the emergence, totaling four cuts. The samples with the green mass were weighed on a precision scale and directed to a forced air heater at 65˚C until reaching constant weight, for estimation of the total dry mass converted into kg∙ha−1. The values of the general averages along with the information on temperature and rainfall were used to classify the years as unfavorable, intermediate and favorable to cultivation. The meteorological data of thermal sum, radiation and pluviometric precipitation were obtained through a meteorological station located at approximately 500 m of the experiments. It should be noted that the thermal sum (Ts) was obtained from the emergence of plants by the following model:
where Tmax = maximum temperature (˚C); Tmin = minimum temperature (˚C); n = number of days of the period of emergence-harvest; Bt = base temperature. The oat base temperature was that presented by [
Catering to the assumptions of homogeneity and normality through Bartlett tests, variance analysis was performed to detect the main and interaction effects. An adjustment of linear regression equation was performed for the estimation of the ideal growth regulator dose for lodging of oat plants by the increase of growth regulator doses. As it is an equation that describes the linear behavior of lodging, it was considered the possibility of plant lodging at a maximum of 5%, value added to the parameter “y” of the equation, obtained by:
According [
where a, b and c are coefficients obtained by polynomial regression and
For the composition of the multiple linear regression model in the estimation of oat biomass productivity, involving meteorological variables (radiation, thermal sum and rainfall), growth regulator doses and nitrogen, the choice of the potential variables was made via Stepwise technique. This procedure iteratively constructs a sequence of regression models by adding and removing variables, selecting those that have the largest relation with the main variable (y), using the partial F statistic, according to the model:
where
where
From these matrices, the value of the regression coefficients is obtained, with
and the variance of these coefficients is obtained by the covariance matrix of the regression coefficients vector:
where
However, since oat grain productivity is the product between biomass productivity and harvest index
All data processing method have been performed using the statistical software Genes.
In
2013. In addition, fertilizer application was followed by rainfall volume greater than 50 mm, volume also observed near grain harvest.
These facts justify the lower productivity obtained in this year (
At the moment of nitrogen application, the soil presented adequate humidity conditions due to accumulation of rainfall on the previous days (
Month | Temperature | Rainfall | Class | ||||||
---|---|---|---|---|---|---|---|---|---|
Min. | Max. | Aver. | Aver.* | Occur. | |||||
2015 | |||||||||
May | 10.5 | 22.7 | 16.6 | 149 | 100 | 3404b | 8450b | IY | |
June | 07.9 | 18.4 | 13.1 | 162 | 191 | ||||
July | 08.3 | 19.2 | 13.7 | 135 | 200 | ||||
August | 09.3 | 20.4 | 14.8 | 138 | 223 | ||||
September | 09.5 | 23.7 | 16.6 | 167 | 046 | ||||
October | 12.2 | 25.1 | 18.6 | 156 | 211 | ||||
Total | - | - | - | 909 | 973 | ||||
2014 | |||||||||
May | 11.1 | 24.5 | 17.8 | 149 | 020 | 2841c | 7695c | UY | |
June | 09.3 | 19.7 | 14.5 | 162 | 059 | ||||
July | 07.4 | 17.5 | 12.4 | 135 | 176 | ||||
August | 12.9 | 23.4 | 18.1 | 138 | 061 | ||||
September | 12.0 | 23.0 | 17.5 | 167 | 194 | ||||
October | 15.0 | 25.5 | 20.2 | 156 | 286 | ||||
Total | - | - | - | 909 | 798 | ||||
2013 | |||||||||
May | 10.0 | 22.6 | 16.3 | 149 | 108 | 4163a | 9373a | FY | |
June | 08.9 | 20.0 | 14.5 | 162 | 086 | ||||
July | 07.0 | 20.6 | 13.8 | 135 | 097 | ||||
August | 06.6 | 19.8 | 13.2 | 138 | 163 | ||||
September | 09.6 | 21.0 | 15.3 | 167 | 119 | ||||
October | 13.2 | 27.1 | 20.2 | 156 | 138 | ||||
Total | - | - | - | 909 | 712 | ||||
* = Historical rainfall average obtained in the months of May to October of 1990 to 2015; Averages followed by same letter in the column do not differ from each other in the probability of 5% error by the Scott-Knott test; FY = favorable year; UY = unfavorable year; IY = intermediate year; Temperature (˚C); Precipitation (mm);
rainfall over the cycle (
Of all the segments of the economy, agriculture is the one that shows greater dependence on meteorological variables, generating production oscillations over the years [
The productivity simulation, when dependent on the condition of the agricultural year, does not contemplate efficient forecasting models, considering the strong variation in each year of cultivation (
N Dose (kg∙ha−1) | Year | Equation | R2 | yE | Ideal dose (mL∙ha−1) | ||
---|---|---|---|---|---|---|---|
30 | 2015 | 23.55 − 0.045x | 80 | * | (5) | ||
2014 | 29.62 − 0.050x | 92 | * | (5) | |||
2013 | 22.53 − 0.037x | 89 | * | (5) | |||
- | 25.23 − 0.044x | 87 | * | (5) | |||
90 | 2015 | 56.83 − 0.103x | 91 | * | (5) | ||
2014 | 46.02 − 0.080x | 82 | * | (5) | |||
2013 | 48.75 − 0.088x | 93 | * | (5) | |||
- | 50.53 − 0.090x | 87 | * | (5) | |||
150 | 2015 | 82.35 − 0.147x | 93 | * | (5) | ||
2014 | 71.25 − 0.127x | 89 | * | (5) | |||
2013 | 75.15 − 0.133x | 94 | * | (5) | |||
- | 76.25 − 0.136x | 92 | * | (5) | |||
- | 50.67 − 0.092x | 89 | * | (5) |
* = Significant at 5% probability of error, respectively, by the probability of F;
linear trend, regardless of the year and nitrogen dose. For this estimation, was taken into account the possibility of plant lodging at a maximum of 5%, value added to the parameter “y” of each equation. Regardless of the condition of the year of cultivation, the optimal doses of use of oat growth regulator are 460, 500 and 520 mL∙ha−1 for the reduced, high and very high condition of nitrogen fertilization, respectively. Overall, regardless of nitrogen condition, the ideal growth regulator dose was adjusted to 495 mL∙ha−1.
In wheat [
In the analysis of the harvest index (
An expected event, since grain productivity evidenced quadratic behavior, and biomass productivity, steady growth. Therefore, the linear favoring of the straw
N | Year | Equation | R2 | Ideal dose (mL∙ha−1) | yE (kg∙ha−1) | |
---|---|---|---|---|---|---|
30 | 2015 | 98 | * | 410 | 0.51 | |
2014 | 99 | * | 495 | 0.41 | ||
2013 | 97 | * | 475 | 0.38 | ||
98 | * | 460 | 0.43 | |||
90 | 2015 | 94 | * | 500 | 0.41 | |
2014 | 99 | * | 510 | 0.38 | ||
2013 | 99 | * | 490 | 0.31 | ||
97 | * | 500 | 0.37 | |||
150 | 2015 | 99 | * | 525 | 0.41 | |
2014 | 93 | * | 520 | 0.44 | ||
2013 | 91 | * | 525 | 0.40 | ||
95 | * | 520 | 0.42 | |||
97 | * | 495 | 0.40 |
P(bx) = parameter that measures the slope of the line by the probability of T at 5% error; R2 = coefficient of determination; * = Significant at 5% probability of error, respectively, by the F test;
biomass expression with the stability in the grain elaboration promoted reduction in the harvest index. In oats, the lowest harvest index is not always reflected in lower grain productivities, since it is natural for the favorable cultivation condition to promote greater straw production than grains. Reference [
The harvest index is an important indicator of productivity, dimensioning how much of the total biomass produced was directed to the elaboration of biomass straw and biomass grains [
In
This fact was expected, since the application of the regulator happened around 65 days after emergence, with the appearance of the first and second visible node of the main stem, according to recommendation. The response to the use of regulator on biomass expression was shown to be effective at 90 days after emergence. At this moment, there was a significant reduction of the biomass productivity at 400 and 600 mL∙ha−1, not differing from each other, regardless of the nitrogen fertilization condition. In the conditions of 30 and 90 kg∙ha−1 of nitrogen, the biomass cut with 120 days after emergence, indicated the greatest reduction of biomass productivity with the use of a 600 mL∙ha−1 dose of the regulator product. At the highest N-fertilizer condition, biomass productivities were strongly reduced with the doses of 400 and 600 mL∙ha−1. In
Therefore, the variables radiation, thermal sum and rainfall presented significance in all conditions of use growth regulator and nitrogen. The possibility of simulation of biomass productivity with the use of a growth regulator dose in the
Variables Selected | N Dose (kg∙ha−1) | R Dose (mL∙ha−1) | Cutting time (DAE) | |||
---|---|---|---|---|---|---|
30 | 60 | 90 | 120 | |||
(2013 + 2014 + 2015) | ||||||
Thermal sum (day degrees) | - | - | 496 | 944 | 1452 | 1982 |
Rainfall (mm∙m−2) | - | - | 167 | 307 | 433 | 620 |
Radiation (V∙m−1) | - | - | 212 | 486 | 814 | 1160 |
Biomass productivity (kg∙ha−1) | 30 | 0 | 310 a | 1813 a | 8997 a | 9505 a |
200 | 306 a | 1849 a | 8675 a | 8853 b | ||
400 | 295 a | 1804 a | 7922 b | 8388 b | ||
600 | 300 a | 1816 a | 7523 b | 7798 c | ||
90 | 0 | 296 a | 1792 a | 9370 a | 10,195 a | |
200 | 282 a | 1849 a | 9030 a | 9604 a | ||
400 | 272 a | 1763 a | 8155 b | 9223 b | ||
600 | 262 a | 1714 a | 7909 b | 8985 c | ||
150 | 0 | 295 a | 1922 a | 9157 a | 9816 a | |
200 | 292 a | 1851 a | 8726 a | 9680 a | ||
400 | 294 a | 1887 a | 7579 b | 9626 b | ||
600 | 295 a | 1870 a | 7438 b | 9322 b |
DAE = days after emergence; R Dose = doses of applied growth regulator; N Dose = doses of nitrogen applied in coverage; Averages followed by the same letter in the column do not differ statistically from each other in a 5% probability of error according to the Scott-Knott test.
Source of Variation | Significance/Step Wise Model | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
0 | 200 | 400 | 600 | 0 - 600 | 30 - 150 | ||||||
(2013 + 2014 + 2015) | |||||||||||
N-30 kg∙ha−1 | |||||||||||
Regression | * | * | * | * | * | * | |||||
Thermal sum | * | * | * | * | * | * | |||||
Rainfall | * | * | * | * | * | * | |||||
Radiation | * | * | * | * | * | * | |||||
Regulator Dose | * | * | |||||||||
Nitrogen | * | ||||||||||
N-90 kg∙ha−1 | |||||||||||
Regression | * | * | * | * | * | * | |||||
Thermal sum | * | * | * | * | * | * | |||||
Rainfall | * | * | * | * | * | * |
---|---|---|---|---|---|---|
Radiation | * | * | * | * | * | * |
Regulator Dose | * | * | ||||
Nitrogen | * | |||||
N-150 kg∙ha−1 | ||||||
Regression | * | * | * | * | * | * |
Thermal sum | * | * | * | * | * | * |
Rainfall | * | * | * | * | * | * |
Radiation | * | * | * | * | * | * |
Regulator Dose | * | * | ||||
Nitrogen | * |
* = Significant at 5% probability of error, respectively, by the probability of F; Thermal sum (day degrees); Rainfall (mm∙m−2); Radiation (V∙m−1); Regulator Dose = ideal dose of regulator for lodging estimate of less than 5% (mL∙ha−1); N = Nitrogen (kg∙ha−1).
range from 0 to 600 mL∙ha−1 was also significant, regardless of the nitrogen dose. However, in the elaboration of a more complete model, involving the use of growth regulator, meteorological variables and the use of the nitrogen dose, the significance of all these elements were confirmed to compose the multiple linear regression model in the biomass productivity simulation.
The Step Wise method for choosing variables to compose the multiple linear regression model is considered as one of the corrective actions for multicollinearity problems [
In the simulation of biological productivity with the inclusion of the growth regulator dose in the multiple model (
Equation | BP | HI | |||
---|---|---|---|---|---|
E | O | LL | UL | ||
(2013 + 2014 + 2015) | |||||
N-30 kg∙ha−1 | |||||
9510 | 9505 | 8613 | 10,281 | ||
8895 | 8853 | 7439 | 10,085 | ||
8395 | 8388 | 7314 | 9150 | ||
7895 | 7798 | 7155 | 8358 | ||
8630 | 8636 | 8160 | 9080 | ||
N-90 kg∙ha−1 | |||||
10,215 | 10,195 | 9174 | 11,027 | ||
9830 | 9604 | 8680 | 10,530 | ||
9670 | 9223 | 8320 | 10,010 | ||
9085 | 8985 | 8061 | 9788 | ||
9710 | 9500 | 9381 | 10,370 | ||
N-150 kg∙ha−1 | |||||
9815 | 9816 | 8495 | 10,965 | ||
9795 | 9680 | 8358 | 11,886 | ||
9600 | 9626 | 7630 | 11,363 | ||
9265 | 9322 | 7217 | 10,283 | ||
9470 | 9610 | 8175 | 11,375 | ||
9345 | 9640 | 9200 | 9864 |
BP = biological productivity (kg∙ha−1); T = thermal sum (day degrees); r = rainfall (mm∙m2); R = radiation (V∙m−1); O = observed; E = estimated; LL = lower limit; UL = upper limit; N = nitrogen (70 kg∙ha−1); RD = ideal dose of regulator (mL∙ha−1); CI = confidence interval.
of N-fertilization (
The simulation by multiple linear regression is a tool that allows efficient estimation of productivity [
Considering that grain productivity is the product between biological productivity (determined by multiple linear regression) and the harvest index (determined by polynomial regression of second degree),
Equation | GPO | GPE | |
---|---|---|---|
(2013 + 2014 + 2015) | |||
N-30 kg∙ha−1 | |||
3421 | 3330 | ||
3720 | 3740 | ||
3520 | 3660 | ||
3120 | 3120 | ||
3625 | 3705 | ||
N-90 kg∙ha−1 | |||
3670 | 3675 | ||
3745 | 3730 | ||
3690 | 3660 | ||
3325 | 3240 | ||
3610 | 3595 | ||
N-150 kg∙ha−1 | |||
3435 | 3435 | ||
3870 | 3920 | ||
3945 | 4065 | ||
3730 | 3890 | ||
3940 | 4020 | ||
3685 | 3760 |
GP = grain productivity (kg∙ha−1); T = thermal sum (day degrees); r = rainfall (mm∙m2); R = radiation (V∙m−1); N = nitrogen (70 kg∙ha−1); RD = ideal dose of regulator (mL∙ha−1); GPO = grain productivity observed in the field; GPE = grain productivity estimated by the model.
For these simulations, were used the values of the meteorological elements presented in
The use of mathematical models to estimate agricultural productivity is an important tool for crop forecasting systems [
To CAPES, CNPq, FAPERGS and UNIJUÍ for the resources to the development of the research and for the scientific, technological initiation and productivity scholarships.
Marolli, A., da Silva, J.A.G., Scremin, O.B., Mantai, R.D., Trautmann, A.P.B., de Mamann, Â.T.W., Car- bonera, R., Kraisig, A.R., Krüger, C.A.M.B. and Arenhardt, E.G. (2017) A Proposal of Oat Productivity Simulation by Meteorological Elements, Growth Regulator and Ni- trogen. American Journal of Plant Scien- ces, 8, 2101-2118. https://doi.org/10.4236/ajps.2017.89141