Optimal Planting Density and Nutrient Application of Soybeans: A Case Study in Northeastern China
Abstract
:1. Introduction
2. Materials and Methods
2.1. Experimental Design
2.2. Field Experimental Design
2.3. Collection of Basic Data
3. Data Analysis and Processing Results
3.1. Single-Factor Regression Design Implementation Data
3.2. Data Processing and Model Optimization in Single-Factor Regression Experiments
3.2.1. Data Processing and Model Optimization in Regression Experiments on Planting Density Effects
3.2.2. Data Processing and Model Optimization in Regression Experiments on Nitrogen (N) Efficiency
3.2.3. Data Processing and Model Optimization in Regression Experiments on Phosphorus (P) Efficiency
3.2.4. Data Processing and Model Optimization in Regression Experiments on Potassium (K) Efficiency
3.3. Second-Order Orthogonal Rotational Composite Design
3.3.1. Data from the First Set of Experimental Implementations in a Second-Order Orthogonal Rotational Composite Design
3.3.2. Processing and Model Optimization of the First Set of Experimental Data in a Second-Order Orthogonal Rotatable Design
3.3.3. Data from the Second Set of Experimental Implementations in a Second-Order Orthogonal Rotational Composite Design
3.3.4. Processing and Model Optimization of the Second Set of Experimental Data in a Second-Order Orthogonal Rotatable Design
3.4. Implementation Data for D-Optimal Regression Experimental Design
3.5. Data Processing and Model Optimization in D-Optimal Regression Experiments
4. Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Experimental Field Dimensional Parameters | Experimental Field | Trial Plot | Aisle | Plantation Conservation |
---|---|---|---|---|
Area | 4587 m2 | 4 × 3.3 = 13.2 m2 | ||
Length | 139 m | 4 m | ||
Width | 33 m | 1.1 m × 3 ridge = 3.3 m | 1.1 m | 1.1 m × 1 row = 1.1 m |
Residential Area Configuration | Number of ridges | Width of ridges | Number of Rows on the Ridge | Row Spacing |
3 | 1.1 m | 3 rows | 0.25 m |
Test Number | Planting Density (104 plants/ha) | Seed Interval (cm) | Row Interval (m) | Urea (kg/ha) | Diammonium Phosphate (kg/ha) | Potassium Sulfate (kg/ha) |
---|---|---|---|---|---|---|
88 | 35 | 7.8 | 0.25 | 139.36 | 147.45 | 12.85 |
89 | 35 | 7.8 | 0.25 | 57.91 | 137.24 | 25.72 |
90 | 35 | 7.8 | 0.25 | 21.62 | 98.92 | 12.85 |
Source | DF | Sum of Squares | Mean Square | F Value | Prob > F | |
---|---|---|---|---|---|---|
Model | 2 | 58,690.851 | 29,345.425 | 55.41 | 5.112 × 10−5 | Significant |
Error | 7 | 3707.219 | 529.603 | |||
Total | 9 | 62,398.07 |
R | R-Square | Adj. R-Square |
---|---|---|
0.97 | 0.941 | 0.924 |
Non-Standardized Coefficients | t-Value | Prob > |t| | ||
---|---|---|---|---|
Value | Standard Error | |||
37.01 | 3.924 | 9.432 | 3.14 × 10−5 | |
−0.40 | 0.046 | −8.613 | 5.673 × 10−5 | |
Intercept | 2045.19 | 78.744 | 25.973 | 3.208 × 10−5 |
Source | DF | Sum of Squares | Mean Square | F Value | Prob > F | |
---|---|---|---|---|---|---|
Model | 2 | 309,809.7 | 154,904.851 | 83.793 | 1.289 × 10−5 | Significant |
Error | 7 | 12,940.62 | 1848.66 | |||
Total | 9 | 322,750.3 |
R | R-Square | Adj. R-Square |
---|---|---|
0.98 | 0.960 | 0.948 |
Non-Standardized Coefficients | t-Value | Prob > |t| | ||
---|---|---|---|---|
Value | Standard Error | |||
624.65 | 51.624 | 12.1 | 6.014 × 10−6 | |
−4.47 | 0.377 | −11.881 | 6.8 × 10−6 | |
Intercept | −18,647.34 | 1760.135 | −10.594 | 1.46 × 10−5 |
Source | DF | Sum of Squares | Mean Square | F Value | Prob > F | |
---|---|---|---|---|---|---|
Model | 2 | 195,752.45 | 97,876.226 | 36.555 | 1.972 × 10−4 | Significant |
Error | 7 | 18,742.52 | 2677.503 | |||
Total | 9 | 214,494.97 |
R | R-Square | Adj. R-Square |
---|---|---|
0.955 | 0.913 | 0.888 |
Non-Standardized Coefficients | t-Value | Prob > |t| | ||
---|---|---|---|---|
Value | Standard Error | |||
5.34 | 0.701 | 7.621 | 1.241 × 10−4 | |
−0.02 | 0.003 | −6.103 | 4.896 × 10−4 | |
Intercept | 2520.03 | 42.989 | 58.62 | 1.103 × 10−10 |
Source | DF | Sum of Squares | Mean Square | F Value | Prob > F | |
---|---|---|---|---|---|---|
Model | 2 | 1,169,660.934 | 584,830.467 | 41.407 | 1.322 × 10−4 | Significant |
Error | 7 | 98,868.068 | 14,124.01 | |||
Total | 9 | 1,268,529.002 |
R | R-Square | Adj. R-Square |
---|---|---|
0.96 | 0.922 | 0.9 |
Non-Standardized Coefficients | t-Value | Prob > |t| | ||
---|---|---|---|---|
Value | Standard Error | |||
67.8 | 8.047 | 8.426 | 6.536 × 10−5 | |
−1.34 | 0.148 | −9.07 | 4.057 × 10−5 | |
Intercept | 2268.22 | 98.735 | 22.973 | 7.507 × 10−8 |
Test Number | Factor (104 plants/ha) | Factor (kg/ha) | Factor (kg/ha) | Factor (kg/ha) | Yield (kg/ha) |
---|---|---|---|---|---|
16 | 50 | 95.16 | 198.76 | 39.65 | 3453.47 |
17 | 50 | 44.84 | 101.24 | 20.35 | 3354.23 |
18 | 55 | 70 | 150 | 30 | 2845.73 |
Source | Sum of Squares | DF | Mean Square | F Value | Prob > F | |
---|---|---|---|---|---|---|
Model | 1.59 × 106 | 14 | 1.13 × 105 | 19.16 | <0.0001 | Significant |
A | 27,983.88 | 1 | 27,983.88 | 4.73 | 0.0412 | |
B | 2.89 × 105 | 1 | 2.89 × 105 | 48.85 | <0.0001 | |
C | 89,773.09 | 1 | 89,773.09 | 15.18 | 0.0008 | |
D | 18,186.32 | 1 | 18,186.32 | 3.08 | 0.0941 | |
AB | 4312.55 | 1 | 4312.55 | 0.7292 | 0.4028 | |
AC | 12,327.66 | 1 | 12,327.66 | 2.08 | 0.1636 | |
AD | 1.29 × 105 | 1 | 1.29 × 105 | 21.81 | 0.0001 | |
BC | 2.17 × 105 | 1 | 2.17 × 105 | 36.69 | <0.0001 | |
BD | 1.20 × 105 | 1 | 1.20 × 105 | 20.24 | 0.0002 | |
CD | 1702.39 | 1 | 1702.39 | 0.2879 | 0.5972 | |
A2 | 1.37 × 105 | 1 | 1.37 × 105 | 23.22 | <0.0001 | |
B2 | 87,763.04 | 1 | 87,763.04 | 14.84 | 0.0009 | |
C2 | 4.51 × 105 | 1 | 4.51 × 105 | 76.24 | <0.0001 | |
D2 | 1926.45 | 1 | 1926.45 | 0.3257 | 0.5742 | |
Residual | 1.24 × 105 | 21 | 5914.04 | |||
Lack of Fit | 54,421.12 | 10 | 5442.11 | 0.858 | 0.5916 | Not significant |
Pure Error | 69,773.69 | 11 | 6343.06 | |||
Cor Total | 1.71 × 106 | 35 |
Source | Sum of Squares | DF | Mean Square | F Value | Prob > F | |
---|---|---|---|---|---|---|
Model | 1.57E + 06 | 10 | 1.57 × 105 | 27.11 | <0.0001 | Significant |
A | 27,983.88 | 1 | 27,983.88 | 4.84 | 0.0372 | |
B | 2.89 × 105 | 1 | 2.89 × 105 | 49.99 | <0.0001 | |
C | 89,773.09 | 1 | 89,773.09 | 15.54 | 0.0006 | |
D | 18,186.32 | 1 | 18,186.32 | 3.15 | 0.0882 | |
AD | 1.29 × 105 | 1 | 1.29 × 105 | 22.33 | <0.0001 | |
BC | 2.17 × 105 | 1 | 2.17 × 105 | 37.55 | <0.0001 | |
BD | 1.20 × 105 | 1 | 1.20 × 105 | 20.72 | 0.0001 | |
A2 | 1.37 × 105 | 1 | 1.37 × 105 | 23.77 | <0.0001 | |
B2 | 87,763.04 | 1 | 87,763.04 | 15.19 | 0.0006 | |
C2 | 4.51 × 105 | 1 | 4.51 × 105 | 78.02 | <0.0001 | |
Residual | 1.45 × 105 | 25 | 5778.55 | |||
Lack of Fit | 74,690.16 | 14 | 5335.01 | 0.8411 | 0.6261 | Not significant |
Pure Error | 69,773.69 | 11 | 6343.06 | |||
Cor Total | 1.71 × 106 | 35 |
Test Number | Factor (104 plants/ha) | Factor (kg/ha) | Factor (kg/ha) | Factor (kg/ha) | Yield (kg/ha) |
---|---|---|---|---|---|
52 | 50 | 95.16 | 198.76 | 39.65 | 3486.8 |
53 | 50 | 44.84 | 101.24 | 20.35 | 3160.65 |
54 | 55 | 70 | 150 | 30 | 2853.97 |
Source | Sum of Squares | DF | Mean Square | F Value | Prob > F | |
---|---|---|---|---|---|---|
Model | 1.36 × 106 | 14 | 97,270.43 | 28.37 | <0.0001 | Significant |
A | 32,410.56 | 1 | 32,410.56 | 9.45 | 0.0058 | |
B | 2.87 × 105 | 1 | 2.87 × 105 | 83.57 | <0.0001 | |
C | 1.57 × 105 | 1 | 1.57 × 105 | 45.73 | <0.0001 | |
D | 26,573.41 | 1 | 26,573.41 | 7.75 | 0.0111 | |
AB | 1109.56 | 1 | 1109.56 | 0.3236 | 0.5755 | |
AC | 3889.39 | 1 | 3889.39 | 1.13 | 0.2989 | |
AD | 1.42 × 105 | 1 | 1.42 × 105 | 41.31 | <0.0001 | |
BC | 85,141.4 | 1 | 85,141.4 | 24.83 | <0.0001 | |
BD | 68,754.08 | 1 | 68,754.08 | 20.05 | 0.0002 | |
CD | 1114.56 | 1 | 1114.56 | 0.3251 | 0.5746 | |
A2 | 1.85 × 105 | 1 | 1.85 × 105 | 54.02 | <0.0001 | |
B2 | 19,588.47 | 1 | 19,588.47 | 5.71 | 0.0263 | |
C2 | 3.53 × 105 | 1 | 3.53 × 105 | 102.88 | <0.0001 | |
D2 | 284.21 | 1 | 284.21 | 0.0829 | 0.7762 | |
Residual | 72,003.15 | 21 | 3428.72 | |||
Lack of Fit | 43,048.41 | 10 | 4304.84 | 1.64 | 0.2158 | Not significant |
Pure Error | 28,954.73 | 11 | 2632.25 | |||
Cor Total | 1.43 × 106 | 35 |
Source | Sum of Squares | DF | Mean Square | F Value | Prob > F | |
---|---|---|---|---|---|---|
Model | 1.36 × 106 | 10 | 1.36 × 105 | 43.22 | <0.0001 | Significant |
A | 32,410.56 | 1 | 32,410.56 | 10.33 | 0.0036 | |
B | 2.87 × 105 | 1 | 2.87 × 105 | 91.36 | <0.0001 | |
C | 1.57 × 105 | 1 | 1.57 × 105 | 50 | <0.0001 | |
D | 26,573.41 | 1 | 26,573.41 | 8.47 | 0.0075 | |
AD | 1.42 × 105 | 1 | 1.42 × 105 | 45.16 | <0.0001 | |
BC | 85,141.4 | 1 | 85,141.4 | 27.15 | <0.0001 | |
BD | 68,754.08 | 1 | 68,754.08 | 21.92 | <0.0001 | |
A2 | 1.85 × 105 | 1 | 1.85 × 105 | 59.06 | <0.0001 | |
B2 | 19,588.47 | 1 | 19,588.47 | 6.25 | 0.0194 | |
C2 | 3.53 × 105 | 1 | 3.53 × 105 | 112.48 | <0.0001 | |
Residual | 78,400.87 | 25 | 3136.03 | |||
Lack of Fit | 49,446.13 | 14 | 3531.87 | 1.34 | 0.316 | Not significant |
Pure Error | 28,954.73 | 11 | 2632.25 | |||
Cor Total | 1.43 × 106 | 35 |
Test Number | Factor (104 plants/ha) | Factor (kg/ha) | Factor (kg/ha) | Factor (kg/ha) | Yield (kg/ha) |
---|---|---|---|---|---|
1 | 35 | 139.36 | 147.46 | 12.85 | 2602.61 |
2 | 55 | 118.38 | 201.09 | 19.72 | 2834.55 |
3 | 35 | 21.62 | 98.91 | 12.85 | 2318.74 |
Source | Sum of Squares | DF | Mean Square |
---|---|---|---|
Model | 1.49 × 106 | 14 | 1.07 × 105 |
A | 2.63 × 105 | 1 | 2.63 × 105 |
B | 43,389.17 | 1 | 43,389.17 |
C | 1419.02 | 1 | 1419.02 |
D | 20,874.21 | 1 | 20,874.21 |
AB | 47,390.93 | 1 | 47,390.93 |
AC | 3.55 × 105 | 1 | 3.55 × 105 |
AD | 1.58 × 105 | 1 | 1.58 × 105 |
BC | 1.28 × 105 | 1 | 1.28 × 105 |
BD | 888.91 | 1 | 888.91 |
CD | 1.9 × 105 | 1 | 1.9 × 105 |
A2 | 35,823.18 | 1 | 35,823.18 |
B2 | 12,369.3 | 1 | 12,369.3 |
C2 | 15,809.88 | 1 | 15,809.88 |
D2 | 6152.91 | 1 | 6152.91 |
Cor Total | 1.49 × 106 | 14 |
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Hao, H.; Lv, S.; Wang, F. Optimal Planting Density and Nutrient Application of Soybeans: A Case Study in Northeastern China. Agronomy 2023, 13, 2902. https://doi.org/10.3390/agronomy13122902
Hao H, Lv S, Wang F. Optimal Planting Density and Nutrient Application of Soybeans: A Case Study in Northeastern China. Agronomy. 2023; 13(12):2902. https://doi.org/10.3390/agronomy13122902
Chicago/Turabian StyleHao, Huicheng, Shixin Lv, and Fulin Wang. 2023. "Optimal Planting Density and Nutrient Application of Soybeans: A Case Study in Northeastern China" Agronomy 13, no. 12: 2902. https://doi.org/10.3390/agronomy13122902