玉米大豆间作种植密度耦合数学模型及其优化方案研究

doi:10.16035/j.issn.1001-7283.2019.02.020

摘要/Abstract

摘要：

云南省大豆的种植主要以与玉米间作为主,适宜的种植密度是获得高产的前提,为研究种植密度对群体产量和经济产值的影响,找到最佳种植密度组合。采用二次饱和D-最优设计,分别在云南嵩明县（A）、会泽县（B）和鲁甸县（C）等3个点进行试验。研究了玉米和大豆种植密度对群体产量和经济产值的影响,并分别建立二元二次数学模型。结果表明：玉米和大豆密度对间作群体产量和经济产值影响显著,均呈凸抛物线型变化,在低密度水平下,群体产量和经济产值随密度的增加而增加。通过模型解析表明,玉米+大豆密度组合分别为64 110株/hm ²+147 013株/hm ²（A）、63 068株/hm ²+147 116株/hm ²（B）、64 059株/hm ²+145 077株/hm ²（C）时,各试验点可分别达到最高群体产量。玉米+大豆密度组合分别为62 909株/hm ²+149 852株/hm ²（A）、61 499株/hm ²+151 807株/hm ²（B）、62 762株/hm ²+147 108株/hm ²（C）时,各试验点可分别达到最高产值。经模拟得出,在本试验条件下,各试验点玉米大豆间作群体产量≥12 270kg/hm ²、经济产值≥24 000元/hm ²的最佳密度组合分别为玉米59 251~66 437株/hm ²、大豆140 075~161 495株/hm ²（A）,玉米58 927~65 366株/hm ²、大豆144 159~169 203株/hm ²（B）,玉米58 821~66 703株/hm ²、大豆139 315~154 886株/hm ²（C）。合理的密度搭配能有效提高群体产量,获得较高经济产值。

关键词: 玉米, 大豆, 间作, 种植密度耦合, 数学模型, 优化方案

Abstract:

Maize and soybean intercropping planting is mainly composed of soybean planting in Yunnan Province. In order to achieve high yield of maize and soybean intercropping system, we must have suitable planting density. The effect of planting density on population grain yield and economic output value was studied with the design of the double saturated D-optimal regression, which was tested at three sites including Songming County (A), Huize County (B) and Ludian County (C), respectively. And a binary quadratic mathematical model was established, in which the planting densities of maize and soybean were independent variables, and population grain yield and economic output value were dependent variables. The results showed that the planting density of maize and soybean on population grain yield and economic output value of intercropping group effect significantly, and the change curve was a convex parabola. The population yield and economic output increased with density under the low level of density. According to model analysis, each test site could reach the highest population grain yield with the optimized combination of maize 64 110 plant/hm ²+ soybean 147 013 plant/hm ² (A), maize 63 068 plant/hm ²+soybean 147 116 plant/hm ² (B) and maize 64 059 plant/hm ²+soybean 145 077 plant/hm ² (C), respectively. Each test site could reach the highest economic output value with the optimized combination of maize 62 909 plant/hm ²+soybean 149 852 plant/hm ² (A), maize 61 499 plant/hm ²+soybean 151 807 plant/hm ² (B) and maize 62 762 plant/hm ²+soybean 147 108 plant/hm ² (C), respectively. According computer simulation, the optimum combination of densities of maize and soybean were 59 251-66 437 plant/hm ² for maize and 140 075-161 495 plant/hm ² for soybean (A), 58 927-65 366 plant/hm ² for maize and 144 159-169 203 plant/hm ² for soybean (B), 58 821-66 703 plant/hm ² for maize and 139 315-154 886 plant/hm ² for soybean (C) in order to obtain population grain yield greater than 12 270kg/hm ² and economic output value greater 24 000 yuan/hm ² under the condition of this experiment. A reasonable density collocation can effectively increase population yield and economic output value.

Key words: Maize, Soybean, Intercropping, Planting density coupling, Mathematics model, Optimization scheme

代希茜,詹和明,崔兴洪,赵银月,单丹丹,张亮,王铁军. 玉米大豆间作种植密度耦合数学模型及其优化方案研究[J]. 作物杂志, 2019 (2): 128–135

Xixi Dai,Heming Zhan,Xinghong Cui,Yinyue Zhao,Dandan Shan,Liang Zhang,Tiejun Wang. A Mathematical Model of Density Coupling and Its Optimization in Maize-Soybean Intercropping[J]. Crops, 2019(2): 128–135

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参考文献 22

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处理 Treatment	水平编码值 Level coding value		田间实际值(株/hm²) Field actual value (plant/hm²)
处理 Treatment	玉米 Maize	大豆 Soybean	玉米 Maize	大豆 Soybean
T1	-1	-1	44 978	89 955
T2	-1	-1	71 964	89 955
T3	-1	-1	44 978	194 903
T4	-0.1315	-0.1315	56 696	135 528
T5	-0.3944	-1	63 793	194 903
T6	-1	-0.3944	71 964	163 124

处理 Treatment	嵩明Songming			会泽Huize			鲁甸Ludian
处理 Treatment	玉米 Maize	大豆 Soybean	群体 Total	玉米 Maize	大豆 Soybean	群体 Total	玉米 Maize	大豆 Soybean	群体 Total
T1	9 499.3a	1 201.3de	10 700.6d	9 778.8c	1 078.1d	10 856.9d	9 960.5d	1 084.5e	11 045.0d
T2	10 655.5b	1 144.7e	11 800.2b	10 984.5ab	888.7e	11 873.2b	10 967.0c	1 011.5f	11 978.5b
T3	9 373.4a	1 338.5bc	10 711.9d	9 713.1c	1 194.0c	10 907.1d	9 835.6e	1 186.4d	11 022.0d
T4	10 651.3b	1 419.2b	12 070.5a	10 991.5ab	1 318.6b	12 310.1a	10 909.6c	1 298.4b	12 207.9a
T5	10 822.6ab	1 293.4cd	12 116.0a	11 121.1a	1 175.9c	12 297.0a	11 108.0b	1 121.4e	12 229.4a
T6	10 669.9b	1 363.2bc	12 033.1ab	10 893.5b	1 240.4c	12 133.9a	10 880.6c	1 236.9c	12 164.9a
SS	-	3 582.2a	3 582.2e	-	3 568.2a	3 568.2e	-	3 647.2a	3 647.2e
MM	11 023.7a	-	11 023.7c	11 155.9a	-	11 155.9c	11 223.4a	-	11 223.4c

处理 Treatment	嵩明Songming			会泽Huize			鲁甸Ludian
处理 Treatment	玉米 Maize	大豆 Soybean	群体 Total	玉米 Maize	大豆 Soybean	群体 Total	玉米 Maize	大豆 Soybean	群体 Total
T1	15 198.8c	6 607.1de	21 805.9c	15 646.1c	5 929.4d	21 575.5d	15 936.8d	5 964.5e	21 901.3f
T2	17 048.8b	6 296.0e	23 344.7b	17 575.2ab	4 887.8e	22 463.0c	17 547.2c	5 563.2f	23 110.4d
T3	14 997.3c	7 361.9bc	22 359.2c	15 541.0c	6 566.7c	22 107.8c	15 736.9e	6 525.2d	22 262.2e
T4	17 042.2b	7 805.4b	24 847.6a	17 586.4ab	7 252.6b	24 839.0a	17 455.3c	7 140.9b	24 596.2a
T5	17 316.1ab	7 113.6cd	24 429.7a	17 793.7a	6 467.5c	24 261.3b	17 772.7b	6 167.9e	23 940.6c
T6	17 071.8b	7 497.6bc	24 569.4a	17 429.7b	6 822.1c	24 251.8b	17 484.9c	6 802.8c	24 287.7b
SS	-	19 699.4a	19 699.4d	-	19 625.2a	19 625.2e	-	20 059.5a	20 059.5g
MM	17 638.4a	-	17 638.4e	17 849.5a	-	17 849.5f	17 957.4a	-	17 957.4h

优化目标 Optimal target value	相关参数 Relevant parameter	嵩明Songming		会泽Huize		鲁甸Ludian
优化目标 Optimal target value	相关参数 Relevant parameter	X₁	X₂	X₁	X₂	X₁	X₂
群体产量≥12 270kg/hm² Population grain yield ≥12 270kg/hm²	优化方案数 Optimization scheme	14		18		19
	平均值Mean	0.3270	0.0751	0.2397	0.0584	0.2797	0.1080
	标准误Standard error	0.1132	0.1198	0.0962	0.1472	0.0994	0.1478
	95%的置信区间 95% confidence interval	0.0824~0.5716	-0.1837~0.3339	0.0368~0.4426	-0.2521~0.3690	0.0709~0.4885	-0.2025~0.4185
	种植密度(株/hm²) Planting density (plant/hm²)	59 612~66 216	132 855~160 032	58 997~64 475	129 263~161 871	59 457~65 095	131 868~164 470
经济产值≥24 000元/hm² Economic output value ≥24000 yuan/hm²	优化方案数 Optimization scheme	15		15		12
	平均值Mean	0.2701	0.2701	0.2701	0.2701	0.3157	0.0876
	标准误Standard error	0.1112	0.1112	0.1112	0.1112	0.1326	0.0674
	95%的置信区间 95% confidence interval	0.0316~0.5086	0.0316~0.5086	0.0316~0.5086	0.0316~0.5086	0.0238~0.6077	-0.0607~0.2359
	种植密度(株/hm²) Planting density (plant/hm²)	58 927~65 366	144 159~169 203	58 927~65 366	144 159~169 203	58 821~66 703	139 315~154 886

变量 Variable	嵩明Songming				会泽Huize				鲁甸Ludian
	X₁		X₂		X₁		X₂		X₁		X₂
	次数 Times	频率 Frequency	次数 Times	频率 Frequency	次数 Times	频率 Frequency	次数 Times	频率 Frequency	次数 Times	频率 Frequency	次数 Times	频率 Frequency
-1	0	0	0	0	0	0	0	0	0	0	0	0
-0.1315	3	0.2308	4	0.3077	4	0.2667	4	0.2667	3	0.25	4	0.3333
0	3	0.2308	4	0.3077	4	0.2667	4	0.2667	3	0.25	4	0.3333
0.3944	4	0.3077	4	0.3077	4	0.2667	4	0.2667	3	0.25	4	0.3333
1	3	0.2308	1	0.0769	3	0.2000	3	0.2000	3	0.25	0	0
合计 Total	13	1	13	1	15	1	15	1	12	1	12	1
平均值 Mean	0.3218		0.1578		0.2701		0.2701		0.3157		0.0876
标准误 Standard error	0.1222		0.0936		0.1112		0.1112		0.1326		0.0674
95%置信区间 95% confidence interval	0.0556~0.5879		-0.0462~0.3618		0.0316~0.5086		0.0316~0.5086		0.0238~0.6077		-0.0607~0.2359
种植密度(株/hm²) Plant density (plant/hm²)	59 251~66 437		140 075~161 495		58 927~65 366		144 159~169 203		58 821~66 703		139 315~154 886