玉米大豆间作种植密度耦合数学模型及其优化方案研究

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。

A Mathematical Model of Density Coupling and Its Optimization in Maize-Soybean Intercropping

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.