马铃薯主要农艺性状的动态模拟研究
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摘要
作物生长发育过程的计算机模拟(简称作物模拟)是近40年来迅速发展起来的一项新技术。它将系统分析方法和计算机技术引入作物科学，根据作物生理学和生态学原理，通过对作物生长发育过程获得的实验数据加以理论概括和数据抽象，建立关于作物物候期、光合生产、器官建成、干物质积累及分配、产量形成等生理过程与环境因子之间关系的动态数学模型，然后在计算机上模拟在给定的环境下作物整个生育期的生长情况。这种模拟是利用计算机，借助数学模型对作物生长发育过程与外界环境之间的变化进行动态仿真的过程，它具有解释能力强，应用面宽，可考虑众多因子的影响和易于控制等优点。
本研究通过对大量文献资料特别是国内外最新研究成果的分析与归纳，并参考其他作物生长发育动态模拟的研究结果，在田间试验的基础上，构建了马铃薯生长发育的动态模拟模型，并开发了基于中文版Visual Basic 6.0的模拟软件，为网上应用本研究的理论和实践成果提供了基础。
本研究的主要成果包括以下几个方面：
1 马铃薯生育期模型
本研究根据作物生长温度三基点的基本原理提出了一个基于高斯方程的马铃薯生育期模型，假定马铃薯的生长量从最低温度到最适温度为增函数，从最适温度到最高温度为减函数，在最适温度时取得最大值为1，并定义为一个发育生理日。模拟的结果表明浙江省马铃薯主栽品种“东农303”从播种到出苗需要12～13个有效生理日，从出苗到现蕾为20～21个有效生理日，从现蕾到成熟为10～11个有效生理日。通过对马铃薯生育期数学模型的解析，笔者给出了地膜覆盖后土壤温度增加对马铃薯生长的数值分解方法和计算结果，实现了从定性分析到定量分析的突破。
2 马铃薯株高、叶龄和叶面积系数的模拟
马铃薯株高、叶龄、叶面积系数的变化与生育期的进展是密不可分的。本研究以累计发育生理日为自变量，以S形曲线模拟株高和叶面积系数的增长过程，以指数函数曲线模拟叶龄和叶面积系数衰退的过程。
浙江大学
中文摘要
硕士学位论文
3马铃薯干物质积累与分配的模拟
本研究以每天的单位叶面积变化、群体上方的有效辐射和温度变化模拟群体的
干物质积累.结果表明，本研究的模型有明确的机理性和较高的精度。同时得出了
随着马铃薯生育期的不断推进，千物质在各器官间的分配规律和各器官干物率变化
的定量规律，并给出了相应的数学模型。模拟结果理想，表明所建设的数学模型不
仅理论上成立，而且也有实用价值。
4模拟软件的开发
笔者以中文版巧sual Basic6.O完成了本研究中涉及到的不同生态条件下马铃薯
生育期、株高、叶龄、叶面积系数、干物质积累和分配、产量形成等模型的模拟软
件开发，软件以可视化的界面、直观的表达和Windows式的菜单设置，有利于具有
一般计算机知识的研究者和推广人员使用。
System simulation of crop growth and development has been a booming technique in the last forty years. It introduces systematic methodology and computer technology into crop science. According to crop physiology and ecology knowledge, with the systematic analysis and numerous digital calculation of field crop experiments, a dynamic model was established to reveal the relationship between the environmental factor and potato phenological development, photosynthesis, apparatus establishment, dry-matter accumulation, distribution, yield and so on. We can simulate the whole crop phenological development in the given environmental condition.
Based on the review of large amount of literatures especially recent research achievements abroad and domestic, the dynamic simulation of other crop growth, we developed a set of simulation models for potato growth, and a simulation software based on Visual Basic 6.0 in Chinese format. And the software has supplied a base for application on Web.
The main achievements are as follows:
1 Potato phenological development model
According to the three-basic-point-temperature principle of crop growth, the author submitted a nonlinear model based on Gauss function for crop growth and development simulation. When the temperature changed from the lowest point for growing to the optimized temperature, the equation was an increase function; then when the temperature changed from the optimized point to the highest point, the equation was a decrease function. It was supposed that the maximum value equaled 1 in the optimized temperature. The whole change was defined as one physiological day. The modeling results showed that the potato variety "Dongnong 303", which was widely planted in Zhejiang Province, needed 11-13 physiological days from seeding to emerging, 21-23 physiological days from emerging to budding and 12-13 physiological days from budding to maturing. According to the analysis of the phenological development model, the
calculation results of soil temperature contribution for the potato planted in mulching were given. This method also improved the analysis approach from qualitative analysis to quantitative analysis.
2 Simulation of plant height, leaf age and leaf area index of potato
There was a high correlation between potato phenological development and plant height, leaf age, and leaf area index. The accumulative physiological day was used as a variable factor, and the S-curve was used to simulate plant height and growth process of leaf area index, and used exponential function to simulate leaf age and declining process of leaf area index.
3 Simulation of dry-matter accumulation and distribution of potato
The study simulated the dry-matter accumulation with the changes of leaf area index, canopy photosynthesis and temperature. The simulation results showed that the model was of high accuracy and clear mechanism. Along with the potato phenological development, the function of dry-matter distribution, the quantity change of dry-matter percentage rate in each apparatus at different stages, and the corresponding mathematics model were also given in this paper. The correlation coefficient between the modeling results and actual field yield was really acceptable.
4 Software developments for potato simulation
The software for potato simulation was completed in this study, which included potato phenological development, plant height, leaf age development, leaf area index change, canopy photosynthesis of the community, dry-matter accumulation and yield formation. The software had a visual interface, direct result expression and the menus designed just like Windows. It was helpful for common researchers and extension workers with basic computer knowledge.
本研究通过对大量文献资料特别是国内外最新研究成果的分析与归纳，并参考其他作物生长发育动态模拟的研究结果，在田间试验的基础上，构建了马铃薯生长发育的动态模拟模型，并开发了基于中文版Visual Basic 6.0的模拟软件，为网上应用本研究的理论和实践成果提供了基础。
本研究的主要成果包括以下几个方面：
1 马铃薯生育期模型
本研究根据作物生长温度三基点的基本原理提出了一个基于高斯方程的马铃薯生育期模型，假定马铃薯的生长量从最低温度到最适温度为增函数，从最适温度到最高温度为减函数，在最适温度时取得最大值为1，并定义为一个发育生理日。模拟的结果表明浙江省马铃薯主栽品种“东农303”从播种到出苗需要12～13个有效生理日，从出苗到现蕾为20～21个有效生理日，从现蕾到成熟为10～11个有效生理日。通过对马铃薯生育期数学模型的解析，笔者给出了地膜覆盖后土壤温度增加对马铃薯生长的数值分解方法和计算结果，实现了从定性分析到定量分析的突破。
2 马铃薯株高、叶龄和叶面积系数的模拟
马铃薯株高、叶龄、叶面积系数的变化与生育期的进展是密不可分的。本研究以累计发育生理日为自变量，以S形曲线模拟株高和叶面积系数的增长过程，以指数函数曲线模拟叶龄和叶面积系数衰退的过程。
浙江大学
中文摘要
硕士学位论文
3马铃薯干物质积累与分配的模拟
本研究以每天的单位叶面积变化、群体上方的有效辐射和温度变化模拟群体的
干物质积累.结果表明，本研究的模型有明确的机理性和较高的精度。同时得出了
随着马铃薯生育期的不断推进，千物质在各器官间的分配规律和各器官干物率变化
的定量规律，并给出了相应的数学模型。模拟结果理想，表明所建设的数学模型不
仅理论上成立，而且也有实用价值。
4模拟软件的开发
笔者以中文版巧sual Basic6.O完成了本研究中涉及到的不同生态条件下马铃薯
生育期、株高、叶龄、叶面积系数、干物质积累和分配、产量形成等模型的模拟软
件开发，软件以可视化的界面、直观的表达和Windows式的菜单设置，有利于具有
一般计算机知识的研究者和推广人员使用。
System simulation of crop growth and development has been a booming technique in the last forty years. It introduces systematic methodology and computer technology into crop science. According to crop physiology and ecology knowledge, with the systematic analysis and numerous digital calculation of field crop experiments, a dynamic model was established to reveal the relationship between the environmental factor and potato phenological development, photosynthesis, apparatus establishment, dry-matter accumulation, distribution, yield and so on. We can simulate the whole crop phenological development in the given environmental condition.
Based on the review of large amount of literatures especially recent research achievements abroad and domestic, the dynamic simulation of other crop growth, we developed a set of simulation models for potato growth, and a simulation software based on Visual Basic 6.0 in Chinese format. And the software has supplied a base for application on Web.
The main achievements are as follows:
1 Potato phenological development model
According to the three-basic-point-temperature principle of crop growth, the author submitted a nonlinear model based on Gauss function for crop growth and development simulation. When the temperature changed from the lowest point for growing to the optimized temperature, the equation was an increase function; then when the temperature changed from the optimized point to the highest point, the equation was a decrease function. It was supposed that the maximum value equaled 1 in the optimized temperature. The whole change was defined as one physiological day. The modeling results showed that the potato variety "Dongnong 303", which was widely planted in Zhejiang Province, needed 11-13 physiological days from seeding to emerging, 21-23 physiological days from emerging to budding and 12-13 physiological days from budding to maturing. According to the analysis of the phenological development model, the
calculation results of soil temperature contribution for the potato planted in mulching were given. This method also improved the analysis approach from qualitative analysis to quantitative analysis.
2 Simulation of plant height, leaf age and leaf area index of potato
There was a high correlation between potato phenological development and plant height, leaf age, and leaf area index. The accumulative physiological day was used as a variable factor, and the S-curve was used to simulate plant height and growth process of leaf area index, and used exponential function to simulate leaf age and declining process of leaf area index.
3 Simulation of dry-matter accumulation and distribution of potato
The study simulated the dry-matter accumulation with the changes of leaf area index, canopy photosynthesis and temperature. The simulation results showed that the model was of high accuracy and clear mechanism. Along with the potato phenological development, the function of dry-matter distribution, the quantity change of dry-matter percentage rate in each apparatus at different stages, and the corresponding mathematics model were also given in this paper. The correlation coefficient between the modeling results and actual field yield was really acceptable.
4 Software developments for potato simulation
The software for potato simulation was completed in this study, which included potato phenological development, plant height, leaf age development, leaf area index change, canopy photosynthesis of the community, dry-matter accumulation and yield formation. The software had a visual interface, direct result expression and the menus designed just like Windows. It was helpful for common researchers and extension workers with basic computer knowledge.
引文
[1] Penning de vries F.W.T., Jansen D.M., ten Berge H.F.M., et al. Simulation of ecophysiological processes of growth in several annual crops. Wageningen: Pudoc, 1989
[2] Whisler F.D., Acock B., Baker D.N., et al. Crop simulation models in agronomic systems. Advances in Agronomy, 1986, 40:141～208
[3] 杜华平．作物生长模拟研究浅析．上海农业科技，1999，(3)：2～4
[4] 曹卫星，罗卫红．作物系统模拟及智能管理．北京：华文出版社，2000
[5] 严力蛟著．水稻生产优化管理模拟系统研究．北京：中国环境科学出版社，2003
[6] Nuttonson M.Y. Some preliminary observations of phenological data as a tool in the study of photoporiodie and thermal vequirements of various plant material vernalization and phoptoperiodism. A Symposimu, 1948:129～143
[7] Brown D.M., Chapman L.J. Soybean ecology Ⅱ: Development-temperature-moisture relationship from field studies. Agron.J., 1960, 52:496～499
[8] 廖桂平，宫春云，黄璜．作物生长模拟模型研究概述．作物研究，1998，(3)：45～48
[9] De Wit C.T. Photosynthesis of leaf canopies. Agricultural Research Report, 1965, 663:1～56
[10] Duncan W.G., Loomis R.S., Williams W.A., et al. A model for simulation photosynthesis in plant communities. Hilgardia, 1967:181～205
[11] Baker D.N., Lambert J.R., Mackinion J.M. GOSSYM: A Simulation of cotton crop growth and yield. South Carolina Agricultural Experiment Station Technical Bulletin, 1983,1089:21～38
[12] Penning de Vries F.W.T., Van Laar H.H. Simulation of plant growth and crop production. Simulation Monographs, 1982:256～308
[13] 德成C．T．等著．裴鑫德等译．农作物同化、呼吸和蒸腾的模拟．北京：科学出版社，1987
[14] 戚昌瀚，殷新佑．作物生长模拟的研究进展．作物杂志，1994，(4)：1～2
[15] Ritchie J.T., Otter S. Description and performance of CERES—Wheat: Auscr-oriented wheat yield model. USDA-ARS. ARS: 38, 1985:159～175
[16] Ritchie J.T., Acock B., Baker D.N., et al. Crop simulation models in agronomic systems. Advance in Agronomy, 1986:141～208
[17] Alocilja E.C., Ritchie J.T. Upland rice simulation and it's use in multieriteria optimization. IBSNAT Research Report Series 01, 1988:23～49
[18] 高亮之，金之庆，黄耀等．水稻计算机模拟模型及其应用之一，水稻钟模型——水稻发育动态的计算机模型。中国农业气象，1989，10(3)：3～10
[19] 高亮之，金庆之，黄耀等．水稻栽培计算机模拟优化决策系统．北京：中国农业科技出版社，1992
[20] 殷新佑，戚昌瀚．水稻生长日历模拟模型与应用研究．作物学报，1994，20(3)：339～346
[21] 潘德云，王兆骞，徐照本．早籼稻生长发育和分蘖动态与潜在产量的模拟及其应用．浙江农业大学学报，增刊总第7期，1991：1～10
[22] 潘德云，王兆骞，陶秀明．华东迟熟晚粳稻感光性与生育期和潜在生产量的模拟．浙江农业大学学报，增刊总第7期，1991：30～36
[23] 郑志明，严力蛟，王兆骞．杂交晚稻生产潜力的动态模拟与优化群体数量指标研究．浙江农业大学学报，1997，23(1)：59～64
[24] 骆世民，彭少麟编著．农业生态系统分析．广州：广东科技出版社，1996：157～206
[25] 郑志明，Ten Berge H．F．M．水稻氮肥管理的ORYZA-O模型之理论与验证．浙江农业大学学报，1994，20(6)：611～616
[26] 杨京平，王兆骞．作物生长模拟模型及其应用．应用生态学报，1999，10(4)：501～505
[27] 谢从华．数学模型在马铃薯研究中的应用．马铃薯杂志，1989，3(3)：176～179
[28] Sands P．J．预测马铃薯出苗期的数学模型．农业新技术新方法译丛，1990，(2)：25～32
[29] Yuan EM., Bland W.L. Light and temperature modulated expolinear growth model for potato (Solanum tuberosum L.). Agricultural and Forest Meteorlolgy, 2004, 121:141～151
[30] 门福义，刘梦芸．马铃薯高产群体生理参数的数学模型．内蒙古农牧学院学报，1989，10(1)：99～104
[31] 张永成，谢连美．马铃薯丰产栽培综合农艺措施数学模型的研究．马铃薯杂志，1989，3(2)：79～87
[32] 社守宇，田恩平．马铃薯栽培综合农艺措施数学模型及优化方案的研究．马铃薯杂志，1991，5(1)：25～31
[33] 高聚林，刘克礼．马铃薯高产优化栽培措施与产量关系模型的研究．中国马铃薯，2003，17(3)：131～137
[34] 刘效瑞，王景才，袁安民等．寒旱生态区地膜马铃薯持续高产栽培数学模型．马铃薯杂志，1998，12(4)：218～224
[35] 段义字，蒲玉宏．旱地坑种马铃薯栽培技术方案优化决策分析．干旱地区农业研究，1999，
17(3)：18～23
[36] 蒲建刚，王廷杰．脱毒马铃薯高产优质栽培数学模型研究．甘肃农业科技，2001，(11)：13～15
[37] Ejieji C.J., Gowing J.W. A dynamic model for responsive scheduling of potato irrigation based on simulated water-use and yield. Journal of Agricultural Science, 2000, 135:161～171
[38] Travasso M.I., Caldiz D.O. Yield prediction using the SUBSTOR-potato model under Argentmian conditions. Potato Research, 1996, 39 (3): 305～312
[39] Fishman S., Bar-Yosef B. Simulation of nitrogen uptake from soil and partitioning in potato plants: model description and sensitivity analysis. Potato Ecology and Modelling of Crops Under Conditions Limiting Growth, 1995, 3:147～166
[40] Hodges T. Water and nitrogen applications for potato: Commercial and experimental rates compared to a simulation model. Journal of Sustainable Agriculture, 1998, 13 (2): 79～90
[41] 谢从华，田恒林，陈耀华．种植密度与马铃薯块茎大小的分布Ⅱ．块茎大小分布的数学模型及其应用．马铃薯杂志，1991，5(3)：141～147
[42] Wolf J., Van Oijen M. Modelling the dependence of European potato yields on changes in climate and CO_2. Agricultural and Forest Meteorology, 2002, 112:217～231
[43] Wolf J., Van Oijen M. Model simulation of effects of changes in climate and atmospheric CO_2 and O_3 on tuber yield potential of potato (cv. Bintje) in the European Union. Agriculture Ecosystems & Environment, 2003, 94:141～157
[44] Tubiello F.N., Rosenzweig C., Goldberg R.A., et al. Effects of climate change on US crop production: simulation results using two different GCM scenarios. Part Ⅰ: Wheat, potato, maize, and citrus. Climate Research, 2002, 20(3): 259～270
[45] Schapendonk A.H.C.M., Van Oijen M., Dijkstra P., et al. Effects of elevated CO_2 concentration on photosynthetic acclimation and productivity of two potato cultivars grown in open-top chambers. Australian Journal of Plant Physiology, 2000, 27(12): 1119～1130
[46] 王爱华，黄冲平．马铃薯生育期进程的计算机模拟模型研究．中国马铃薯，2003，17(2)：74～78
[47] 黄冲平，王爱华，胡秉民．马铃薯生育期和干物质积累的动态模拟研究．生物数学学报，2003，18(3)：314～320
[2] Whisler F.D., Acock B., Baker D.N., et al. Crop simulation models in agronomic systems. Advances in Agronomy, 1986, 40:141～208
[3] 杜华平．作物生长模拟研究浅析．上海农业科技，1999，(3)：2～4
[4] 曹卫星，罗卫红．作物系统模拟及智能管理．北京：华文出版社，2000
[5] 严力蛟著．水稻生产优化管理模拟系统研究．北京：中国环境科学出版社，2003
[6] Nuttonson M.Y. Some preliminary observations of phenological data as a tool in the study of photoporiodie and thermal vequirements of various plant material vernalization and phoptoperiodism. A Symposimu, 1948:129～143
[7] Brown D.M., Chapman L.J. Soybean ecology Ⅱ: Development-temperature-moisture relationship from field studies. Agron.J., 1960, 52:496～499
[8] 廖桂平，宫春云，黄璜．作物生长模拟模型研究概述．作物研究，1998，(3)：45～48
[9] De Wit C.T. Photosynthesis of leaf canopies. Agricultural Research Report, 1965, 663:1～56
[10] Duncan W.G., Loomis R.S., Williams W.A., et al. A model for simulation photosynthesis in plant communities. Hilgardia, 1967:181～205
[11] Baker D.N., Lambert J.R., Mackinion J.M. GOSSYM: A Simulation of cotton crop growth and yield. South Carolina Agricultural Experiment Station Technical Bulletin, 1983,1089:21～38
[12] Penning de Vries F.W.T., Van Laar H.H. Simulation of plant growth and crop production. Simulation Monographs, 1982:256～308
[13] 德成C．T．等著．裴鑫德等译．农作物同化、呼吸和蒸腾的模拟．北京：科学出版社，1987
[14] 戚昌瀚，殷新佑．作物生长模拟的研究进展．作物杂志，1994，(4)：1～2
[15] Ritchie J.T., Otter S. Description and performance of CERES—Wheat: Auscr-oriented wheat yield model. USDA-ARS. ARS: 38, 1985:159～175
[16] Ritchie J.T., Acock B., Baker D.N., et al. Crop simulation models in agronomic systems. Advance in Agronomy, 1986:141～208
[17] Alocilja E.C., Ritchie J.T. Upland rice simulation and it's use in multieriteria optimization. IBSNAT Research Report Series 01, 1988:23～49
[18] 高亮之，金之庆，黄耀等．水稻计算机模拟模型及其应用之一，水稻钟模型——水稻发育动态的计算机模型。中国农业气象，1989，10(3)：3～10
[19] 高亮之，金庆之，黄耀等．水稻栽培计算机模拟优化决策系统．北京：中国农业科技出版社，1992
[20] 殷新佑，戚昌瀚．水稻生长日历模拟模型与应用研究．作物学报，1994，20(3)：339～346
[21] 潘德云，王兆骞，徐照本．早籼稻生长发育和分蘖动态与潜在产量的模拟及其应用．浙江农业大学学报，增刊总第7期，1991：1～10
[22] 潘德云，王兆骞，陶秀明．华东迟熟晚粳稻感光性与生育期和潜在生产量的模拟．浙江农业大学学报，增刊总第7期，1991：30～36
[23] 郑志明，严力蛟，王兆骞．杂交晚稻生产潜力的动态模拟与优化群体数量指标研究．浙江农业大学学报，1997，23(1)：59～64
[24] 骆世民，彭少麟编著．农业生态系统分析．广州：广东科技出版社，1996：157～206
[25] 郑志明，Ten Berge H．F．M．水稻氮肥管理的ORYZA-O模型之理论与验证．浙江农业大学学报，1994，20(6)：611～616
[26] 杨京平，王兆骞．作物生长模拟模型及其应用．应用生态学报，1999，10(4)：501～505
[27] 谢从华．数学模型在马铃薯研究中的应用．马铃薯杂志，1989，3(3)：176～179
[28] Sands P．J．预测马铃薯出苗期的数学模型．农业新技术新方法译丛，1990，(2)：25～32
[29] Yuan EM., Bland W.L. Light and temperature modulated expolinear growth model for potato (Solanum tuberosum L.). Agricultural and Forest Meteorlolgy, 2004, 121:141～151
[30] 门福义，刘梦芸．马铃薯高产群体生理参数的数学模型．内蒙古农牧学院学报，1989，10(1)：99～104
[31] 张永成，谢连美．马铃薯丰产栽培综合农艺措施数学模型的研究．马铃薯杂志，1989，3(2)：79～87
[32] 社守宇，田恩平．马铃薯栽培综合农艺措施数学模型及优化方案的研究．马铃薯杂志，1991，5(1)：25～31
[33] 高聚林，刘克礼．马铃薯高产优化栽培措施与产量关系模型的研究．中国马铃薯，2003，17(3)：131～137
[34] 刘效瑞，王景才，袁安民等．寒旱生态区地膜马铃薯持续高产栽培数学模型．马铃薯杂志，1998，12(4)：218～224
[35] 段义字，蒲玉宏．旱地坑种马铃薯栽培技术方案优化决策分析．干旱地区农业研究，1999，
17(3)：18～23
[36] 蒲建刚，王廷杰．脱毒马铃薯高产优质栽培数学模型研究．甘肃农业科技，2001，(11)：13～15
[37] Ejieji C.J., Gowing J.W. A dynamic model for responsive scheduling of potato irrigation based on simulated water-use and yield. Journal of Agricultural Science, 2000, 135:161～171
[38] Travasso M.I., Caldiz D.O. Yield prediction using the SUBSTOR-potato model under Argentmian conditions. Potato Research, 1996, 39 (3): 305～312
[39] Fishman S., Bar-Yosef B. Simulation of nitrogen uptake from soil and partitioning in potato plants: model description and sensitivity analysis. Potato Ecology and Modelling of Crops Under Conditions Limiting Growth, 1995, 3:147～166
[40] Hodges T. Water and nitrogen applications for potato: Commercial and experimental rates compared to a simulation model. Journal of Sustainable Agriculture, 1998, 13 (2): 79～90
[41] 谢从华，田恒林，陈耀华．种植密度与马铃薯块茎大小的分布Ⅱ．块茎大小分布的数学模型及其应用．马铃薯杂志，1991，5(3)：141～147
[42] Wolf J., Van Oijen M. Modelling the dependence of European potato yields on changes in climate and CO_2. Agricultural and Forest Meteorology, 2002, 112:217～231
[43] Wolf J., Van Oijen M. Model simulation of effects of changes in climate and atmospheric CO_2 and O_3 on tuber yield potential of potato (cv. Bintje) in the European Union. Agriculture Ecosystems & Environment, 2003, 94:141～157
[44] Tubiello F.N., Rosenzweig C., Goldberg R.A., et al. Effects of climate change on US crop production: simulation results using two different GCM scenarios. Part Ⅰ: Wheat, potato, maize, and citrus. Climate Research, 2002, 20(3): 259～270
[45] Schapendonk A.H.C.M., Van Oijen M., Dijkstra P., et al. Effects of elevated CO_2 concentration on photosynthetic acclimation and productivity of two potato cultivars grown in open-top chambers. Australian Journal of Plant Physiology, 2000, 27(12): 1119～1130
[46] 王爱华，黄冲平．马铃薯生育期进程的计算机模拟模型研究．中国马铃薯，2003，17(2)：74～78
[47] 黄冲平，王爱华，胡秉民．马铃薯生育期和干物质积累的动态模拟研究．生物数学学报，2003，18(3)：314～320