油菜分枝拓扑结构随机模拟
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摘要
油菜(Brassica napus L.)具有复杂的分枝结构,其分枝为向顶式发生(出现)、向基式扩展,这种独特的生长模式使得油菜个体植株间的构型存在很大的差异.本研究利用与位置有关的生长延迟函数,计算各分枝从发生到扩展的时间间隔,来模拟油菜分枝这种独特的生长模式.此外,利用随机概率模型来模拟油菜植株间分枝数、主干和分枝的叶元数等.通过实际测量的四个油菜品种(ZY18, ZY50, ZS72和ZS11)的数据,采用最小二乘法对该模型的参数进行校准.结果表明,该随机模型能够模拟油菜植株拓扑结构,并根据参数估计的结果分析不同品种的拓扑结构差异性.本研究提出了新的简化方法模拟油菜分枝的生长模式,该模型可与油菜生长模型相结合,从而模拟油菜的动态生长过程.
The structure of oilseed rape is complex due to the development patterns of inflorescence: initiate acropetally but expand basipetally.This unique physiological characteristic makes a big difference in the morphological structure of individual plants in oilseed rape.The time lag between the appearance and elongation of a branch, called "growth delay", needs to be quantified in order to simulate the developmental pattern of oilseed rape. This study computes the time interval between the appearance and expansion of branches by using a growth delay function. Moreover, a stochastic probabilistic model is built to simulate the differences of the numbers of branches, phytomers of the stems and branches within and among plants for four cultivars. Furthermore, model parameters can be estimated using the experimental measurements for four cultivars(ZY18, ZY50, ZS72 and ZS11) with the generalized least square method. The results indicate that the differences of structure among individual plants for different cultivars can be simulated using the stochastic model. This work provides a new and simple method to describe the differences of structure among plants using a stochastic model. This method can simulate the branch development of oilseed rape, which can be combined to a functional-structural model to simulate the growth and development of oilseed rape.
The structure of oilseed rape is complex due to the development patterns of inflorescence: initiate acropetally but expand basipetally.This unique physiological characteristic makes a big difference in the morphological structure of individual plants in oilseed rape.The time lag between the appearance and elongation of a branch, called "growth delay", needs to be quantified in order to simulate the developmental pattern of oilseed rape. This study computes the time interval between the appearance and expansion of branches by using a growth delay function. Moreover, a stochastic probabilistic model is built to simulate the differences of the numbers of branches, phytomers of the stems and branches within and among plants for four cultivars. Furthermore, model parameters can be estimated using the experimental measurements for four cultivars(ZY18, ZY50, ZS72 and ZS11) with the generalized least square method. The results indicate that the differences of structure among individual plants for different cultivars can be simulated using the stochastic model. This work provides a new and simple method to describe the differences of structure among plants using a stochastic model. This method can simulate the branch development of oilseed rape, which can be combined to a functional-structural model to simulate the growth and development of oilseed rape.
引文
1 Guo Y Z,Yang Y L,Sun J M.The current situation and solutions of rapeseed industry development in China.Agr Econ,2016,7:44-46
2 Kiniry J R,Williams J R,Major D J,et al.EPIC model parameters for cereal,oilseed,and forage crops in the northern great plains region.Can JPlant Sci,1995,75:679-688
3 HabekottéB.A model of the phenological development of winter oilseed rape(Brassica napus L.).Field Crops Res,1997,54:127-136
4 Gabrielle B,Denoroy P,Gosse G,et al.Development and evaluation of a CERES-type model for winter oilseed rape.Field Crops Res,1998,57:95-111
5 Robertson M J,Holland J F,Kirkegaard J A,et al.Simulating growth and development of canola in Australia.In:10th International Rapeseed Congress.Canberra:Organising Committee,1999
6 Robertson M J,Lilley J M.Simulation of growth,development and yield of canola(Brassica napus)in APSIM.Crop Pasture Sci,2016,67:332-344
7 Deligios P A,Farci R,Sulas L,et al.Predicting growth and yield of winter rapeseed in a mediterranean environment:model adaptation at a field scale.Field Crops Res,2013,144:100-112
8 Gilardelli C,Stella T,Frasso N,et al.WOFOST-GTC:a new model for the simulation of winter rapeseed production and oil quality.Field Crops Res,2016,197:125-132
9 Liu H,Jin Z Q.A phenological model to simulate rape development.J Appl Meteor Sci,2003,14:634-640[刘洪,金之庆.油菜发育动态模拟模型.应用气象学报,2003,14:634-640]
10 Cao H X,Zhang C L,Li G M,et al.Researches of simulation models of rape(Brassica napus L.)growth and development(in Chinese).Acta Agron Sinica,2006,32:1530-1536[曹宏鑫,张春雷,李光明,等.油菜生长发育模拟模型研究.作物学报,2006,32:1530-1536]
11 Liu T M,Hu L Y,Zhao Z H,et al.A mechanistic of phasic and phenological development in rape.I.description of the model(in Chinese).Chin JOil Crop Sci,2004,26:28-32[刘铁梅,胡立勇,赵祖红,等.油菜发育过程及生育期机理模型的研究Ⅰ模型的描述.中国油料作物学报,2004,26:28-32]
12 Tang L,Zhu Y,Liu T M,et al.A process-based model for simulating phenological development in rapeseed(in Chinese).Sci Agric Sin,2008,41:2493-2498[汤亮,朱艳,刘铁梅,等.油菜生育期模拟模型研究.中国农业科学,2008,41:2493-2498]
13 Yue Y B,Zhu Y,Cao H X,et al.Models and openGL-based visual technology for rapeseed(Brassica napus L.)flower(in Chinese).Jiangsu Agric Sci,2011,27:264-270[岳延滨,朱艳,曹宏鑫.基于几何参数模型和OpenGL的油菜花朵可视化研究.江苏农业学报,2011,27:264-270]
14 Yue Y B,Zhu Y,Cao H X,et al.Models and openGL-based visual technology for rapeseed(Brassica napus L.)pod(in Chinese).Jiangsu Agric Sci,2011:438-441[岳延滨,朱艳,曹宏鑫.基于几何参数模型和OpenGL的油菜角果可视化研究.江苏农业科学,2011:438-441]
15 Zhao L L,Guo X Y,Wen W L,et al.Research on digital design for 3D shape of the rape inflorescence(in Chinese).J Agri Mechanization Res,2011,33:191-194[赵丽丽,郭新宇,温维亮,等.油菜花序三维形态结构数字化设计技术研究.农机化研究,2011,33:191-194]
16 Li D,Lin B G,Shi T X,et al.Modeling and visualization of 3D architecture of oilseed rape(Brassica napus L.)(in Chinese).Acta Agric Zhejiangensis,2013,25:926-932[李冬,林宝刚,史同鑫,等.油菜植株三维结构的测量与可视化建模研究.浙江农业学报,2013,25:926-932]
17 Li D,Lin B G,Zhang D Q,et al.Three-dimensional modeling of oilseed rape(Brassica napus L.)and its application in canopy architecture analysis(in Chinese).J Wuhan Univ(Philos Sci Ed,2016,62:575-580[李冬,林宝刚,张冬青,等.三维结构模型在油菜冠层分析中的应用.武汉大学学报(理学版),2016,62:575-580]
18 Zhang W X,Cao H X,Zhu Y,et al.Biomass-based rapeseed(Brassica napus L.)plant primary ramification morphological structural model.The proceedings of Annual Conference on Agricultural Electrification and Informatization Engineering and Discipline Innovation and Development,Lanzhou,2014.680-696[张伟欣,曹宏鑫,朱艳,等.基于生物量的油菜植株分枝形态结构模型研究.见:2014年“农业电气化与信息化工程与学科创新发展”学术年会.兰州,2014.680-696]
19 Jullien A,Mathieu A,Allirand J M,et al.Modelling of branch and flower expansion in GreenLab model to account for the whole crop cycle of winter oilseed rape(Brassica napus L.).In:The Third International Symposium on Plant Growth Modeling,Simulation,Visualization and Applications(PMA’09).Washington:IEEE Computer Society,2009.167-174
20 Jullien A,Mathieu A,Allirand J M,et al.Characterization of the interactions between architecture and source-sink relationships in winter oilseed rape(Brassica napus)using the GreenLab model.Ann Bot,2011,107:765-779
21 Zhang B,De Reffye P,Liu L,et al.Analysis and modeling of the root system architecture of winter wheat seedlings.In:International Symposium on Plant Growth Modeling,Simulation,Visualization and their Applications(PMA′03),Washington:IEEE Computer Society,2003.321-328
22 de Reffye P.Modelisation de l′architecture des arbres par des processus stochastiques.Simulation spatiale des modeles tropicaux sous l′effet de la pesanteur.Application au Coffea robusta.Centre d’Orsay,France:Universite Paris-Sud,1979
23 de Reffye P,Elguero E,Costes E.Growth units construction in trees:a stochastic approach.Acta Biotheor,1991,39:325-342
24 Wang F,Kang M,Lu Q,et al.A stochastic model of tree architecture and biomass partitioning:application to Mongolian Scots pines.Ann Bot,2011,107:781-792
25 Diao J,De Reffye P,Lei X,et al.Simulation of the topological development of young eucalyptus using a stochastic model and sampling measurement strategy.Comput Electron Agr,2012,80:105-114
26 Vavitsara M E,Sabatier S,Kang M Z,et al.Yield analysis as a function of stochastic plant architecture:case of Spilanthes acmella in the wet and dry season.Comput Electron Agr,2017,138:105-116
27 de Reffye P.Modèle mathèmatique aleatoire et simulation de la croissance et de l′architecture du caféier Robusta.1ère Partie.CaféCacao Thé,1981,25:83-104
28 Kang M Z,Heuvelink E,de Reffye P.Modelling the growth of inflorescence.In:The Third International Symposium on Plant Growth Modeling,Simulation,Visualization and Applications(PMA’09).Washington:IEEE Computer Society,2009.303-310
29 Barthélémy D,Caraglio Y.Plant architecture:a dynamic,multilevel and comprehensive approach to plant form,structure and ontogeny.Ann Bot,2007,99:375-407
30 Jaeger M,De Reffye P H.Basic concepts of computer simulation of plant growth.J Biosci,1992,17:275-291
31 Yan H P,Kang M Z,de Reffye P,et al.A dynamic,architectural plant model simulating resource-dependent growth.Ann Bot,2004,93:591-602
32 HalléF,Oldeman R A A,Tomlinson P B.Tropical Trees and Forests.Berlin,Heidelberg:Springer,1978
33 Kang M Z,Heuvelink E,Carvalho S M P,et al.A virtual plant that responds to the environment like a real one:the case for chrysanthemum.New Phytol,2012,195:384-395
34 Cournède P H,Letort V,Mathieu A,et al.Some parameter estimation issues in functional-structural plant modelling.Math Model Nat Phenom,2011,6:133-159
35 Letort V,Cournède P-H,de Reffye P.Impact of topology on plant functioning:a theoretical analysis based on the GreenLab model equations.In The Third International Symposium on Plant Growth Modeling,Simulation,Visualization and Applications(PMA’09).Washington:IEEEComputer Society,2009.341-348
36 Kang M Z,Evers J B,Vos J,et al.The derivation of sink functions of wheat organs using the GREENLAB Model.Ann Bot,2008,101:1099-1108
37 Wang X J,Mathieu A,Cournède P-H,et al.Stochastic models in floral biology and its application to the study of oilseed rape(Brassica napu L.)fertility.In:The Third International Symposium on Plant Growth Modeling,Simulation,Visualization and Applications(PMA’09)Washington:IEEE Computer Society,2009.175-182
38 Wang X J,Mathieu A,Cournède P H,et al.Application of a probabilistic model for analysing the abortion of seeds and pods in winter oilseed rape(Brassica napus).Ann Appl Biol,2014,165:414-428
39 Wang X J,Mathieu A,Cournède P H,et al.Variability and regulation of the number of ovules,seeds and pods according to assimilate availability in winter oilseed rape(Brassica napus L.).Field Crops Res,2011,122:60-69
2 Kiniry J R,Williams J R,Major D J,et al.EPIC model parameters for cereal,oilseed,and forage crops in the northern great plains region.Can JPlant Sci,1995,75:679-688
3 HabekottéB.A model of the phenological development of winter oilseed rape(Brassica napus L.).Field Crops Res,1997,54:127-136
4 Gabrielle B,Denoroy P,Gosse G,et al.Development and evaluation of a CERES-type model for winter oilseed rape.Field Crops Res,1998,57:95-111
5 Robertson M J,Holland J F,Kirkegaard J A,et al.Simulating growth and development of canola in Australia.In:10th International Rapeseed Congress.Canberra:Organising Committee,1999
6 Robertson M J,Lilley J M.Simulation of growth,development and yield of canola(Brassica napus)in APSIM.Crop Pasture Sci,2016,67:332-344
7 Deligios P A,Farci R,Sulas L,et al.Predicting growth and yield of winter rapeseed in a mediterranean environment:model adaptation at a field scale.Field Crops Res,2013,144:100-112
8 Gilardelli C,Stella T,Frasso N,et al.WOFOST-GTC:a new model for the simulation of winter rapeseed production and oil quality.Field Crops Res,2016,197:125-132
9 Liu H,Jin Z Q.A phenological model to simulate rape development.J Appl Meteor Sci,2003,14:634-640[刘洪,金之庆.油菜发育动态模拟模型.应用气象学报,2003,14:634-640]
10 Cao H X,Zhang C L,Li G M,et al.Researches of simulation models of rape(Brassica napus L.)growth and development(in Chinese).Acta Agron Sinica,2006,32:1530-1536[曹宏鑫,张春雷,李光明,等.油菜生长发育模拟模型研究.作物学报,2006,32:1530-1536]
11 Liu T M,Hu L Y,Zhao Z H,et al.A mechanistic of phasic and phenological development in rape.I.description of the model(in Chinese).Chin JOil Crop Sci,2004,26:28-32[刘铁梅,胡立勇,赵祖红,等.油菜发育过程及生育期机理模型的研究Ⅰ模型的描述.中国油料作物学报,2004,26:28-32]
12 Tang L,Zhu Y,Liu T M,et al.A process-based model for simulating phenological development in rapeseed(in Chinese).Sci Agric Sin,2008,41:2493-2498[汤亮,朱艳,刘铁梅,等.油菜生育期模拟模型研究.中国农业科学,2008,41:2493-2498]
13 Yue Y B,Zhu Y,Cao H X,et al.Models and openGL-based visual technology for rapeseed(Brassica napus L.)flower(in Chinese).Jiangsu Agric Sci,2011,27:264-270[岳延滨,朱艳,曹宏鑫.基于几何参数模型和OpenGL的油菜花朵可视化研究.江苏农业学报,2011,27:264-270]
14 Yue Y B,Zhu Y,Cao H X,et al.Models and openGL-based visual technology for rapeseed(Brassica napus L.)pod(in Chinese).Jiangsu Agric Sci,2011:438-441[岳延滨,朱艳,曹宏鑫.基于几何参数模型和OpenGL的油菜角果可视化研究.江苏农业科学,2011:438-441]
15 Zhao L L,Guo X Y,Wen W L,et al.Research on digital design for 3D shape of the rape inflorescence(in Chinese).J Agri Mechanization Res,2011,33:191-194[赵丽丽,郭新宇,温维亮,等.油菜花序三维形态结构数字化设计技术研究.农机化研究,2011,33:191-194]
16 Li D,Lin B G,Shi T X,et al.Modeling and visualization of 3D architecture of oilseed rape(Brassica napus L.)(in Chinese).Acta Agric Zhejiangensis,2013,25:926-932[李冬,林宝刚,史同鑫,等.油菜植株三维结构的测量与可视化建模研究.浙江农业学报,2013,25:926-932]
17 Li D,Lin B G,Zhang D Q,et al.Three-dimensional modeling of oilseed rape(Brassica napus L.)and its application in canopy architecture analysis(in Chinese).J Wuhan Univ(Philos Sci Ed,2016,62:575-580[李冬,林宝刚,张冬青,等.三维结构模型在油菜冠层分析中的应用.武汉大学学报(理学版),2016,62:575-580]
18 Zhang W X,Cao H X,Zhu Y,et al.Biomass-based rapeseed(Brassica napus L.)plant primary ramification morphological structural model.The proceedings of Annual Conference on Agricultural Electrification and Informatization Engineering and Discipline Innovation and Development,Lanzhou,2014.680-696[张伟欣,曹宏鑫,朱艳,等.基于生物量的油菜植株分枝形态结构模型研究.见:2014年“农业电气化与信息化工程与学科创新发展”学术年会.兰州,2014.680-696]
19 Jullien A,Mathieu A,Allirand J M,et al.Modelling of branch and flower expansion in GreenLab model to account for the whole crop cycle of winter oilseed rape(Brassica napus L.).In:The Third International Symposium on Plant Growth Modeling,Simulation,Visualization and Applications(PMA’09).Washington:IEEE Computer Society,2009.167-174
20 Jullien A,Mathieu A,Allirand J M,et al.Characterization of the interactions between architecture and source-sink relationships in winter oilseed rape(Brassica napus)using the GreenLab model.Ann Bot,2011,107:765-779
21 Zhang B,De Reffye P,Liu L,et al.Analysis and modeling of the root system architecture of winter wheat seedlings.In:International Symposium on Plant Growth Modeling,Simulation,Visualization and their Applications(PMA′03),Washington:IEEE Computer Society,2003.321-328
22 de Reffye P.Modelisation de l′architecture des arbres par des processus stochastiques.Simulation spatiale des modeles tropicaux sous l′effet de la pesanteur.Application au Coffea robusta.Centre d’Orsay,France:Universite Paris-Sud,1979
23 de Reffye P,Elguero E,Costes E.Growth units construction in trees:a stochastic approach.Acta Biotheor,1991,39:325-342
24 Wang F,Kang M,Lu Q,et al.A stochastic model of tree architecture and biomass partitioning:application to Mongolian Scots pines.Ann Bot,2011,107:781-792
25 Diao J,De Reffye P,Lei X,et al.Simulation of the topological development of young eucalyptus using a stochastic model and sampling measurement strategy.Comput Electron Agr,2012,80:105-114
26 Vavitsara M E,Sabatier S,Kang M Z,et al.Yield analysis as a function of stochastic plant architecture:case of Spilanthes acmella in the wet and dry season.Comput Electron Agr,2017,138:105-116
27 de Reffye P.Modèle mathèmatique aleatoire et simulation de la croissance et de l′architecture du caféier Robusta.1ère Partie.CaféCacao Thé,1981,25:83-104
28 Kang M Z,Heuvelink E,de Reffye P.Modelling the growth of inflorescence.In:The Third International Symposium on Plant Growth Modeling,Simulation,Visualization and Applications(PMA’09).Washington:IEEE Computer Society,2009.303-310
29 Barthélémy D,Caraglio Y.Plant architecture:a dynamic,multilevel and comprehensive approach to plant form,structure and ontogeny.Ann Bot,2007,99:375-407
30 Jaeger M,De Reffye P H.Basic concepts of computer simulation of plant growth.J Biosci,1992,17:275-291
31 Yan H P,Kang M Z,de Reffye P,et al.A dynamic,architectural plant model simulating resource-dependent growth.Ann Bot,2004,93:591-602
32 HalléF,Oldeman R A A,Tomlinson P B.Tropical Trees and Forests.Berlin,Heidelberg:Springer,1978
33 Kang M Z,Heuvelink E,Carvalho S M P,et al.A virtual plant that responds to the environment like a real one:the case for chrysanthemum.New Phytol,2012,195:384-395
34 Cournède P H,Letort V,Mathieu A,et al.Some parameter estimation issues in functional-structural plant modelling.Math Model Nat Phenom,2011,6:133-159
35 Letort V,Cournède P-H,de Reffye P.Impact of topology on plant functioning:a theoretical analysis based on the GreenLab model equations.In The Third International Symposium on Plant Growth Modeling,Simulation,Visualization and Applications(PMA’09).Washington:IEEEComputer Society,2009.341-348
36 Kang M Z,Evers J B,Vos J,et al.The derivation of sink functions of wheat organs using the GREENLAB Model.Ann Bot,2008,101:1099-1108
37 Wang X J,Mathieu A,Cournède P-H,et al.Stochastic models in floral biology and its application to the study of oilseed rape(Brassica napu L.)fertility.In:The Third International Symposium on Plant Growth Modeling,Simulation,Visualization and Applications(PMA’09)Washington:IEEE Computer Society,2009.175-182
38 Wang X J,Mathieu A,Cournède P H,et al.Application of a probabilistic model for analysing the abortion of seeds and pods in winter oilseed rape(Brassica napus).Ann Appl Biol,2014,165:414-428
39 Wang X J,Mathieu A,Cournède P H,et al.Variability and regulation of the number of ovules,seeds and pods according to assimilate availability in winter oilseed rape(Brassica napus L.).Field Crops Res,2011,122:60-69