基于GreenLab结构—功能模型的油松随机形态结构模拟及个体竞争效应研究
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摘要
结构-功能模型，是指能明确表达由生理过程和环境因子调控的植物三维结构生长和变化的一类模型。它既考虑了林木的形态结构，又考虑了其生理生态过程，能描述林木各器官的三维动态的生长和拓扑结构的发展，并且可以考虑环境因素的影响。目前该模型主要应用于单木的模拟，缺少在林分层次的应用研究及森林经营的结合。本研究以我国北方主要针叶树种油松(Pinus tabulaeformis)为对象，基于16株实测的油松数据，在GreenLab结构-功能模型框架内，建立了油松形态结构的随机模型，模拟了油松个体在不同发育阶段的随机形态；建立了异速生长的混合效应模型，更真实地反映了油松的异速生长规律和参数在树木之间及内部的变异性；建立了包含竞争和随机形态参数的结构-功能模型，获得了GreenLab结构-功能模型参数与年龄之间的关系规律，定量研究竞争对油松形态及生物量生产和分配过程的影响，并对采伐进行了模拟。
1）建立了油松叶面积和比叶面积的估计模型。叶面积和比叶面积是GreenLab结构-功能模型中的重要参数。本文通过winSEEDLE种子和针叶图像分析系统获得油松522个单个针叶的表面积LA、针叶长度L、针叶宽W、针叶周长P，分别建立了以针叶长、针叶宽、针叶周长等形状属性为自变量的叶面积估计模型和以针叶干重为自变量的叶面积估计模型。通过对算术平均法、比估计法、最小二乘法三种方法的比较，得到油松的比叶面积为0.708m2/kg。
2）建立了包含随机效应的油松节间异速生长模型。异速生长模型是GreenLab结构-功能模型中的一部分，它可以提供节间的形状参数与比例参数。本研究考虑树木之间以及各级枝枝与枝之间的存在的差异，建立了不同生理年龄的节间异速生长的混合效应模型。通过AIC与BIC指标选出最优的混合效应模型。与基础模型相比，混合效应模型的决定系数R2一级枝节间提高了27.84%,二级枝提高了31.59%,三级枝提高了24.53%，大大提高了节间异速生长模型的精度。通过形状参数和比例参数的随机效应的方差发现,在树木水平节间异速生长的差异性要大于分枝水平，一级枝水平上的差异要大于二级枝，说明随着分枝级别的增加，节间的差异性有所下降。因此需要建立单个分枝和单株木的异速生长模型，更真实地反映油松节间的生长规律和随机效应。
3）建立了油松形态结构的随机模型，模拟了油松个体在不同发育阶段的随机形态。树木由于受到环境的影响，形态结构相当复杂，生长过程会出现一些随机性，如芽的休眠、生长、死亡等，分枝的出现的时间以及死亡等。本文主要通过主干及各级枝节间的生长概率、生长节律、分枝概率、分枝的死亡概率以及芽的存活概率等参数来构建油松的随机形态结构，参数的求解主要是通过分枝节间数的均值以及之间的方差等统计量获得；通过参数主干及各级枝节间的生长概率、生长节律结合实测主干及各级枝的节间数，可以得到主干及各级枝的节间数量，通过分枝概率以及分枝的死亡概率得到油松的分枝情况，从而得到油松的形态结构。结果显示随着分枝级别的增加，分枝的生长概率和分枝概率均有所下降，随着年龄的增加，除了主干的生长速度基本不变外，主干及各级枝的分枝概率以及各级枝的生长概率均呈现先增加后减小的趋势，模型可以合理并较为逼真地描述油松的随机形态结构。
4）通过拟合不同年龄不同密度油松的GreenLab结构-功能模型，获得了相应的参数，拟合结果表明模型对于主干节间生物量、针叶生物量以及主干节间长度的拟合效果较好，决定系数均在0.7以上。主干节间直径的模拟值比实际值要高，这可能是由于模型对于次生生长汇强参数的估计有所偏差造成的。模型输出了与森林经营直接相关的单木树高、胸径、冠幅以及冠长，其拟合值和实际值的决定系数分别为0.85、0.65、0.82和0.91，拟合效果较好。
5）分析了油松GreenLab结构-功能模型参数随年龄的变化规律，建立了油松年龄与结构-功能模型参数之间的关系模型。对油松的结构和生物量生产和分配进行了预测。通过经验模型得到的幼龄到成熟油松的总生物量、树干生物量、枝以及针叶生物量,与由GreenLab结构-功能模型模拟得到相应年龄油松各生物量，二者之间的决定系数分别为0.80、0.56、0.92和0.91,模型的预估效果较好。
6)分析了不同年龄不同密度的油松林分竞争单元内对象木与竞争木在形态上和生物量上的差异，包括主干及各级枝最后一个节间的平均长度、平均直径、平均重量、树木分枝的活枝数、死枝数、分枝的总生物量以及其上针叶的总生物量等的；GreenLab结构-功能模型的模拟结果显示，对象木与竞争木的植株投影面积、各节间以及针叶的汇强、次生汇强等参数有很大差异，从而影响了结构-功能模型中生物量的生产与分配，导致竞争木与对象木在形态和生物量方面有很大差异。根据模型输出的形态信息和生物量信息与实测数据检验得到各级枝最后一个节间的平均长度、平均直径以及平均重量的决定系数均大于0.5，分枝的活枝个数的模拟的决定系数为0.93。活枝生物量与针叶生物量的决定系数分别为0.91和0.89，说明GreenLab结构-功能模型可以很好的模拟树木之间的竞争效应。
7）建立了经验模型中的竞争指数-生存面积指数与结构-功能模型中的竞争指数植株投影面积之间的关系模型，利用GreenLab结构-功能模型模拟了采伐对形态结构和生物量生产和分配的影响。模拟结果表明：采伐2株竞争木与1株竞争木相比，对象木的总生物量、树高、胸径、冠幅、冠长以及活枝个数的生长量均大于采伐1株竞争木。采伐改变了对象木的植株投影面积，对GreenLab模型中的生物量的生产方程产生影响，增加了树木的生物量的生产，从而导致导对象木的总生物量、树高、胸径、冠幅、冠长以及活枝个数的增加，研究为基于结构-功能模型的森林经营决策提供了方法和依据。
Functional-structural tree models (FSTMs) refer to models which can explicitlydescribe thedevelopment over time of the3D architecture of trees as governedby physiological processesand environmental factors. They consider not only tree structure development, but alsophysiological process and interactions with the environment.At present, this model is mainlyused in individual tree simulation, lackingof applicationat stand level and the linkwith forestmanagement. The main coniferous tree species Chinese Pine trees in north China were chosenas research object in this paper. Within the framework of GreenLab functional-structural model,the stochatic model on morphological structures of Chinese pine trees with differentdevelopmental stages were developed based on the measured data; the mixed effect models ofallometric growth were established which couldrealistically reflect the allometric growth lawof Chinese Pine trees and parameters variability withinand between trees; Functional-structuralmodels for Chinese pine trees with different developmental stages were developed with theconsiderationof competition mechanism and random morphological parameters; the modelsbetween tree age and parameters of GreenLab functional-structural tree models wereestablished; the influence of the competition on morphology and biomass production anddistribution process was quantitatively studied and the felling effectswas simulated.
1) Models for estimating leaf area and specific leaf area were developed. Leaf area and specificleaf area are important parameters in GreenLab functional-structural tree models. We sampled522needles of Chinese pine in Mulanweichang and obtained needle surface area LA, needlelength L, needle width W and needle perimeter P by winSEEDLE software. The modelsbetween leaf area and shape attributes including leaf length, leaf width, leaf perimeter andmodels between leaf area and leaf dry weight were developed, respectively. The specific leafarea of Chinese pine is7.08m2/kg derived from the comparison among the arithmetic averagemethod, ratio estimation method, and the least square method. It provides a simple and reliablemethod for estimating leaf area of Chinese pine.
2)Internode allometric growth models including random effectswere established.Allometricgrowth models are important parts of the GreenLab functional-structural tree models, whichcan provide the shape parameter and scale parameter of internode in the GreenLabFunctional-structural tree models for Chinese Pine trees.This study considered the differencesamong trees and among branches to develop the internode allometric growth models withmixedeffect.Optimal mixed effects models were selectedthrough statistics AIC and BIC. Thedetermination coefficientR2of the mixed effect models increases27.84%,31.59%,24.53%compared to those of base models for the1st-, the2nd-and the3rd-order branches, respectively.Random effect variance of shape parameters and scale parameters shows differencesat treelevel are more obvious than those atbranch level and differences in the1st-order branchesaregreater than those in the2nd-order branches.The differences of internode decreased with theincrease of branch level. Allometric growthmodels ofspecific branchesortrees need to beestablished so that they can more accurately reflect internode growth regulation and randomeffects of Chinese Pine trees.
3) Stochastic morphological models of Chinese Pine trees were developed and stochasticmorphological structure of Chinese Pine treeswith different growth stages were simulated.Trees morphological structure is very complex due to the influence of environment and somerandomness can exist in tree grow process, such as bud dormancy, growth and death, the timeof the branches, the dead of the branches and so on.The model in the study employed growthprobability, rhythm ratio, branching probability, survival probability of buds and mortalityprobability of branches for producing random morphological structure for Chinese Pine trees.These parameters were attained by calculating statisticssuch as branches internode numbermean and the variance.The number of internode on the trunk and branches can be calculated byparameters growth probability and rhythm ratio.The situation of branchescan be simulated byparameter branching probability, and mortality probability of branches. The morphologicalstructures of Chinese Pine trees were obtained.The results showed that the growthprobabilityand the branchprobability of all branches declined with branch levelincreasing.Branch probability and branch growth probabilityshowed a trend of decrease after increasing with ageincreasing. The model could reasonably and realistically describe thetopological structure of Chinese pine trees.
4) The GreenLab functional-structural modelsof Chinese Pine trees with different ages,different densities were established andthe parameters were obtained. Results showed that thesimulations of internode length, internode biomass and needle biomass on the trunk were well.The fitting values and measureddata are close and their determine coefficients are all above0.7.The simulated values of internode diameter on the trunk are bigger than measured data.This may result from the deviated estimation of the model parameters sink strong for thesecondary growth.The model also simulated tree height, diameter at the breast height(DBH),canopy and crown length of all measured trees and the determination coefficients were0.85,0.65,0.82and0.85, respectively.
5)The models between age and the parameters of GreenLab functional-structural models weredeveloped. The total biomass, biomass of trunk, branches and needles biomass of9-47year-oldChinese Pine treeswere obtained by empirical model. We compared biomass values obtainedfrom the two types of models and found that theirdetermination coefficients were0.80,0.56,0.92and0.91, respectively.
6) The differences on the morphology and biomass for different ages and different densitiesChinese Pine trees having the competitive relationship with each other were analyzed. Theaverage length, average diameter, average weight of last internode,the number of livingbranches and dead branches, the total biomass of branches and biomass of needle on thebranches were analyzed. Results of individual plant simulation using GreenLab showed thatthe direct parameters and the hidden parameters for target tree and competitive tree vary largely,such as plant projection area, the sink strength of internode and needles, the sink strength ofsecondary growth. These influence the biomass production and distribution of GreenLabmodels and result in the diffrences between target and competitive trees.The determinationcoefficientsofthe average length, average diameter, average weight of last internode are allabove0.5according to the morphological and the biomass information model outputed.Thedetermination coefficients of the number of living branches, living branches biomass and needle biomass are0.93,0.91and0.89, respectively.The results showed that GreenLabmodelscan simulate tree competition well.
7）The model between theissen polygon area and plant projection area was developed. Thecutting influences on the morphology and biomass production and distribution were simulatedusing GreenLab model. The parameter plant projection areachanged with theissen polygonsarea after cutting. The results showed that the growth of total biomass, tree height, DBH,crown, crown length and living branch number of target trees for removal of two competivetrees are larger than those forremoval of one competive tree. The reasons are that the parameterplant projection area increases after cutting which result in thebiomass production increasing.When plant projection area increased by10%,20%and30%, the changes of the biomasswerealso simulated in this paper. It can provide the basis for forest management practice.
1）建立了油松叶面积和比叶面积的估计模型。叶面积和比叶面积是GreenLab结构-功能模型中的重要参数。本文通过winSEEDLE种子和针叶图像分析系统获得油松522个单个针叶的表面积LA、针叶长度L、针叶宽W、针叶周长P，分别建立了以针叶长、针叶宽、针叶周长等形状属性为自变量的叶面积估计模型和以针叶干重为自变量的叶面积估计模型。通过对算术平均法、比估计法、最小二乘法三种方法的比较，得到油松的比叶面积为0.708m2/kg。
2）建立了包含随机效应的油松节间异速生长模型。异速生长模型是GreenLab结构-功能模型中的一部分，它可以提供节间的形状参数与比例参数。本研究考虑树木之间以及各级枝枝与枝之间的存在的差异，建立了不同生理年龄的节间异速生长的混合效应模型。通过AIC与BIC指标选出最优的混合效应模型。与基础模型相比，混合效应模型的决定系数R2一级枝节间提高了27.84%,二级枝提高了31.59%,三级枝提高了24.53%，大大提高了节间异速生长模型的精度。通过形状参数和比例参数的随机效应的方差发现,在树木水平节间异速生长的差异性要大于分枝水平，一级枝水平上的差异要大于二级枝，说明随着分枝级别的增加，节间的差异性有所下降。因此需要建立单个分枝和单株木的异速生长模型，更真实地反映油松节间的生长规律和随机效应。
3）建立了油松形态结构的随机模型，模拟了油松个体在不同发育阶段的随机形态。树木由于受到环境的影响，形态结构相当复杂，生长过程会出现一些随机性，如芽的休眠、生长、死亡等，分枝的出现的时间以及死亡等。本文主要通过主干及各级枝节间的生长概率、生长节律、分枝概率、分枝的死亡概率以及芽的存活概率等参数来构建油松的随机形态结构，参数的求解主要是通过分枝节间数的均值以及之间的方差等统计量获得；通过参数主干及各级枝节间的生长概率、生长节律结合实测主干及各级枝的节间数，可以得到主干及各级枝的节间数量，通过分枝概率以及分枝的死亡概率得到油松的分枝情况，从而得到油松的形态结构。结果显示随着分枝级别的增加，分枝的生长概率和分枝概率均有所下降，随着年龄的增加，除了主干的生长速度基本不变外，主干及各级枝的分枝概率以及各级枝的生长概率均呈现先增加后减小的趋势，模型可以合理并较为逼真地描述油松的随机形态结构。
4）通过拟合不同年龄不同密度油松的GreenLab结构-功能模型，获得了相应的参数，拟合结果表明模型对于主干节间生物量、针叶生物量以及主干节间长度的拟合效果较好，决定系数均在0.7以上。主干节间直径的模拟值比实际值要高，这可能是由于模型对于次生生长汇强参数的估计有所偏差造成的。模型输出了与森林经营直接相关的单木树高、胸径、冠幅以及冠长，其拟合值和实际值的决定系数分别为0.85、0.65、0.82和0.91，拟合效果较好。
5）分析了油松GreenLab结构-功能模型参数随年龄的变化规律，建立了油松年龄与结构-功能模型参数之间的关系模型。对油松的结构和生物量生产和分配进行了预测。通过经验模型得到的幼龄到成熟油松的总生物量、树干生物量、枝以及针叶生物量,与由GreenLab结构-功能模型模拟得到相应年龄油松各生物量，二者之间的决定系数分别为0.80、0.56、0.92和0.91,模型的预估效果较好。
6)分析了不同年龄不同密度的油松林分竞争单元内对象木与竞争木在形态上和生物量上的差异，包括主干及各级枝最后一个节间的平均长度、平均直径、平均重量、树木分枝的活枝数、死枝数、分枝的总生物量以及其上针叶的总生物量等的；GreenLab结构-功能模型的模拟结果显示，对象木与竞争木的植株投影面积、各节间以及针叶的汇强、次生汇强等参数有很大差异，从而影响了结构-功能模型中生物量的生产与分配，导致竞争木与对象木在形态和生物量方面有很大差异。根据模型输出的形态信息和生物量信息与实测数据检验得到各级枝最后一个节间的平均长度、平均直径以及平均重量的决定系数均大于0.5，分枝的活枝个数的模拟的决定系数为0.93。活枝生物量与针叶生物量的决定系数分别为0.91和0.89，说明GreenLab结构-功能模型可以很好的模拟树木之间的竞争效应。
7）建立了经验模型中的竞争指数-生存面积指数与结构-功能模型中的竞争指数植株投影面积之间的关系模型，利用GreenLab结构-功能模型模拟了采伐对形态结构和生物量生产和分配的影响。模拟结果表明：采伐2株竞争木与1株竞争木相比，对象木的总生物量、树高、胸径、冠幅、冠长以及活枝个数的生长量均大于采伐1株竞争木。采伐改变了对象木的植株投影面积，对GreenLab模型中的生物量的生产方程产生影响，增加了树木的生物量的生产，从而导致导对象木的总生物量、树高、胸径、冠幅、冠长以及活枝个数的增加，研究为基于结构-功能模型的森林经营决策提供了方法和依据。
Functional-structural tree models (FSTMs) refer to models which can explicitlydescribe thedevelopment over time of the3D architecture of trees as governedby physiological processesand environmental factors. They consider not only tree structure development, but alsophysiological process and interactions with the environment.At present, this model is mainlyused in individual tree simulation, lackingof applicationat stand level and the linkwith forestmanagement. The main coniferous tree species Chinese Pine trees in north China were chosenas research object in this paper. Within the framework of GreenLab functional-structural model,the stochatic model on morphological structures of Chinese pine trees with differentdevelopmental stages were developed based on the measured data; the mixed effect models ofallometric growth were established which couldrealistically reflect the allometric growth lawof Chinese Pine trees and parameters variability withinand between trees; Functional-structuralmodels for Chinese pine trees with different developmental stages were developed with theconsiderationof competition mechanism and random morphological parameters; the modelsbetween tree age and parameters of GreenLab functional-structural tree models wereestablished; the influence of the competition on morphology and biomass production anddistribution process was quantitatively studied and the felling effectswas simulated.
1) Models for estimating leaf area and specific leaf area were developed. Leaf area and specificleaf area are important parameters in GreenLab functional-structural tree models. We sampled522needles of Chinese pine in Mulanweichang and obtained needle surface area LA, needlelength L, needle width W and needle perimeter P by winSEEDLE software. The modelsbetween leaf area and shape attributes including leaf length, leaf width, leaf perimeter andmodels between leaf area and leaf dry weight were developed, respectively. The specific leafarea of Chinese pine is7.08m2/kg derived from the comparison among the arithmetic averagemethod, ratio estimation method, and the least square method. It provides a simple and reliablemethod for estimating leaf area of Chinese pine.
2)Internode allometric growth models including random effectswere established.Allometricgrowth models are important parts of the GreenLab functional-structural tree models, whichcan provide the shape parameter and scale parameter of internode in the GreenLabFunctional-structural tree models for Chinese Pine trees.This study considered the differencesamong trees and among branches to develop the internode allometric growth models withmixedeffect.Optimal mixed effects models were selectedthrough statistics AIC and BIC. Thedetermination coefficientR2of the mixed effect models increases27.84%,31.59%,24.53%compared to those of base models for the1st-, the2nd-and the3rd-order branches, respectively.Random effect variance of shape parameters and scale parameters shows differencesat treelevel are more obvious than those atbranch level and differences in the1st-order branchesaregreater than those in the2nd-order branches.The differences of internode decreased with theincrease of branch level. Allometric growthmodels ofspecific branchesortrees need to beestablished so that they can more accurately reflect internode growth regulation and randomeffects of Chinese Pine trees.
3) Stochastic morphological models of Chinese Pine trees were developed and stochasticmorphological structure of Chinese Pine treeswith different growth stages were simulated.Trees morphological structure is very complex due to the influence of environment and somerandomness can exist in tree grow process, such as bud dormancy, growth and death, the timeof the branches, the dead of the branches and so on.The model in the study employed growthprobability, rhythm ratio, branching probability, survival probability of buds and mortalityprobability of branches for producing random morphological structure for Chinese Pine trees.These parameters were attained by calculating statisticssuch as branches internode numbermean and the variance.The number of internode on the trunk and branches can be calculated byparameters growth probability and rhythm ratio.The situation of branchescan be simulated byparameter branching probability, and mortality probability of branches. The morphologicalstructures of Chinese Pine trees were obtained.The results showed that the growthprobabilityand the branchprobability of all branches declined with branch levelincreasing.Branch probability and branch growth probabilityshowed a trend of decrease after increasing with ageincreasing. The model could reasonably and realistically describe thetopological structure of Chinese pine trees.
4) The GreenLab functional-structural modelsof Chinese Pine trees with different ages,different densities were established andthe parameters were obtained. Results showed that thesimulations of internode length, internode biomass and needle biomass on the trunk were well.The fitting values and measureddata are close and their determine coefficients are all above0.7.The simulated values of internode diameter on the trunk are bigger than measured data.This may result from the deviated estimation of the model parameters sink strong for thesecondary growth.The model also simulated tree height, diameter at the breast height(DBH),canopy and crown length of all measured trees and the determination coefficients were0.85,0.65,0.82and0.85, respectively.
5)The models between age and the parameters of GreenLab functional-structural models weredeveloped. The total biomass, biomass of trunk, branches and needles biomass of9-47year-oldChinese Pine treeswere obtained by empirical model. We compared biomass values obtainedfrom the two types of models and found that theirdetermination coefficients were0.80,0.56,0.92and0.91, respectively.
6) The differences on the morphology and biomass for different ages and different densitiesChinese Pine trees having the competitive relationship with each other were analyzed. Theaverage length, average diameter, average weight of last internode,the number of livingbranches and dead branches, the total biomass of branches and biomass of needle on thebranches were analyzed. Results of individual plant simulation using GreenLab showed thatthe direct parameters and the hidden parameters for target tree and competitive tree vary largely,such as plant projection area, the sink strength of internode and needles, the sink strength ofsecondary growth. These influence the biomass production and distribution of GreenLabmodels and result in the diffrences between target and competitive trees.The determinationcoefficientsofthe average length, average diameter, average weight of last internode are allabove0.5according to the morphological and the biomass information model outputed.Thedetermination coefficients of the number of living branches, living branches biomass and needle biomass are0.93,0.91and0.89, respectively.The results showed that GreenLabmodelscan simulate tree competition well.
7）The model between theissen polygon area and plant projection area was developed. Thecutting influences on the morphology and biomass production and distribution were simulatedusing GreenLab model. The parameter plant projection areachanged with theissen polygonsarea after cutting. The results showed that the growth of total biomass, tree height, DBH,crown, crown length and living branch number of target trees for removal of two competivetrees are larger than those forremoval of one competive tree. The reasons are that the parameterplant projection area increases after cutting which result in thebiomass production increasing.When plant projection area increased by10%,20%and30%, the changes of the biomasswerealso simulated in this paper. It can provide the basis for forest management practice.
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