| 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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