Computer Simulation And Mathematic Model Of Growth Dynamics Of Plants In The Typical Steppe Of Inner Mongolia In Growing Season

The study on population is developing from static to dynamic, qualitative to quantitative and modeled, and integrated with other scientific branches. The plant growth dynamic model can describe the plant growth, development yield formation and environment reaction quantitatively by using mathematic model, systematic analysis and computer simulation. So the model can predict the biomass, analyze the growth process and reveal the inner rules of the biomass formation of different plant, which can help us to find the growth characteristics and the complementation function of the populations in the steppe communities, and has the significance for the sustainable utilization of the grassland.Based on the population ecological theory and the Logistic formula, a mathematic model which reflect the relations of plant biomass accumulation and the single or multi-factors were established. Using the model, statistic method, differential equation and computer simulation, the growth dynamics in one growth season of the Leymus chinensis, Stipa grandis, Agropyron michnoi and Artemisia frigida growing in the Leymus chinensis + Stipa grandis plots fenced for 24 years in different degenerated stages in the typical steppe of Inner Mongolia were simulated and compared. By applying the Lotka-Volterra model the water use competitive model was established to simulate the growth dynamics of Leymus chinensis and Stipa grandis under the inter-species competition, and analyze the stability of the plant growth system. Results showed;(1) The biomass data of the four species fitted the normal distribution;(2) According to the investigated data and the quantitative indexes, the growth dynamics, absolute growth rates and relative growth rates in a growth season were compared. Results showed that the aboveground biomass increased with the shape of "S" and got the maximum value in middle August. Aboveground biomasses of plants increased in middle August. The sensitiveness of the plants to the water stress in growth season was L. chinensis > A. michnoi> S. grandis > A. frigida. The plants grew mainly in early middle growth stage. The order of the AGR was A. frigida (0.099 g·plant⁹-1)·d^-1) > S. grandis (0.029 g·plant ^-1·d^-1) > L.chinensis (0.003 g·plant^-1·d^-1) > A. michnoi (0.002 g·plant^-1·d^-1). The RGR of the four plants showed the highest in early growth season, and their order was A.frigida (0.108 g·plant^-1·d^-1·g^-1) > S. grandis (0.064 g·plant^-1·d^-1·g^-1) >L. chinensis (0.055g·plant ^-1·d^-1·g^-1)>A. michnoi (0.042 g·plant^-1·d^-1·g^-1). The growth curve and growth rate of the plants with different life form were obviously different, but that of L. chinensis and A. michnoi which were all rhizomatous were evidently similar.(3) The growth dynamics in a growth season of the four plants were simulated and compared using Logistic model. According to the normal form of the population dynamic model the mathematic basis of the individual growth model was extrapolated. Based on the solution and the analysis of Logistic model and the ecological theories the plant growth was divided into four stages, and the rapid growth stage and the abrupt change point were determined. The physical meaning of the model was explained with the model analysis. The temporal definition of the sustained growth period of the plants was given from the ecological aspect. According to which the suggestions for the grassland management and sustainable utilization were brought forward. The fit test was done with measured data. Results showed the growth of four plants fitted with the Logistic model; The fit formula were y= 0.200/1+e^2.032-0.060t,y=1.205/1+e^2.608-0.042t, y=0.156/1+e^1.858-0.040t , y=3.177/+=1+e^2.770-0.077t respectively. The maximum growth rates of the plants were obtained by the model, the order was A. frigida 6.112e-02(g/plant·d) > S. grandis 1.267e-02(g/plant·d) > L. chinensis 2.995e-03(g/plant·d) > A. michnoil .561 e-03(g/plant·d); The growth rates and the growth curves of L. chinensis, S. grandis and A. frigida belonging to different life forms were apparently different, and that of L. chinensis and A. michnoi with same life form showed little different, and appeared similar dynamic changes in one growth season.(4)The improved growth model (?) was proposed,and the single factor growth model and multi-factor growth model were extrapolated; The multiple linear regression and Logistic formula wereintegrated and applied to demonstrate that the model wj =(?)could simulate and predict the biomasses of different years; The changes of the relative biomass growth rate (W) with time (t) affected by multi-factors were still fitted the Logistic rule, meanwhile the estimation method for integration parameters of (?) and (?) was given.(5) The application of partial correlation analysis and stepwise regression determined that the precipitation and accumulated temperature were the important factors influencing the biomass formation, between them the precipitation was more effective than accumulated temperature(r_12,3>r_13,2;R₁₍₂₎² > R₁₍₃₎²; The effectiveness of the precipitation to the four plants was L. chinensis (0.964) > A. michnoi (0.937) > S. grandis(0.928) > A. frigida (0.906) , that of the accumulative temperature was L chinensis(0.918)>S. grandis(0.909)>A. michnoi(0.875)>A. frigida (0.754) . The growth characteristics of the four species were simulated and compared by using single factor growth model and multi-factor growth model. Results showed the potential maximum change of the individual biomass with the changes of precipitation, accumulative temperature or them two was A. frigida> S. grandis > L. chinensis > A. michnoi, which meant A. frigida has the maximum yield potential among the four species; The maximum RGR was A. frigida> S. grandis > L. chinensis > A. michnoi; The yield potential, the maximum RGR and the time reaching the maximum RGR were similar in L. chinensis and A. michnoi, which meant they have the similar growth characters.(6) The establishment and analysis of inter-species competition model. Arming at the fact that the moisture is the restriction factor for the plant growth, an inter-species competition model was established conditioning upon water: dN₁/dt = r₁N₁/K₁(K₁-N₁-αλ₂K₁/r₁V_V1N₂)dN₂/dt = r₂N₂/K₂(K₂-N₂-βλ₁K₂/r₂V_V2N₁)Compared with classical Lotka-Volterra model, the eco-factors were introduced into the model to describe the growth dynamics of I. chinensis and S. grandis under competition; The stability of the plant growth system was analyzed by applying the theory of differential equation stability. According to the meaning of parameters (p₃,q₂), supposing q₂=q₂(N₂)=r₁/1+a₂N₂, p₃ = p₃(N₁) =r₂/1+a₁N₁, all parameters and simulation image were obtained by computer simulation and numerical analysis. Results demonstrated that the growth of L. chinensis and S. grandis appeared adaptability to environment to some extent, and L. chinensis was at more dominant position than S. grandis and was becoming the dominant species, whereas S. grandis was in the status of being inhibited. Because there were some ecological niche differences between the two species, it formed the pattern of either competition or stability, and made the community grew sustained and stable, and some characteristics of the community were approximate to the original community.