A PROPOSED MULTIDIMENSIONAL TIME SERIES MODEL OF INDIVIDUAL AGE AND DIAMETER IN TSUGA LONGIBRACTEATA
长苞铁杉种群个体年龄与胸径的多维时间序列模型研究

Determining individual ages of endangered plants is the purpose of studying its age structure and population dynamics. There are three main methods of determining individual age, but all have their shortcomings, such as low precision, worse serviceability, and so on. In this paper, based on methods of determining individual age presented by previous workers, a new method for determining plant population age more accurately is presented. The relationship model of individual age of Tsuga longibracteata population and diameter at breast height is built, combining multidimensional time series analysis and determination of individual age using tree ring analysis. Based on the stem analysis, the multidimensional time series model of diameter growth at breast height in Tsuga longibracteata population was established: Y t=1.7870785Y t-1 -0.8950167Y t-2 0.4509997U t-0.8036035U t-1 0.3950577U t-2 , where Y t, Y t-1 , Y t-2 represent diameter growth of Tsuga longibracteata population at t , t-5 and t-10 years respectively, and U t, U t-1 , U t-2 represent individual age of Tsuga longibracteata population at t, t-5 and t-10 years respectively. Based on this model, diameter growth at breast height and its corresponding diameter of Tsuga longibracteata population can be simulated at different ages. The mean simulating precision of this model was 97.84%, the maximum relative error was 12.5% but the next was only 4.30% and the minimum relative error was 0.27%, which showed that the multidimensional time series model was satisfactory in estimating diameter growth at breast height. Using the multidimensional time series model of diameter growth, diameter growth of Tsuga longibracteata population for longer time series was estimated, in order to gain more data for establishing the relationship model of individual age and diameter growth and to increase its precision in determining individual age by tree ring analysis. A combination method of determining individual age of Tsuga longibracteata population by integrating annual ring data with its diameter using multidimensional time series model was produced: A=23.12949- 0.05022788D 0.07179599D 2-0.0005765389D 3 , where A and D represent individual age and diameter at breast height respectively of Tsuga longibracteata populations. The combination method combines the method of determining individual age by tree ring width based on stem analysis data with the method of determining individual age using diameter at breast height and tree height, and the former is used to reflect the relationship between diameter growth at breast height and individual age by a multidimensional time series model in which the individual age and its corresponding diameter were used as control factors. The combination model, which shows that the regression relationship is significant and the model can exactly predict individual age of Tsuga longibracteata population, is a valuable tool for determining individual ages of endangered plants.