《Table 1 Empirical fitting equations for tree growth process》

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《Study on Mature Age of An Individual Pinus thunbergii Parl》

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A linear equation was obtained by taking the logarithm of the tree growth equations，which was then used to get the values of parameters a，b.The F-test and correlation coefficient R test of the2 parameters were performed[2].Through the tests，the tree growth fitting equations were established（Table 1）.As shown in Table 1，in addition to the fitting equations of ground diameter，the fitting equations for other items all passed the F-test and R-test with the reliability over 99.9%，indicating that this mathematical model（the empirical fitting equation）was applicable as a whole.All items passed the correlation coefficient R test with reliability of99.9%，suggesting that the fitting equation relationship was established.Wood volume 1 and 2 were far different from the actual conditions，so in this study，the fitting equation of wood volume 1was used as a kind of actual state，while the fitting equation of wood volume 2 was used as a kind of ideal state.The maximum time of current annual increment and numerical mature age of trees by the fitting equations were illustrated with the ground diameter as an example.For the equation of growth rate of ground diameter（current annual increment was completed by the derivation of the function Y （t）in Table 1，and only the extreme point was given in the paper） ，the extreme point tz=5.0 a，that is，the current annual increment reached the peak when the tree reached 5 years old or so，and the peak was a single one.For the equation of average growth rate of trees Y（t）/t（annual average increment，and only the extreme point was given in the paper），the extreme point tm=9.9 a，so the numerical mature age of the tree was 9.9 a.In this paper，only the fitting equations for ground diameter were stated，and all other fitting equations were done in the same way.The meanings were all the same for growth fitting equation，tree growth rate equation，tree average growth speed equation，so were the significances of symbols of tz，tm，so the calculation results were given directly in the paper.The numerical mature ages of each item were shown in Table 1.As shown in Table 1，the parameter values of DBH square were doubled compared with the values of DBH，but the accuracies were equal to the F-test values and R-test values.This was caused by the exponential mathematical relationship.In order to compare with the accumulation fitting equation，the fitting equation of DBH square was deliberately established.The average values of accumulated ideal mature age and actual mature age were close to the mature age of DBH square.In Table 1，the values of tnwere the ages at the points of intersections of the curves of current annual increments and annual average increments of the sample wood，which could be used as the actual mature ages of the tree.In addition to DBH，which was very close to the tmvalues of the fitting equation，and wood volume，which was hard to determine because of the young age of the tree，the values of all other parameters were far different from the tmvalues.It was caused by the distortion of the relationship between the current annual growth and total average growth amount.However，the use of empirical equation could well solve such technical problems，and the research results were more reliable.Therefore，according to the research results and the needs for production practice，it was more suitable to set the mature age of accumulation volume as the mature age of the tree.