《Table 1 Empirical fitting equations for tree growth process》

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《Study on Mature Age of An Individual Robinia pseudoacacia》

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Wood volume 5-7 are the fitting tests using the wood volumes obtained from the empirical formula.

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，the fitting equations for ground diameter 1，ground diameter 3，DBH 2-4 and their squares，tree height and wood volumes passed the F-test with the reliability of 90%，fitting equations for ground diameter 2，ground diameter 4 and wood volume 7 passed with the reliability of 95%，and the others 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 of 99.9%，suggesting that the fitting equation relationship was established.The maximum time of current annual increment and numerical maturity age of trees by the fitting equations were illustrated with ground diameter 1 as an example.For the growth rate equation 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=6.00 a，that is，the current annual increment reached the peak when the tree reached 6 years old，and the peak was a single one.For the equation of average tree growth rate Y（t）/t（annual average increment，and only the extreme point was given in the paper），the extreme point tm=11.99 a，so the numerical maturity age of the tree was 11.99 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 maturity ages of each item were shown in Table 1.As shown in Table 1，the squares of the indices were doubled compared with the indices，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，such fitting equation was deliberately established in this study.The fitting results of DBH 2 square，wood volumes 2 and 5 were very close，and the fitting results of DHB 3square，wood volumes 3 and 6 were close to each other.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（those for the trees with ages over 34 a were obtained from the trend chart of growth curve），which could be used as the actual mature ages of the tree.The fitting results showed that the fitted values tmand tnwere close to each other.However，the fitted values from the equations from wood volume were close to the tnvalues of DBH（DBH square），so the values were set as the mature age of wood volume.The maturity of a tree is mainly concerned with the maturity of wood volume，so according to the research results and the needs in production practice，it was more suitable to set the mature age of accumulation volume as the mature age of the tree.