论文部分内容阅读
Abstract Through analysis on materials， the fitting empirical equation for growth process of Pinus tabuliformis was obtained， i.e.， the function with increment as variable and time as the independent variable. The mature age of P. tabuliformis was obtained by mathematical operation. The mature age of forest plantation was determined as 61 a， and that of public welfare forest was 81 a. And P. tabuliformis age groups were divided according to related technical requirements.
Key words Mature age； Empirical equation； Analytic tree
Pinus tabuliformis forest is a kind of forestry community distributed the widest in temperate coniferous forest. P. tabuliformis forest is a typical coniferous forest type the same as P. densiflora forest in Shandong Province， and has the area and stocking volume ranking only second to P. densiflora. It is a type of forest commonly seen in mountainous region with an altitude over 700 m. Shandong Province is the south edge of the natural distribution of P. tabuliformis， and Mount Meng is the south end of P. tabuliformis distribution in Shandong Province. P. tabuliformis forest is distributed in highaltitude areas in Shandong Province， where human activities are relatively less， the soil is more humid with more intact vertical structure， and plant composition is also richer. During the formulation of forestry development planning and forest management scheme， and examination and approval of tree harvesting and forest management， it is urgent to solve the problem of mature age of trees. Based on the information of analytic trees obtained from years of research， according to the methods in references[1-3]and the research results in reference[6]， the writers studied the mature age of single trees[4]. However， the information of analytic trees is the growth index of peeled trees， and the collected sample trees all grow normally with straight trunk and， and thus could not accurately reflect the mature age of P. tabuliformis. Conventional research method is to create tree increment coordinate graphs by analytic tree method， and the intersection of annual average increment and current increment is the mature age of trees. However， the conventional method has the disadvantages of larger workload and not high precision. In this study， the empirical equation method was applied， achieving the effect of yielding twice the results with half the effort. The mature age of P. densiflora was studied at first using first class checking information by empirical equation method[5]， followed by the study on the mature age of P. tabuliformis. Data source
The data were first class treechecking information of Shandong Province in 1988， 1992， 1997 and 2002， including average DBH， average tree height， average age and sample plot stocking data of P. tabuliformis and P. densiflora.
Research method
Continuous forestry resources checking information about P. tabuliformis and P. densiflora stands were searched and managed in table format， and the items including sample plot number， average age （A， unit： a）， average DBH （D， unit： cm）， average height （H， unit： m）， stand volume （M， unit： 0.000 1 m3） were reserved； the increment of average DBH was calculated according to D-=D/A （unit： cm/a）， the increment of average tree height was calculated according to H-=H/A （unit： m/a）， and the annual average increment was calculated according to Z= M/A （unit： 0.000 1 m3； and N is the number of sample plots， i.e.， the number of investigated samples. All these data were listed in spreadsheets for later statistic analysis.
For all the investigation， each sample plot was square and had an area of 667 m2 （the sampling point was the southwest corner of the sample plot， and each sample plot was located in the east， west， south and north of coordinate azimuth）. Furthermore， sampling was performed by mechanical engineering method according to 1∶5 topographic map dualsquare grid （1988： 2×2 km， other years： 4×4 km）. All the sample plots were treated equally， and all obeyed normal distribution.
In order to save research cost， fitting tests were carried out to various regression equations using tree growth empirical equations according to "Forest mensuration" edited by Northeast Forestry University， and finally， the mixed type empirical equation， y（t）=ea-b/t （a and b are tobedetermined exponential parameters， and e is the base number of natural logarithm： 2.718 28……）， was selected for the study of tree growth process. The writers tried to fit the tree growth process using empirical equations， and through the acquisition of the maximum age according to DBH fitting equations （including the equation obtained in derivation， as described in the research process）， the quantitative mature age of the DBH growth was obtained； and through the acquisition of the maximum age according to tree height fitting equation， the mature age of tree height growth was obtained. By the same method， the quantitative mature age of volume of timber was also obtained.
Research process of fitting empirical equation A linear equation was formed by taking the logarithm of the tree growth process equation. Then， parameters a and b were obtained by unary linear regression， and F test and significance test of regression coefficient were carried out. If t test is passed， a tree growth fitting equation is established， and the calculation results are shown in Table 1-Table 3. It might be due to the reason that the samples were not enough， the fitting precision of P. tabuliformis was greatly reduced compared with that of P. densiflora equation as control. The tree height equation had a very low precision in 2002， and was of no practical significance. The P. tabuliformis volume fitting equation had precision values lower than 90% in 1997 and 2002， but passed F test and t test with the reliability over 90%， indicating that the mathematical model （empirical fitting equation） is applicable overall. If the correlation coefficient （R） test is passed， then the fitting equation relation is established. The fitting degree of P. tabuliformis equation was lower in 2002 and 1977， which might be due to that the number of samples was small， and therefore， fitting equations were established using all samples in 1988-1997 and 1988-2002， respectively， and compared with the study on P. densiflora in the same time period. For the 1988-1997 and 1988-2002 fitting equations， except that the tree height fitting equation of 1988-2002 had a precision reaching 96%， the precision of other items all exceeded 99.9%， and the 1988-1977 fitting equations had precision higher than the 1988-2002 equations. The problem of solving the maximum current annual increment time and quantitative maturity of trees using fitting equations was illustrated taking the DBH item of P. tabuliformis in 1988 as an example. The tree growth rate equation of P. densiflora DBH （the current annual increment， obtained by derivation of Y（t） function， the process of which was omitted， only the extreme point was given， the same below） showed the extreme value tz=17.4 a， i.e.， the current increment of trees reached its peak value at about 18 a， and had only one peak value. The average growth rate equation Y（t）/t （annual average growth， the calculation process was omitted， only the extreme point was given， the same below） had the extreme value tm=34.7 a， i.e.， the quantitative mature age of trees was 35 a. only the calculation of DBH fitting equation was described above， other fitting equations were the same as it， and detailed description was omitted. In the discussion below， the growth fitting equation， tree growth rate equation and tree average growth rate equation had the same meaning， symbols such as tz and tm also had the same meaning， and the calculation results were given without repeated description and explanation. The research results of P. densiflora were used as control of P. tabuliformis. The quantitative mature ages calculated according to various items are shown in tables. It could be seen from above tables that P. tabuliformis DBH and volume items had the highest precision in 1988， and the tree height item had the highest precision in 1997. The DBH fitting equations of 1992 and 1997 were more proximate， exhibiting a relative error only of 1.7%. Compared with P. densiflora， the fitting results of DBH equation in 1988-2002 were more proximate to those of the P. densiflora equation in 1977， with a relative error only of 0.1%. The fitting precision of the volume of P. tabuliformis in 1988-1997 was surprisingly similar to that of P. densiflora in 2002， with a relative error only of 1.7%， namely P. tabuliformis and P. densiflora had the same mature age with a reliability of 98.3%. The fitting results of tree mature age， DBH and tree height equations were quite different from national standards， while for the fitting results of volume， P. tabuliformis was quite close to P. densiflora in 1997， and the mature age was slightly higher than national standard. Therefore， according to the research results and production practice， it is more reliable to use accumulative mature age as tree mature age. The fitting results of the volume equation of P. tabuliformis in 1988 showed a P. tabuliformis mature age of 74.9 a， with a fitting precision over 99.9% and correlation coefficient up to 0.96， which were far higher than national mature age standards， and the forest could be determined as the mature forest at ideal state， for specialpurpose forest and protection forest （public welfare forest）. Furthermore， the fitting results of the volume equation of 1988-1997 with the second best precision showed a P. tabuliformis mature age of 56.08 a， and the forest was determined as the mature forest at normal state， and used as the standard of mature forest for timber （commercial forest）. The results substantially accorded with the results of P. densiflora. The anticipant mature ages of public welfare forest and commercial P. densiflora forest were determined as 75 and 56 a， respectively. Conclusions and Application
Through the analysis and judgment of research result， according to the quantitative maturity of stand volume， the fitting value of volume of timber was selected as the tree mature age， and taking age grade （10 a as an age grade） into consideration， with the highest precision as judgment standard， the anticipant mature ages of commercial and public welfare P. tabuliformis forests were determined as 61 and 81 a， respectively. Over time， various interference activities against P. tabuliformis forest were reduced， so the forest could grow and propagate. The age groups of P. tabuliformis forest are shown in Table 4.
Forest categoryYoung forest Middleaged forestNearmature forestMature forest Overmature forest
Timber forest 1-3031-5051-6061-70Over 71
Protection forest， special purpose forest1-4041-7071-8081-90Over 91
This study showed that the anticipant mature age of P. tabuliformis forest was higher than related national standard， which might be due that the stand quality was improved relatively， and the interference from human factors was reduced.
Discussion
The original mature age standard of P. tabuliformis forest is 41 a， and the results of this study were higher than the original standard by 20 and 40 a. Because the used data were first class checking information， the fitting empirical equation of tree growth was used to make up the insufficiency of the age of analytic trees， the noise effects of differences in various natural conditions in time and space and tree differentiation phenomenon on test results were also avoided， and the anticipant stand mature age of P. tabuliformis was obtained. Through repeated verification， analysis and judgment， the suitability of empirical equation for tree growth exists exactly， but it is difficult to scientifically explain it， and due to the limitations of time and level， various deviations are unavoidable. Improvement and development is needed in future produc tion practice and scientific research. The production advises put forward by the writers are only individual opinions， which were concluded from the analysis and fitting of relatively less data information， and they could only be put into use after being identification by relevant experts and checked by production practice.
References
[1]Northeast Forestry University. Forest mensuration[M]. Internal teaching material， 1985. （in Chinese）
[2]Northeast Forestry University. Mathematical statistics[M]. Beijing： China Forestry Publishing House，1985. （in Chinese）
[3]LIU GJ. Review of registered consulting engineer （investment） certified qualification examination textbook[M]. Tianjin： Tianjin University Press， 2003. P231-246.（in Chinese）
[4]HU HY， SU WL， QU HY. Study on actual mature age of single plant of Pinus densiflora[J]. Journal of Shandong Forestry Science and Technology， 2010， 6： 36-37. （in Chinese）
[5]LI LP， DONG HF， ZHANG HB， et al. Study on anticipant mature age of Pinus densiflora in Shandong Province[J]. Journal of Anhui Agricultural Sciences， 2017， 3： 184-186. （in Chinese）
[6]GAO JH， PAI QZ， ZHANG DQ. Approach into desirable period of forest management in Shandong Province[J]. China Forestry Science and Technology， 2003（3）： 6-8 . （in Chinese）
Editor： Yingzhi GUANG Proofreader： Xinxiu ZHU
Key words Mature age； Empirical equation； Analytic tree
Pinus tabuliformis forest is a kind of forestry community distributed the widest in temperate coniferous forest. P. tabuliformis forest is a typical coniferous forest type the same as P. densiflora forest in Shandong Province， and has the area and stocking volume ranking only second to P. densiflora. It is a type of forest commonly seen in mountainous region with an altitude over 700 m. Shandong Province is the south edge of the natural distribution of P. tabuliformis， and Mount Meng is the south end of P. tabuliformis distribution in Shandong Province. P. tabuliformis forest is distributed in highaltitude areas in Shandong Province， where human activities are relatively less， the soil is more humid with more intact vertical structure， and plant composition is also richer. During the formulation of forestry development planning and forest management scheme， and examination and approval of tree harvesting and forest management， it is urgent to solve the problem of mature age of trees. Based on the information of analytic trees obtained from years of research， according to the methods in references[1-3]and the research results in reference[6]， the writers studied the mature age of single trees[4]. However， the information of analytic trees is the growth index of peeled trees， and the collected sample trees all grow normally with straight trunk and， and thus could not accurately reflect the mature age of P. tabuliformis. Conventional research method is to create tree increment coordinate graphs by analytic tree method， and the intersection of annual average increment and current increment is the mature age of trees. However， the conventional method has the disadvantages of larger workload and not high precision. In this study， the empirical equation method was applied， achieving the effect of yielding twice the results with half the effort. The mature age of P. densiflora was studied at first using first class checking information by empirical equation method[5]， followed by the study on the mature age of P. tabuliformis. Data source
The data were first class treechecking information of Shandong Province in 1988， 1992， 1997 and 2002， including average DBH， average tree height， average age and sample plot stocking data of P. tabuliformis and P. densiflora.
Research method
Continuous forestry resources checking information about P. tabuliformis and P. densiflora stands were searched and managed in table format， and the items including sample plot number， average age （A， unit： a）， average DBH （D， unit： cm）， average height （H， unit： m）， stand volume （M， unit： 0.000 1 m3） were reserved； the increment of average DBH was calculated according to D-=D/A （unit： cm/a）， the increment of average tree height was calculated according to H-=H/A （unit： m/a）， and the annual average increment was calculated according to Z= M/A （unit： 0.000 1 m3； and N is the number of sample plots， i.e.， the number of investigated samples. All these data were listed in spreadsheets for later statistic analysis.
For all the investigation， each sample plot was square and had an area of 667 m2 （the sampling point was the southwest corner of the sample plot， and each sample plot was located in the east， west， south and north of coordinate azimuth）. Furthermore， sampling was performed by mechanical engineering method according to 1∶5 topographic map dualsquare grid （1988： 2×2 km， other years： 4×4 km）. All the sample plots were treated equally， and all obeyed normal distribution.
In order to save research cost， fitting tests were carried out to various regression equations using tree growth empirical equations according to "Forest mensuration" edited by Northeast Forestry University， and finally， the mixed type empirical equation， y（t）=ea-b/t （a and b are tobedetermined exponential parameters， and e is the base number of natural logarithm： 2.718 28……）， was selected for the study of tree growth process. The writers tried to fit the tree growth process using empirical equations， and through the acquisition of the maximum age according to DBH fitting equations （including the equation obtained in derivation， as described in the research process）， the quantitative mature age of the DBH growth was obtained； and through the acquisition of the maximum age according to tree height fitting equation， the mature age of tree height growth was obtained. By the same method， the quantitative mature age of volume of timber was also obtained.
Research process of fitting empirical equation A linear equation was formed by taking the logarithm of the tree growth process equation. Then， parameters a and b were obtained by unary linear regression， and F test and significance test of regression coefficient were carried out. If t test is passed， a tree growth fitting equation is established， and the calculation results are shown in Table 1-Table 3. It might be due to the reason that the samples were not enough， the fitting precision of P. tabuliformis was greatly reduced compared with that of P. densiflora equation as control. The tree height equation had a very low precision in 2002， and was of no practical significance. The P. tabuliformis volume fitting equation had precision values lower than 90% in 1997 and 2002， but passed F test and t test with the reliability over 90%， indicating that the mathematical model （empirical fitting equation） is applicable overall. If the correlation coefficient （R） test is passed， then the fitting equation relation is established. The fitting degree of P. tabuliformis equation was lower in 2002 and 1977， which might be due to that the number of samples was small， and therefore， fitting equations were established using all samples in 1988-1997 and 1988-2002， respectively， and compared with the study on P. densiflora in the same time period. For the 1988-1997 and 1988-2002 fitting equations， except that the tree height fitting equation of 1988-2002 had a precision reaching 96%， the precision of other items all exceeded 99.9%， and the 1988-1977 fitting equations had precision higher than the 1988-2002 equations. The problem of solving the maximum current annual increment time and quantitative maturity of trees using fitting equations was illustrated taking the DBH item of P. tabuliformis in 1988 as an example. The tree growth rate equation of P. densiflora DBH （the current annual increment， obtained by derivation of Y（t） function， the process of which was omitted， only the extreme point was given， the same below） showed the extreme value tz=17.4 a， i.e.， the current increment of trees reached its peak value at about 18 a， and had only one peak value. The average growth rate equation Y（t）/t （annual average growth， the calculation process was omitted， only the extreme point was given， the same below） had the extreme value tm=34.7 a， i.e.， the quantitative mature age of trees was 35 a. only the calculation of DBH fitting equation was described above， other fitting equations were the same as it， and detailed description was omitted. In the discussion below， the growth fitting equation， tree growth rate equation and tree average growth rate equation had the same meaning， symbols such as tz and tm also had the same meaning， and the calculation results were given without repeated description and explanation. The research results of P. densiflora were used as control of P. tabuliformis. The quantitative mature ages calculated according to various items are shown in tables. It could be seen from above tables that P. tabuliformis DBH and volume items had the highest precision in 1988， and the tree height item had the highest precision in 1997. The DBH fitting equations of 1992 and 1997 were more proximate， exhibiting a relative error only of 1.7%. Compared with P. densiflora， the fitting results of DBH equation in 1988-2002 were more proximate to those of the P. densiflora equation in 1977， with a relative error only of 0.1%. The fitting precision of the volume of P. tabuliformis in 1988-1997 was surprisingly similar to that of P. densiflora in 2002， with a relative error only of 1.7%， namely P. tabuliformis and P. densiflora had the same mature age with a reliability of 98.3%. The fitting results of tree mature age， DBH and tree height equations were quite different from national standards， while for the fitting results of volume， P. tabuliformis was quite close to P. densiflora in 1997， and the mature age was slightly higher than national standard. Therefore， according to the research results and production practice， it is more reliable to use accumulative mature age as tree mature age. The fitting results of the volume equation of P. tabuliformis in 1988 showed a P. tabuliformis mature age of 74.9 a， with a fitting precision over 99.9% and correlation coefficient up to 0.96， which were far higher than national mature age standards， and the forest could be determined as the mature forest at ideal state， for specialpurpose forest and protection forest （public welfare forest）. Furthermore， the fitting results of the volume equation of 1988-1997 with the second best precision showed a P. tabuliformis mature age of 56.08 a， and the forest was determined as the mature forest at normal state， and used as the standard of mature forest for timber （commercial forest）. The results substantially accorded with the results of P. densiflora. The anticipant mature ages of public welfare forest and commercial P. densiflora forest were determined as 75 and 56 a， respectively. Conclusions and Application
Through the analysis and judgment of research result， according to the quantitative maturity of stand volume， the fitting value of volume of timber was selected as the tree mature age， and taking age grade （10 a as an age grade） into consideration， with the highest precision as judgment standard， the anticipant mature ages of commercial and public welfare P. tabuliformis forests were determined as 61 and 81 a， respectively. Over time， various interference activities against P. tabuliformis forest were reduced， so the forest could grow and propagate. The age groups of P. tabuliformis forest are shown in Table 4.
Forest categoryYoung forest Middleaged forestNearmature forestMature forest Overmature forest
Timber forest 1-3031-5051-6061-70Over 71
Protection forest， special purpose forest1-4041-7071-8081-90Over 91
This study showed that the anticipant mature age of P. tabuliformis forest was higher than related national standard， which might be due that the stand quality was improved relatively， and the interference from human factors was reduced.
Discussion
The original mature age standard of P. tabuliformis forest is 41 a， and the results of this study were higher than the original standard by 20 and 40 a. Because the used data were first class checking information， the fitting empirical equation of tree growth was used to make up the insufficiency of the age of analytic trees， the noise effects of differences in various natural conditions in time and space and tree differentiation phenomenon on test results were also avoided， and the anticipant stand mature age of P. tabuliformis was obtained. Through repeated verification， analysis and judgment， the suitability of empirical equation for tree growth exists exactly， but it is difficult to scientifically explain it， and due to the limitations of time and level， various deviations are unavoidable. Improvement and development is needed in future produc tion practice and scientific research. The production advises put forward by the writers are only individual opinions， which were concluded from the analysis and fitting of relatively less data information， and they could only be put into use after being identification by relevant experts and checked by production practice.
References
[1]Northeast Forestry University. Forest mensuration[M]. Internal teaching material， 1985. （in Chinese）
[2]Northeast Forestry University. Mathematical statistics[M]. Beijing： China Forestry Publishing House，1985. （in Chinese）
[3]LIU GJ. Review of registered consulting engineer （investment） certified qualification examination textbook[M]. Tianjin： Tianjin University Press， 2003. P231-246.（in Chinese）
[4]HU HY， SU WL， QU HY. Study on actual mature age of single plant of Pinus densiflora[J]. Journal of Shandong Forestry Science and Technology， 2010， 6： 36-37. （in Chinese）
[5]LI LP， DONG HF， ZHANG HB， et al. Study on anticipant mature age of Pinus densiflora in Shandong Province[J]. Journal of Anhui Agricultural Sciences， 2017， 3： 184-186. （in Chinese）
[6]GAO JH， PAI QZ， ZHANG DQ. Approach into desirable period of forest management in Shandong Province[J]. China Forestry Science and Technology， 2003（3）： 6-8 . （in Chinese）
Editor： Yingzhi GUANG Proofreader： Xinxiu ZHU