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Abstract To determine the age of oiltea camellia trees， regression equations including Logistic， Mitscherlich， Gompertz， Korf， and Richards were used to calculate accumulative growth rate using basal trunk disc and investigate the relations between the age of oiltea camellia trees and their growth rate of secondary trunk. The Gompertz equation Y=71.296 1exp （-3.874 4exp （-0.006 4t）） was the most optimal equation to simulate the accumulative growth rate of basal trunk disc. This equation could be used to estimate the age of oiltea camellia trees that grow under similar environmental conditions. The Korf equation Y=576.900 1exp （-4.153 0x-0.314 2） was the best equation to describe the relation between the age and growth rate of different secondary trunks. With the adjustment coefficient and average growth of different secondary trunk discs， it is possible to predict the age of ancient oiltea camellia trees that grow under similar environmental conditions. In addition， taking three or more discs from the same diameter group and calculating their average growth rate could lead to more accurate results. For trees that grow in different areas， environmental conditions should be carefully considered when using the above two equations to predict the age of ancient oiltea camellia trees.
Key words Ancient tree； Basal trunk disc； Growth equation； Oiltea camellia
Ancient trees are precious natural resources and play an important role in ecosystem， landscape， tourism， and scientific research[1-4]. In the field of dendrochronology， they are also excellent materials to understand historical climate changes[2，4]. Ancient trees are highquality ornamental plants[5-7]. According to Shan Hai Jing （the Chinese Classic of Mountains and Rivers）， oiltea camellia was a main crop in southern China， and the history of cultivating oiltea plants dates back to 2 000 years ago. The protection and proper utilization of ancient oiltea camellia trees would conserve these precious natural resources.
To determine the age of the ancient oiltea camellia trees is of importance to conservation program[8]. Currently， a variety of methods are used to determine the age of ancient trees including regression models[9-10]， Xray[11-12]， CT scanning[13]， literature searching[14]， growth cone[15-16]， and 14C dating[3，14]. This study was conducted to estimate the age of ancient oiltea camellia trees using regression models.
Material and Methods
Plant materials An oiltea camellia standard tree located in Hekou （E109°51′53.27″， N29°32′52.79″， Altitude is 406 m）， Shangzhi County， Hunan Province was chosen. The basal diameter （the average of southnorth distance and eastwest distance） without skin measured using straightedge reader was 32.03 cm， whereas the basal diameter （round） with skin measured using tapeline reader was 34.80 cm. The bark thickness is 0.37 cm， the height is 4.98 m and the tree age is 150 years old. The primary （basal） trunk and secondary trunks were cut， and crosssection discs were obtained. The crosssection discs were polished to count tree rings， and the diameters of the discs with skin were measured using tapeline.
An estimated oiltea camellia tree of #1 located in Wudaoshui （E109°54′57.68″， N29°42′13.23″， Altitude is 516 m）， Shangzhi County， and Hunan Province was chosen； and the basal diameter （round） with skin was 58.00 cm. An estimated oiltea camellia tree of #2 located in Zhouping （E113°07′40.84″， N27°49′52.01″， Altitude is 46 m）， Zhuzhou County， and Hunan Province was chosen； the basal diameter （round） with skin was 32.00 cm； and the actual age of tree #2 was 108 years. An estimated oiltea camellia tree of #3 located in Changchun （E112°17′9.49″， N28°42′20.37″， Altitude is 48 m）， Ziyang County， and Hunan Province was chosen； the basal diameter （round） with skin was 48.00 cm.
Growth equation
Theoretical growth equations are widely used to simulate the growth and development of trees， especially height， trunk diameter， and crosssection area[17-20]. Gompertz， Korf， Logistic， Mitscherlich and Richards theoretical growth equations were used in the current study[21].
Tree age determination
Two simulation equations were used to predict the age of trees. The first one was to calculate the accumulative growth using basal diameter， and the other one was to determine the relations between the age and diameter of crosssection discs cut from different secondary trunks. The first simulation equation has been used to predict the tree age with its good extensionality [21]. The second equation predicts the tree age with the following steps： ① obtaining crosssection disc of the tree to be measured， and measuring the diameter and growth of the tree； ② calculating the age of trees with similar size disc using the simulation equation established based on the standard tree， and ③ calculating average growth of the crosssection discs of standard tree. Because the growth of discs cut from secondary trunks at different height is different from that calculated using basal diameter， an adjustment coefficient， a ratio of average growth rate of crosssection disc of secondary trunk at different heights on the standard tree and that calculated using the basal diameter， is needed. With the average growth rate of the discs of secondary trunk at different heights and the adjustment coefficient， the average growth rate could be calculated using the diameter of basal trunk of the tree. The age of the tree could be estimated using the ratio of the basal radius of the estimated tree and the average growth rate. The specific computation formula is as follows： （1）Calculation of the age of the lateral branch disc with the same diameter as the standard tree use the optimal equation， which is fitted by the relationship between the age and diameter of the standard tree branch disc.
（2） Adjustment coefficient=Standard tree different heights branch disc radius/Standard tree different heights branch disc ageStandard tree basal radius/Standard tree basal disc age.
（3） Computing formula for the calculation of ancient tree age based on relation between age and diameter of different heights branch discs：
Age of the tree to be estimated = Basal radius of the tree to be estimated/
Tree to be estimated lateral branch disc radius/Tree to be estimated lateral branch disc ageAdjusment coefficient.
（4） Calculation of ancient tree ages based on basal diameter growth volume， using the optimal equation is simulating total growth rate of basal disc.
In addition， the age of crosssection discs and growth of basal discs was obtained using LINTAB treering analyzer （Germany， Rinntech）.
Data analysis
All data analyses were carried out using EXCEL， 1st0pt （7DSoft High Technology Inc.， Peking， China）.
Results and Discussion
Diameter and average growth rate of secondary trunk at different heights
The discs varied in diameter from 4 to 18 cm （Table 1）. The smallest disc was 4.3 cm in diameter， while the largest one was 18.5 cm， and their corresponding age was 41 and 103 years， respectively. All discs were classified into eight groups （every 2 cm as a group）. The number of discs among groups followed normal distribution （Fig. 1； Table1）.
As the diameter of discs increased， the average age and growth rate of discs increased. The diameter of basal trunk discs was larger than that of the discs within corresponding diameter group （Table 1）. Secondary trunk at different heights grew relatively slowly and crosssection discs on the basal trunk had larger growth rate than those from secondary trunk at different heights.
Estimation of tree age using growth rate of basal trunk disc
Growth rate of basal trunk disc
The growth of tree rings on basal trunk disc is presented in Fig. 2A. There were many peaks indicating different growth rates over years. The accumulated growth of tree rings of basal trunk disc increased over time （Fig. 2B）， while the average growth decreased rapidly to 0.100 cm， subsequently increased to around 0.122 cm， then decreased gradually to 0.087 cm followed by a gradual increase to 0.107 cm （Fig. 2C）. Estimation of parameters in the growth equations using basal trunk disc diameter of oiltea camellia trees
The accumulated growth of basal trunk disc （Y） and the age of tree ring of basal trunk disc （t） were collected. These data were used to simulate the growing process of oiltea camellia trees using five growth theories in Table 2. All five equations displayed good results as indicated by meansquare deviation （RMSE） and determination coefficient （R2）. Gompertz equation was the best one， followed by Logistic equation， Richards's equation， Mitscherlich equation， and Korf equation.
Agricultural Biotechnology2018
Tree age determined using basal trunk disc
Fig. 3 shows all simulation results of the accumulative growth of basal trunk discs using different growth equations. The optimal equation was Gompertz equation Y=71.296 1exp [-3.874 4exp （-0.006 4t）]. With this equation， the estimated accumulative growth of basal trunk disc stayed very close to actual value （Fig. 3）. This indicated that Gompertz equation could accurately simulate the growing process of basal trunk disc of oil]tea camellia trees with over 30.0 cm in diameter （older than 140 years）.
Other growth equations also produced good results （Fig. 3）， and Mitscherlich equation could be employed for oil]tea camellia trees with diameters less than 8.3 cm （age 0-40）. Logistics equation was good for those with diameters range 8.3 to 30.0 cm （age 40-140）.
Relations between age and diameter of secondary trunk discs at different height
The difference between the actual age and the estimated age that calculated using Korf equation was relatively small with a 9year difference （Fig. 4）. This result assured that Korf equation could be used to accurately simulate the growing process of ancient oil]tea camellia trees with different trunk size.
Prediction of the age of ancient trees using secondary trunk disc at different heights
There was a large variation between the estimated age of ancient trees and their actual age when secondary trunk discs at different heights were used （Fig. 5A）. The estimated age of ancient trees was around 150 years. If the discs with different diameter were classified into different groups with 2 cm difference， the disc groups were used to calculate the age of ancient trees； better results were obtained with an error of -9 to 8 years （Fig. 5B）. These results showed that classification of the discs with different diameters into groups was necessary to accurately estimate the age of ancient oil]tea camellia trees. A comparison of the two equations in estimating the age of ancient oil]tea camellia tree
The optimal equation for basal trunk disc Y=576.900 1exp （-4.153 0x-0.314 2） and for secondary trunk disc at different heights Y=71.296 1exp [-3.874 4exp （-0.006 4t）]was used to estimate the age of ancient oiltea camellia trees （Table 4）. When secondary trunk discs at different heights were classified into two groups （4 and 6 cm）， the estimated age of the standard tree was 149 and 155 years， respectively， with an average of 152 years and an error ranging from -15 to 18 years. The estimated age of #1， 2， and 3 trees were 215， 74， and 135 years if secondary trunk discs at 4cm group were used to calculate， while the estimated age of #1， 2， and 3 trees was 221， 72， and 151 years if secondary trunk discs at 6 cm group were used. The average age of #1， 2， and 3 trees was 218， 73， and 143 years with an error ranging from -21 to 33 years， -3 to 2 years， -21 to 10 years， respectively.
The estimated age using accumulative growth of basal trunk disc was 150， 224， 144， and 198 years for standard tree and tree #1， 2， 3， respectively. Interestingly， when the established equations were used to estimate the age of tree #1， 2， and 3， the estimated ages of tree #1 were similar between two methods， while the estimated ages of tree #2 and 3 were different. Given the fact that tree #1 grew within the same area as standard tree and tree #2 and 3 grew far away from standard tree， the above results indicated that equations established using standard tree were applicable depending on growing conditions.
Discussions
Five theoretical growth equations were used to simulate the growth of oiltea camellia trees. The optimal equation for estimating the tree’s age using total growth of basal trunk disc is Gompertz equation Y=71.296 1exp [-3.874 4exp （-0.006 4t）]. This equation can accurately predict the age of ancient oiltea camellia trees with careful consideration in environmental conditions. Establishing a sitespecific Gompertz equation with accumulated growth of basal disc can produce more accurate estimation.
The age of oiltea camellia trees have close relationship with the size of branch discs at different heights. The optimal simulation equation for predicting the age of oiltea camellia trees was Korf equation Y=576.900 1exp （-4.153 0x-0.314 2）. This equation produced the best estimation of the age of oiltea camellia trees with an error within 9 years. Due to different diameter of secondary trunks， an adjustment coefficient based on the ratio of the average growth of secondary trunk disc and that of basal trunk disc is need to achieve better results. Besides， taking three or more discs， which come from the same diameter group， as sub samples and using the average values of their predicted results as the tree age can reduce the errors which are resulted from the effects of different secondary trunk diameter. With the adjustment coefficient and average growth of secondary trunk discs， it is possible to predict the age of ancient oiltea camellia trees that grew under similar environmental conditions. Environmental and climate conditions should be carefully considered when using the above two equations to predict the age of ancient oiltea camellia trees. The #1 tree had similar numbers of the age using both equations because it grew in the same location as standard tree. However， #2 and #3 tree yielded really large variations between two methods. They both grew far away from the standard tree. Establishing sitespecific equations for basal disc and lateral disc can significantly reduce the influences of environmental conditions and produce more accurate estimation of ancient oiltea camellia trees.
References
[1]ANDERSSON R， STLUND L. Spatial patterns， density changes and implications on biodiversity for old trees in the boreal landscape of northern Sweden[J]. Biological conservation， 2004， 118（4）： 443-453.
[2]BRIFFA KR. Annual climate variability in the Holocene： interpreting the message of ancient trees[J]. Quaternary Science Reviews， 2000， 19（1）： 87-105.
[3]CHAMBERS JQ， HIGUCHI N， SCHIMEL JP. Ancient trees in Amazonia[J]. Nature， 1998， 391（6663）： 135-136.
[4]SHRODER JF. Dendrogeomorphology： review and new techniques of treering dating[J]. Progress in Physical geography， 1980， 4（2）： 161-188.
[5]BECKER N， FREEMAN S. The economic value of old growth trees in Israel[J]. Forest Policy and Economics， 2009， 11（8）： 608-615.
[6]FUKAMACHI K， OKU H， KUMAGAI Y， et al. Changes in landscape planning and land management in Arashiyama National Forest in Kyoto[J]. Landscape and urban planning， 2000， 52（2）： 73-87.
[7]JIM CY. Spatial differentiation and landscapeecological assessment of heritage trees in urban Guangzhou （China）[J]. Landscape and Urban Planning， 2004， 69（1）： 51-68.
[8]WANG YX， DAI WS， BAI SB， et al. Improved survey method of ancient and famous trees[J]. Journal of Zhejiang Forestry College （China）， 2006， 23（5）： 549-553.
[9]CLARK SL， HALLGREN SW. Age estimation of Quercus marilandica and Quercus stellata： applications for interpreting stand dynamics[J]. Canadian journal of forest research， 2004， 34（6）： 1353-1358.
[10]ROZAS V. Tree age estimates in Fagus sylvatica and Quercus robur： testing previous and improved methods[J]. Plant Ecology， 2003， 167（2）： 193-212.
[11]HELAMA S， VARTIAINEN M， KOLSTRM T， et al. Xray microdensitometry applied to subfossil treerings： growth characteristics of ancient pines from the southern boreal forest zone in Finland at intraannual to centennial timescales[J]. Vegetation History and Archaeobotany， 2008， 17（6）： 675-686. [12]SCHWEINGRUBER FH， FRITTS HC， BRKER OU， et al. The Xray technique as applied to dendroclimatology[J]. TreeRing Bulletin， 1978.
[13]METTLER JR FA， WIEST PW， LOCKEN JA， et al. CT scanning： patterns of use and dose[J]. Journal of radiological Protection， 2000， 20（4）： 353.
[14]FICHTLER E， CLARK DA， WORBES M. Age and longterm growth of trees in an oldgrowth tropical rain forest， based on analyses of tree rings and 14C[J]. Biotropica， 2003， 35（3）： 306-317.
[15]FRAVER S， BRADFORD JB， PALIK BJ. Improving tree age estimates derived from increment cores： A case study of red pine[J]. Forest Science， 2011， 57（2）： 164-170.
[16]NORTON DA， PALMER JG， OGDEN J. Dendroecological studies in New Zealand 1. An evaluation of tree age estimates based on increment cores[J]. New Zealand Journal of Botany， 1987， 25（3）： 373-383.
[17]HUANG S， TITUS SJ， WIENS DP. Comparison of nonlinear heightdiameter functions for major Alberta tree species[J]. Canadian Journal of Forest Research， 1992， 22（9）： 1297-1304.
[18]MURPHY PA， SHELTON MG. An individualtree basal area growth model for loblolly pine stands[J]. Canadian journal of forest research， 1996， 26（2）： 327-331.
[19]SHARMA M， YIN ZHANG S. Height–diameter models using stand characteristics for Pinus banksiana and Picea mariana[J]. Scandinavian Journal of Forest Research， 2004， 19（5）： 442-451.
[20]ALLEN MG， BURKHART HE. A comparison of alternative data sources for modeling site index in loblolly pine plantations[J]. Canadian Journal of Forest Research， 2015， 45（8）： 1026-1033.
[21]LIU P， MA LY， JIA LM， et al. Study on Individual Tree Height Growth Model for Pinus tabulaeformis Plantation[J]. Forest Resources Management（China）， 2008， 10（5）： 50-56.
Editor： Yingzhi GUANG Proofreader： Xinxiu ZHU
Key words Ancient tree； Basal trunk disc； Growth equation； Oiltea camellia
Ancient trees are precious natural resources and play an important role in ecosystem， landscape， tourism， and scientific research[1-4]. In the field of dendrochronology， they are also excellent materials to understand historical climate changes[2，4]. Ancient trees are highquality ornamental plants[5-7]. According to Shan Hai Jing （the Chinese Classic of Mountains and Rivers）， oiltea camellia was a main crop in southern China， and the history of cultivating oiltea plants dates back to 2 000 years ago. The protection and proper utilization of ancient oiltea camellia trees would conserve these precious natural resources.
To determine the age of the ancient oiltea camellia trees is of importance to conservation program[8]. Currently， a variety of methods are used to determine the age of ancient trees including regression models[9-10]， Xray[11-12]， CT scanning[13]， literature searching[14]， growth cone[15-16]， and 14C dating[3，14]. This study was conducted to estimate the age of ancient oiltea camellia trees using regression models.
Material and Methods
Plant materials An oiltea camellia standard tree located in Hekou （E109°51′53.27″， N29°32′52.79″， Altitude is 406 m）， Shangzhi County， Hunan Province was chosen. The basal diameter （the average of southnorth distance and eastwest distance） without skin measured using straightedge reader was 32.03 cm， whereas the basal diameter （round） with skin measured using tapeline reader was 34.80 cm. The bark thickness is 0.37 cm， the height is 4.98 m and the tree age is 150 years old. The primary （basal） trunk and secondary trunks were cut， and crosssection discs were obtained. The crosssection discs were polished to count tree rings， and the diameters of the discs with skin were measured using tapeline.
An estimated oiltea camellia tree of #1 located in Wudaoshui （E109°54′57.68″， N29°42′13.23″， Altitude is 516 m）， Shangzhi County， and Hunan Province was chosen； and the basal diameter （round） with skin was 58.00 cm. An estimated oiltea camellia tree of #2 located in Zhouping （E113°07′40.84″， N27°49′52.01″， Altitude is 46 m）， Zhuzhou County， and Hunan Province was chosen； the basal diameter （round） with skin was 32.00 cm； and the actual age of tree #2 was 108 years. An estimated oiltea camellia tree of #3 located in Changchun （E112°17′9.49″， N28°42′20.37″， Altitude is 48 m）， Ziyang County， and Hunan Province was chosen； the basal diameter （round） with skin was 48.00 cm.
Growth equation
Theoretical growth equations are widely used to simulate the growth and development of trees， especially height， trunk diameter， and crosssection area[17-20]. Gompertz， Korf， Logistic， Mitscherlich and Richards theoretical growth equations were used in the current study[21].
Tree age determination
Two simulation equations were used to predict the age of trees. The first one was to calculate the accumulative growth using basal diameter， and the other one was to determine the relations between the age and diameter of crosssection discs cut from different secondary trunks. The first simulation equation has been used to predict the tree age with its good extensionality [21]. The second equation predicts the tree age with the following steps： ① obtaining crosssection disc of the tree to be measured， and measuring the diameter and growth of the tree； ② calculating the age of trees with similar size disc using the simulation equation established based on the standard tree， and ③ calculating average growth of the crosssection discs of standard tree. Because the growth of discs cut from secondary trunks at different height is different from that calculated using basal diameter， an adjustment coefficient， a ratio of average growth rate of crosssection disc of secondary trunk at different heights on the standard tree and that calculated using the basal diameter， is needed. With the average growth rate of the discs of secondary trunk at different heights and the adjustment coefficient， the average growth rate could be calculated using the diameter of basal trunk of the tree. The age of the tree could be estimated using the ratio of the basal radius of the estimated tree and the average growth rate. The specific computation formula is as follows： （1）Calculation of the age of the lateral branch disc with the same diameter as the standard tree use the optimal equation， which is fitted by the relationship between the age and diameter of the standard tree branch disc.
（2） Adjustment coefficient=Standard tree different heights branch disc radius/Standard tree different heights branch disc ageStandard tree basal radius/Standard tree basal disc age.
（3） Computing formula for the calculation of ancient tree age based on relation between age and diameter of different heights branch discs：
Age of the tree to be estimated = Basal radius of the tree to be estimated/
Tree to be estimated lateral branch disc radius/Tree to be estimated lateral branch disc ageAdjusment coefficient.
（4） Calculation of ancient tree ages based on basal diameter growth volume， using the optimal equation is simulating total growth rate of basal disc.
In addition， the age of crosssection discs and growth of basal discs was obtained using LINTAB treering analyzer （Germany， Rinntech）.
Data analysis
All data analyses were carried out using EXCEL， 1st0pt （7DSoft High Technology Inc.， Peking， China）.
Results and Discussion
Diameter and average growth rate of secondary trunk at different heights
The discs varied in diameter from 4 to 18 cm （Table 1）. The smallest disc was 4.3 cm in diameter， while the largest one was 18.5 cm， and their corresponding age was 41 and 103 years， respectively. All discs were classified into eight groups （every 2 cm as a group）. The number of discs among groups followed normal distribution （Fig. 1； Table1）.
As the diameter of discs increased， the average age and growth rate of discs increased. The diameter of basal trunk discs was larger than that of the discs within corresponding diameter group （Table 1）. Secondary trunk at different heights grew relatively slowly and crosssection discs on the basal trunk had larger growth rate than those from secondary trunk at different heights.
Estimation of tree age using growth rate of basal trunk disc
Growth rate of basal trunk disc
The growth of tree rings on basal trunk disc is presented in Fig. 2A. There were many peaks indicating different growth rates over years. The accumulated growth of tree rings of basal trunk disc increased over time （Fig. 2B）， while the average growth decreased rapidly to 0.100 cm， subsequently increased to around 0.122 cm， then decreased gradually to 0.087 cm followed by a gradual increase to 0.107 cm （Fig. 2C）. Estimation of parameters in the growth equations using basal trunk disc diameter of oiltea camellia trees
The accumulated growth of basal trunk disc （Y） and the age of tree ring of basal trunk disc （t） were collected. These data were used to simulate the growing process of oiltea camellia trees using five growth theories in Table 2. All five equations displayed good results as indicated by meansquare deviation （RMSE） and determination coefficient （R2）. Gompertz equation was the best one， followed by Logistic equation， Richards's equation， Mitscherlich equation， and Korf equation.
Agricultural Biotechnology2018
Tree age determined using basal trunk disc
Fig. 3 shows all simulation results of the accumulative growth of basal trunk discs using different growth equations. The optimal equation was Gompertz equation Y=71.296 1exp [-3.874 4exp （-0.006 4t）]. With this equation， the estimated accumulative growth of basal trunk disc stayed very close to actual value （Fig. 3）. This indicated that Gompertz equation could accurately simulate the growing process of basal trunk disc of oil]tea camellia trees with over 30.0 cm in diameter （older than 140 years）.
Other growth equations also produced good results （Fig. 3）， and Mitscherlich equation could be employed for oil]tea camellia trees with diameters less than 8.3 cm （age 0-40）. Logistics equation was good for those with diameters range 8.3 to 30.0 cm （age 40-140）.
Relations between age and diameter of secondary trunk discs at different height
The difference between the actual age and the estimated age that calculated using Korf equation was relatively small with a 9year difference （Fig. 4）. This result assured that Korf equation could be used to accurately simulate the growing process of ancient oil]tea camellia trees with different trunk size.
Prediction of the age of ancient trees using secondary trunk disc at different heights
There was a large variation between the estimated age of ancient trees and their actual age when secondary trunk discs at different heights were used （Fig. 5A）. The estimated age of ancient trees was around 150 years. If the discs with different diameter were classified into different groups with 2 cm difference， the disc groups were used to calculate the age of ancient trees； better results were obtained with an error of -9 to 8 years （Fig. 5B）. These results showed that classification of the discs with different diameters into groups was necessary to accurately estimate the age of ancient oil]tea camellia trees. A comparison of the two equations in estimating the age of ancient oil]tea camellia tree
The optimal equation for basal trunk disc Y=576.900 1exp （-4.153 0x-0.314 2） and for secondary trunk disc at different heights Y=71.296 1exp [-3.874 4exp （-0.006 4t）]was used to estimate the age of ancient oiltea camellia trees （Table 4）. When secondary trunk discs at different heights were classified into two groups （4 and 6 cm）， the estimated age of the standard tree was 149 and 155 years， respectively， with an average of 152 years and an error ranging from -15 to 18 years. The estimated age of #1， 2， and 3 trees were 215， 74， and 135 years if secondary trunk discs at 4cm group were used to calculate， while the estimated age of #1， 2， and 3 trees was 221， 72， and 151 years if secondary trunk discs at 6 cm group were used. The average age of #1， 2， and 3 trees was 218， 73， and 143 years with an error ranging from -21 to 33 years， -3 to 2 years， -21 to 10 years， respectively.
The estimated age using accumulative growth of basal trunk disc was 150， 224， 144， and 198 years for standard tree and tree #1， 2， 3， respectively. Interestingly， when the established equations were used to estimate the age of tree #1， 2， and 3， the estimated ages of tree #1 were similar between two methods， while the estimated ages of tree #2 and 3 were different. Given the fact that tree #1 grew within the same area as standard tree and tree #2 and 3 grew far away from standard tree， the above results indicated that equations established using standard tree were applicable depending on growing conditions.
Discussions
Five theoretical growth equations were used to simulate the growth of oiltea camellia trees. The optimal equation for estimating the tree’s age using total growth of basal trunk disc is Gompertz equation Y=71.296 1exp [-3.874 4exp （-0.006 4t）]. This equation can accurately predict the age of ancient oiltea camellia trees with careful consideration in environmental conditions. Establishing a sitespecific Gompertz equation with accumulated growth of basal disc can produce more accurate estimation.
The age of oiltea camellia trees have close relationship with the size of branch discs at different heights. The optimal simulation equation for predicting the age of oiltea camellia trees was Korf equation Y=576.900 1exp （-4.153 0x-0.314 2）. This equation produced the best estimation of the age of oiltea camellia trees with an error within 9 years. Due to different diameter of secondary trunks， an adjustment coefficient based on the ratio of the average growth of secondary trunk disc and that of basal trunk disc is need to achieve better results. Besides， taking three or more discs， which come from the same diameter group， as sub samples and using the average values of their predicted results as the tree age can reduce the errors which are resulted from the effects of different secondary trunk diameter. With the adjustment coefficient and average growth of secondary trunk discs， it is possible to predict the age of ancient oiltea camellia trees that grew under similar environmental conditions. Environmental and climate conditions should be carefully considered when using the above two equations to predict the age of ancient oiltea camellia trees. The #1 tree had similar numbers of the age using both equations because it grew in the same location as standard tree. However， #2 and #3 tree yielded really large variations between two methods. They both grew far away from the standard tree. Establishing sitespecific equations for basal disc and lateral disc can significantly reduce the influences of environmental conditions and produce more accurate estimation of ancient oiltea camellia trees.
References
[1]ANDERSSON R， STLUND L. Spatial patterns， density changes and implications on biodiversity for old trees in the boreal landscape of northern Sweden[J]. Biological conservation， 2004， 118（4）： 443-453.
[2]BRIFFA KR. Annual climate variability in the Holocene： interpreting the message of ancient trees[J]. Quaternary Science Reviews， 2000， 19（1）： 87-105.
[3]CHAMBERS JQ， HIGUCHI N， SCHIMEL JP. Ancient trees in Amazonia[J]. Nature， 1998， 391（6663）： 135-136.
[4]SHRODER JF. Dendrogeomorphology： review and new techniques of treering dating[J]. Progress in Physical geography， 1980， 4（2）： 161-188.
[5]BECKER N， FREEMAN S. The economic value of old growth trees in Israel[J]. Forest Policy and Economics， 2009， 11（8）： 608-615.
[6]FUKAMACHI K， OKU H， KUMAGAI Y， et al. Changes in landscape planning and land management in Arashiyama National Forest in Kyoto[J]. Landscape and urban planning， 2000， 52（2）： 73-87.
[7]JIM CY. Spatial differentiation and landscapeecological assessment of heritage trees in urban Guangzhou （China）[J]. Landscape and Urban Planning， 2004， 69（1）： 51-68.
[8]WANG YX， DAI WS， BAI SB， et al. Improved survey method of ancient and famous trees[J]. Journal of Zhejiang Forestry College （China）， 2006， 23（5）： 549-553.
[9]CLARK SL， HALLGREN SW. Age estimation of Quercus marilandica and Quercus stellata： applications for interpreting stand dynamics[J]. Canadian journal of forest research， 2004， 34（6）： 1353-1358.
[10]ROZAS V. Tree age estimates in Fagus sylvatica and Quercus robur： testing previous and improved methods[J]. Plant Ecology， 2003， 167（2）： 193-212.
[11]HELAMA S， VARTIAINEN M， KOLSTRM T， et al. Xray microdensitometry applied to subfossil treerings： growth characteristics of ancient pines from the southern boreal forest zone in Finland at intraannual to centennial timescales[J]. Vegetation History and Archaeobotany， 2008， 17（6）： 675-686. [12]SCHWEINGRUBER FH， FRITTS HC， BRKER OU， et al. The Xray technique as applied to dendroclimatology[J]. TreeRing Bulletin， 1978.
[13]METTLER JR FA， WIEST PW， LOCKEN JA， et al. CT scanning： patterns of use and dose[J]. Journal of radiological Protection， 2000， 20（4）： 353.
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