Using nonlinear mixed model and dummy variable model approaches to develop origin-based individual tree biomass equations Wei-Sheng Zeng
Trees Structure and Function ISSN 0931-1890 Trees DOI 10.1007/s00468-014-1112-0
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Author's personal copy Trees DOI 10.1007/s00468-014-1112-0
ORIGINAL PAPER
Using nonlinear mixed model and dummy variable model approaches to develop origin-based individual tree biomass equations Wei-Sheng Zeng
Received: 17 February 2014 / Revised: 8 October 2014 / Accepted: 10 October 2014 Ó Springer-Verlag Berlin Heidelberg 2014
Abstract Key message Based on above- and below-ground biomass measurements from 604 and 212 sample trees respectively, aboveground biomass models for different origins didn’t have significant difference while belowground biomass models did. Abstract Based on the measurement data of aboveground biomass from 604 sample trees and belowground biomass from 212 sample trees of Chinese fir (Cunninghamia lanceolata) and Masson pine (Pinus massoniana) in southern China, the individual tree above- and belowground biomass models involving forest origin were developed using nonlinear mixed model and dummy variable model approaches, and the effect of forest origin on biomass models was analyzed. The results showed that the aboveground biomass models for different origins had no significant difference, while the belowground biomass models were significantly different; and the belowground biomass estimate of a natural tree was highly greater than that of a planted tree with the same diameter and height. Specially, the belowground biomass estimates of natural trees were nearly 30 % and about 45 % greater than those of planted trees for Chinese fir and Masson pine, respectively. The mean prediction errors of aboveground biomass models and belowground biomass models developed in this
Communicated by R. Matyssek. W.-S. Zeng (&) Department of Forest Resource Management, State Forestry Administration, Beijing 100714, China e-mail:
[email protected] W.-S. Zeng Academy of Forest Inventory and Planning, State Forestry Administration, Beijing 100714, China
study were less than 5 % and 15 %, respectively, which meant the biomass models could be applied to estimate forest biomass of the two species at large scale. Keywords Aboveground biomass Belowground biomass Forest origin Cunninghamia lanceolata Pinus massoniana
Introduction The carbon sequestration capacity of forest ecosystems has increasingly attracted wide public concerns in response to global climate change. Forest biomass is the major index for assessment of the carbon sequestration capacity of forest ecosystems, and individual tree biomass modeling is the basis of forest biomass estimation. Since the 1950s, the scientists of Japan, the former Soviet Union, and England had began to implement field survey and data collection on biomass and productivity of main ecological forest types in their countries (Feng et al. 1999; Xiang et al. 2003). During 1964–1974, the International Union of Forestry Research Organization (IUFRO) executed the International Biological Program (IBP), which promoted the research on global terrestrial forest ecosystem biomass (Xue and Yang 2004; Wang 2006). Especially, forest biomass was considered as an important item in global, regional and national forest resources monitoring by IUFRO (1994), which led to more study of forest biomass worldwide. According to Chojnacky (2002), there were more than 2,300 biomass equations for various wood, bark, foliage, branch, and root components for over 100 species. In recent years, many scholars have made strong efforts to estimate forest biomass at large scale, and developed a number of biomass equations which could be used for widely distributed tree
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Author's personal copy Trees Table 1 The general situation of individual tree biomass modeling samples Species
Origins
Samples
Chinese fir
Natural
86 (29)
Planted
Masson pine
Natural
216 (79)
164 (67)
Variables
Mean
SD
CV/(%)
Diameter D (cm)
17.7
1.6
42.0
12.5
70.4
11.9
1.9
27.0
6.9
58.6
Aboveground biomass Ma (kg)
130.6
0.3
521.4
164.0
125.6
Belowground biomass Mb (kg)
25.7
0.2
101.7
31.3
121.8
Diameter D (cm)
15.9
1.3
42.4
11.5
72.3
Height H (m)
11.3
1.9
33.0
7.2
63.1
Aboveground biomass Ma (kg)
110.0
0.4
644.9
152.1
138.2
Belowground biomass Mb (kg)
25.9
0.1
174.9
40.0
154.3
Diameter D (cm)
16.9
1.2
47.2
9.9
71.9
12.2
1.6
27.8
4.8
55.9
175.9 37.0
0.2 0.1
1,079.3 285.0
59.0 53.5
132.6 144.7
Aboveground biomass Ma (kg) Belowground biomass Mb (kg) 138 (37)
Max
Height H (m)
Height H (m)
Planted
Min
Diameter D (cm)
16.2
1.5
40.7
10.1
73.2
Height H (m)
12.0
1.7
30.3
4.8
63.6
Aboveground biomass Ma (kg)
169.5
0.2
983.6
41.1
133.8
Belowground biomass Mb (kg)
32.7
0.0
234.5
54.8
167.6
The figures in brackets are numbers of sample trees for belowground measurement
species (Jenkins et al. 2003; Zianis et al. 2005; Snorrason and Einarsson 2006; Muukkonen 2007; Na´var 2009; Blujdea et al. 2012; Fayolle et al. 2013). To improve the accuracy of forest carbon accounting, China launched a national program on modeling individual tree biomass for the major tree species in the country in 2009. This program aimed to develop new biomass equations at large-scale for 34 tree species or species groups with a total of 10,500 trees for 70 modeling populations across the country in the near future (Zeng et al. 2010a). Up to now, some preliminary study results of the program have been achieved (Zeng et al. 2010b, 2011; 2013; Yin et al. 2010; Wang et al. 2012; Zeng and Tang 2012). There are obvious differences between natural forests and plantations in species composition, growth process (carbon allocation), productivity and stability (Li et al. 2011). However, among the great amount of literature about biomass worldwide, only a few studies involved the effect of forest origin on individual tree biomass modeling. Wang et al. (2008) studied forest biomass and root-to-shoot ratio allocation in northeastern China, and concluded that forest origin could explain 31–37 % of variation in biomass, and that root-to-shoot ratio biomass relationships differed significantly between natural and planted forests. Zeng and Tang (2010a) established compatible national and regional single tree biomass equations for Masson pine, and concluded that the biomass estimate of natural forest was greater than that of planted forest, but the difference was not statistically significant. Luo et al. (2012) analyzed the rootto-shoot ratios (RSR’s) of forest types across China and concluded that the RSR’s of plantations were lower than
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those of natural forests. Wu et al. (2012) summarized the biomass and productivity of forests in southwestern China and concluded that the biomass of natural forest was greater than that of planted forest. Li and Ning (2012) developed individual tree biomass models by tree origin, site classes and age groups for Masson pine and larch, and the results showed that the biomass models of different origins were not significantly different. To understand the effect of forest origin on individual tree biomass modeling, further studies are necessary. In this study, the author will: (1) utilize the measurement biomass data of 604 sample trees of Chinese fir (Cunninghamia lanceolata) and Masson pine (Pinus massoniana) to analyze whether or not the biomass model parameters of different origins are significantly different through nonlinear mixed model and dummy model approaches (Zeng et al. 2011; Fu et al. 2012; 2013); (2) develop above- and below-ground biomass models applicable at large-scale for the two tree species of great importance, to provide a basis for forest biomass estimation.
Materials and methods Data Data used in this study were from the National Biomass Modeling Program in Continuous Forest Inventory (NBMP-CFI) funded by the State Forestry Administration of China. They included diameter, tree height, above- and below-ground biomass from 604 sample trees of Chinese fir and Masson pine in southern China. The sample trees
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Chinese fir Masson pine
Sample size
302 302
were collected from 11 provinces, i.e., Jiangsu, Zhejiang, Anhui, Fujian, Jiangxi, Hubei, Hunan, Guangdong, Guangxi, Sichuan, and Guizhou (between 35–438N, and 97–1238E). The number of sample trees for each species were distributed evenly in the 10 diameter classes of 2, 4, 6, 8, 12, 16, 20, 26, 32 cm, and C38 cm, and the sample trees in each diameter class was about 30. All sample trees were located by province according to the proportion of stocking volume, and selected by forest origin according to the proportions of natural and planted forest volume. The final composition of all sample trees was: 302 for Chinese fir, where natural and planted trees were 86 and 216, respectively; and also 302 for Masson pine, where natural and planted trees were 164 and 138, respectively. Diameter at breast height of each sample tree was measured in the field. After the tree was felled, the total length of tree (tree height) and length of live crown were also measured. The fresh weights of stem wood, stem bark, branches, and foliage were measured, respectively, and subsamples were selected and weighed in the field. After taken to the laboratory, all subsamples were oven-dried at 85 °C until a constant weight was reached. According to the ratio of dry weight to fresh weight, each compartment biomass could be computed and the above-ground biomass of the tree was obtained by summation. Moreover, about 1/3 sample trees were selected by diameter class and height class for measuring below-ground biomass. The whole roots were excavated out, and fresh weights of stump, coarse roots (more than 10 mm), and small roots (2–10 mm, not including fine roots less than 2 mm) were measured respectively, and subsamples were selected to obtain the ratio of dry weight to fresh weight which were used to compute the belowground biomass. The general situation of modeling samples is showed in Table 1, and the scatterplots between above- or below-ground biomass and diameter for each species are showed in Figs. 1, 2, 3 and 4. Biomass models The common biomass equation is as follows (Parresol 1999; Zianis et al. 2005; Zeng 2011): b
b
b
y ¼ b0 x1 1 x2 2 xj j þ e
ð1Þ
Models
a0
a1
a2
Random parameter ua0
One-variable
0.08997
2.3325
–
±0.00290
Two-variable
0.06451
1.9998
0.5060
±0.00085
One-variable
0.12985
2.3445
–
±0.00000
Two-variable
0.09659
2.0160
0.4783
±0.00002
Fixed parameters
700
Aboveground biomass (kg)
Species
Planted
Natural
600
500 400 300
200 100 0
0
10
20
30
40
50
D (cm)
Fig. 1 The scatterplot between aboveground biomass and diameter for Chinese fir
1200
Aboveground biomass (kg)
Table 2 The parameter estimates of nonlinear mixed aboveground biomass models
Planted
Natural
1000 800 600 400 200 0
0
10
20
D (cm)
30
40
50
Fig. 2 The scatterplot between aboveground biomass and diameter for Masson pine
where y is aboveground biomass (Ma) or belowground biomass (Mb), xj are variables which reflect the dimension of trees, such as diameter at breast height (D) and tree height (H), bj are parameters, and e is the error term. Consideration of a one-variable model based on D or a two-variable model based on both D and H is common in many applications, in this paper, both one- and two-variable models will be developed. The two-variable models for above- and below-ground biomass are expressed, respectively as: Ma ¼ a0 Da1 H a2 þ e
ð2Þ
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Belowground biomass (kg)
200
Planted
method was more feasible. In this study, both mixed model and dummy variable model approaches were applied and compared.
Natural
160 120
Modeling methods
80
Nonlinear mixed model
40 0
0
10
20
D (cm)
30
40
50
Fig. 3 The scatterplot between belowground biomass and diameter for Chinese fir
Belowground biomass (kg)
300
Planted
Natural
250 200 150 100 50 0
0
10
20
D (cm)
30
40
50
Fig. 4 The scatterplot between belowground biomass and diameter for Masson pine
Mb ¼ b0 Db1 H b2 þ e
ð3Þ
where ai, bi are parameters of above- and below-ground biomass models, respectively, and the other symbols are same as above. If the terms involving H in Eqs. (2) and (3) are omitted, then the equations are becoming one-variable models. Because the data of biomass are heteroscedastic significantly, some countermeasures should be taken to eliminate heteroscedasticity for parameter estimation. In this study, weighted regression approach was applied, and the specific weight functions were derived from the residuals of independently fitted equations by ordinary least squares (Parresol 1999; Zeng 2011; Zeng and Tang 2011a). To analyze the effect of forest origin on individual tree above- and below-ground biomass models, the author used the nonlinear mixed model and dummy variable model approaches to test the significance of the parameter reflecting the effect of forest origin. According to the conclusion from related studies (Wang et al. 2008; Fu et al. 2012), in the case of large sample, the mixed model and dummy variable model approaches were not significantly different from each other while the mixed modeling
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A mixed model is a model that includes both fixed-effect variables and random-effect variables. In recent years, the nonlinear mixed model method was widely applied in forestry modeling (Meng et al. 2008; Li and Zhang 2010; Fu et al. 2013). In this study, the author used the nonlinear mixed model method to develop origin-specific biomass models. The author defined a discrete variable z as randomeffect variable to reflect the difference of two origins, and defined diameter D and height H, which reflected the dimensions of a tree, as fixed-effect variables. The general forms of nonlinear mixed two-variable above- and belowground biomass models are respectively expressed as: Ma ¼ ða0 þ ua0 zÞDða1 þua1 zÞ H ða2 þua2 zÞ þ e
ð4Þ
Mb ¼ ðb0 þ ub0 zÞDðb1 þub1 zÞ H ðb2 þub2 zÞ þ e
ð5Þ
where Ma, Mb are above- and below-ground biomass, ai, bi are fixed parameters, uai, ubi are random parameters, which are independent to each other and the mathematical expectation value is zero, that is, E(uai) = 0 or E(ubi) = 0, and cov (uai, uaj) = 0 or cov (ubi, ubj) = 0 for (i = j). Whether or not random parameters uai, or ubi are significantly different from zero depends upon the significance test results. If random parameters uai or ubi were not significantly different from zero, then we subtracted them from the model and developed a generalized model (or population average model) suitable for different origins. Dummy variable model A dummy model is a model that includes dummy variable(s). If a variable z was defined as a dummy variable to indicate whether the tree origin was natural or planted, then the mixed model could be changed to a dummy model. The dummy model method was also frequently used in forestry modeling (Wang et al. 2008; Zeng et al. 2011; Fu et al. 2012). The general forms of dummy model corresponding to mixed models (2) and (3) are respectively expressed as: Ma ¼ ða0 þ va0 zÞDða1 þva1 zÞ H ða2 þva2 zÞ þ e
ð6Þ
Mb ¼ ðb0 þ vb0 zÞDðb1 þvb1 zÞ H ðb2 þvb2 zÞ þ e
ð7Þ
where Ma, Mb are above- and below-ground biomass, ai, bi are global parameters, and vai, vbi are origin-specific parameters. To ensure the comparability between global
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parameters in dummy models and fixed parameters in mixed models, the author changed assignment of dummy variable from (0, 1) to (1,-1), namely, z = 1 for natural forest and z = -1 for plantation. In this way, the estimated values of origin-specific parameter vai or vbi were positive and negative offset, which performed similar feature as random parameter uai or ubi in the mixed model. Consequently, from comparing the estimated values of vai and uai or vbi and ubi, the difference between dummy model and mixed model could be analyzed. Model evaluation Many statistical indices could be used to evaluate individual tree biomass models (Parresol 1999). Zeng and Tang (2011b) conducted a synthetic analysis on the evaluation of individual tree biomass models, and presented six important ones, namely the coefficient of determination (R2), standard error of estimate (SEE), mean prediction error (MPE), total relative error (TRE), average systematic error (ASE) and mean average percent standard error (MPSE). In this study, the same six statistical indices were used for model evaluation: X X R2 ¼ 1 ðyi y^i Þ2 = ðyi yÞ2 ð8Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X ð9Þ SEE ¼ ðyi y^i Þ2 =ðn pÞ X X TRE ¼ ðyi y^i Þ= y^i 100 ð10Þ X ASE ¼ ðyi y^i Þ=^ yi =n 100 ð11Þ pffiffiffi yÞ= n 100 ð12Þ MPE ¼ ta ðSEE= X MPSE ¼ ð13Þ yi j=n 100 jðyi y^i Þ=^ where yi are observed values, y^i are estimated values, y is mean value of samples, n is the number of samples, p is the number of parameters, and ta is the t-value at confidence level a with n-p degrees of freedom.
Results Aboveground biomass models Based on the measurements of diameter, height, origin, and aboveground biomass of 604 sample trees for Chinese fir and Masson pine across their whole distribution ranges in China, the author fitted the two-variable model (5) and the corresponding one-variable model using the ‘‘nonlinear mixed model’’ approach with the ForStat software (Tang et al. 2008; Fu et al. 2013). The results showed that the random effects of ua1 and ua2 were not significantly
different from zero, indicating that the exponent parameters of different origins in the aboveground biomass models were not statistically different, and thus might take the same value in the models. Then the author refitted one- and two-variable aboveground biomass models again by removing the random effects of ua1 and ua2, and the results of parameter estimates are listed in Table 2. The results in Table 2 show that the estimates of random parameter ua0 in both one- and two-variable models for Masson pine are close to zero, indicating that forest origin does not affect the estimation of aboveground biomass. And for Chinese fir, the aboveground biomass estimates of natural trees are slightly greater than those of planted trees. Exactly, the estimate of natural trees from one-variable model is 6.7 % greater than that of planted trees, and that from two-variable model is 2.7 % greater. However, the differences are not statistically significant, even for one-variable model, the statistical index for confidence is 0.12, which has not yet reached ‘‘low significant’’ level with a = 0.10. When the dummy variable model approach was used to fit the one- and two-variable models for Chinese fir, the biomass estimates of natural trees were 8.3 and 4.3 % greater, respectively than those of planted trees. The difference of biomass estimates from one-variable model was statistically ‘‘significant’’ at a = 0.05 level, but the difference from two-variable model had not yet reached ‘‘low significant’’ level with a = 0.10 (see Table 3). In summary, the estimates of random or specific parameters reflecting forest origin in seven aboveground biomass models, among a total number of eight models developed using the mixed model and dummy variable model approaches for two tree species, were not significantly different from zero. Therefore, the origin-free or generalized aboveground biomass models were finally established, and the fitting results are listed in Table 4. It was found that the statistical indices of two-variable models were slightly better than those of one-variable models, but the difference was not great. It was also found that the statistical indices of biomass models for Chinese fir were better than those for Masson pine, the determination coefficients (R2) of one- and two-variable models for Chinese fir were more than 0.96, and the mean prediction errors (MPE’s) were less than 3 %. Moreover, one- and two-variable stem volume equations were also fitted through using nonlinear mixed model approach. The results showed that whether Chinese fir or Masson pine, all random parameters in the volume equations were nearly equal to zero, indicating that forest origin did not affect stem volume model, and origin-free stem volume model for each tree species was suitable for all natural forests and plantations.
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Author's personal copy Trees Table 3 The parameter estimates of nonlinear dummy aboveground biomass models Species
Sample size
Models
Global parameters
Specific parameter
a0
a1
a2
va0
0.08992
2.3317
–
0.00359a
Chinese fir
302
One-variable Two-variable
0.06456
2.0059
0.4977
0.00136
Masson pine
302
One-variable
0.12987
2.3444
–
0.00011
Two-variable
0.09655
2.0156
0.4788
0.00028
a
Indicating significant at a = 0.05 level
Table 4 The parameter estimates and statistical indices of aboveground biomass models Species
Chinese fir Masson pine
Sample size
302 302
Models
Parameter estimates
Statistical indices
a0
a1
a2
R2
SEE
TRE (%)
ASE (%)
MPE/%
MPSE (%)
One-variable
0.09201
2.3292
–
0.9624
30.22
2.83
0.77
2.96
21.48
Two-variable
0.06500
1.9892
0.5173
0.9780
23.17
0.89
5.36
2.27
22.21
One-variable
0.12985
2.3445
–
0.9299
61.00
0.17
0.95
4.00
23.54
Two-variable
0.09659
2.0160
0.4782
0.9410
56.05
0.36
2.96
3.67
22.30
Table 5 The fitting results of nonlinear mixed belowground biomass models Species
Chinese fir Masson pine a
Sample size
108 104
Models
Fixed parameters b0
b1
b2
Random parameter ub0
One-variable
0.05402
2.0096
–
±0.00617a
Two-variable
0.04950
1.4956
0.61767
±0.00694a
One-variable
0.02521
2.2979
–
Two-variable
0.02967
2.5100
-0.30309
Statistical indices R2
SEE
TRE/ %
ASE/ %
MPE/ %
MPSE/ %
0.7259
19.83
25.36
0.7152
20.31
27.97
2.46
14.61
40.36
3.54
14.97
±0.00457a
0.7676
26.03
40.50
20.13
3.62
14.26
41.13
±0.00551a
0.7641
26.10
20.53
4.51
14.29
41.73
Indicating significant at a = 0.05 level
Belowground biomass models Based on the measurements of diameter, height, origin, and belowground biomass of 212 sample trees for Chinese fir and Masson pine, one- and two-variable belowground biomass models were fitted using the ‘‘nonlinear mixed model’’ approach with the ForStat software (Tang et al. 2008; Fu et al. 2013). The results showed that the random effects of ub1 and ub2 were not significantly different from zero, indicating that the exponent parameters of different origins in the belowground biomass models were not statistically different and thus might take the same value in the models. Then one- and two-variable aboveground biomass models were refitted again by removing the random effects of ub1 and ub2, and the fitting results are listed in Table 5. The results in Table 5 show that whether one- or twovariable models, the random parameter ub0 in the belowground biomass models for both Chinese fir and Masson
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pine is significantly different from zero, indicating that forest origin does obviously affect the belowground biomass models. According to the estimates of random parameter ub0, the random effect on natural trees was positive and that on planted trees was negative, which indicated that the belowground biomass estimates of natural trees were greater than those of planted trees. From the exact values in Table 5, it is found that the estimate of natural trees from one-variable model for Chinese fir is 26 % greater than that of planted trees, and that from twovariable model is 33 % greater. And for Masson pine, the estimates of natural trees from one- and two-variable models are 44 % and 46 % greater, respectively than those of planted trees. When the dummy variable model approach was used to fit the belowground biomass models, the differences between natural and planted trees were greater than those in mixed models. The estimates of natural trees from one- and two-variable models for Chinese fir were 34 % and 39 % greater, respectively than those of planted trees, while
Author's personal copy Trees Table 6 The fitting results of nonlinear dummy belowground biomass models Species
Chinese fir Masson pine a
Sample size
108 104
Models
One-variable
Global parameters b0
b1
b2
Specific parameter vb0
Statistical indices R2
SEE
TRE/ %
ASE/ %
MPE/ %
MPSE/ %
0.05729
1.9892
–
0.00827a
0.7021
20.68
28.19
3.83
15.24
41.22
a
Two-variable
0.05184
1.4768
0.62118
0.00853
0.6970
20.95
30.29
4.70
15.44
41.11
One-variable
0.02609
2.2771
–
0.00555a
0.7477
27.12
23.27
5.56
14.85
42.67
Two-variable
0.03092
2.5063
-0.32500
0.00668a
0.7451
27.13
23.51
6.62
14.86
43.28
Indicating significant at a = 0.01 level
the estimates of natural trees from one- and two-variable models for Masson pine were 54 % and 55 % greater, respectively than those of planted trees (see Table 6). From the statistical indices in Tables 5 and 6, it is found that the one-variable belowground biomass models are slightly better than the two-variable models, and the mixed models are also slightly better than the dummy variable models. It is also found that the belowground biomass models for Masson pine are slightly better than those for Chinese fir, but the difference is not great; and the MPE’s of all belowground biomass mixed model for two species are less than 15 %. In addition, based on the measurements of diameter, height, origin, and aboveground biomass of 212 sample trees for Chinese fir and Masson pine, one- and two-variable aboveground biomass mixed models were fitted. The results show that all random parameters of mixed models for Chinese fir and Masson pine are close to zero, indicating that in the case of smaller sample size similar fitting results as those in Sect. ‘‘Aboveground biomass models’’ are obtained. Forest origin has no significant effect on aboveground biomass models, but does affect the belowground biomass, and also affects the root-to-shoot ratio. According to the analysis results for Chinese fir and Masson pine, the root-to-shoot ratio of trees from natural forests was about one-third to half greater than that of trees from plantations.
Discussion and conclusions In this study, using the nonlinear mixed model approach, the above- and below-ground biomass models and stem volume models were developed, and the effect of forest origin on estimation of biomass and volume was analyzed. The results showed that the effects of forest origin on estimation of aboveground biomass and stem volume were small and not statistically significant, indicating that the effects were not necessary to take into consideration when developing aboveground biomass and volume models. However, the effect of forest origin on estimation of
belowground biomass could not be ignorable, because the belowground biomass estimates of trees with different origins were significantly different from each other, and the belowground biomass estimate of trees from natural forests was obviously greater than that of trees from plantations. These findings were consistent with the conclusions from Wang et al. (2008) and Wu et al. (2012). The belowground biomass of natural trees was greater than that of planted trees indicating that the roots of natural trees developed better than those of planted trees, and suggesting that the natural forests performed better ecological functions of water and soil conservation, carbon fixation, and oxygen release than plantations. As for the two species of Chinese fir and Masson pine, the differences of belowground biomass estimates between natural and planted trees were not the same. The belowground biomass estimate of natural trees for Chinese fir was about 30 % greater than that of planted trees while the estimate for Masson pine was about 45 % greater. Chinese fir and Masson pine belong to shallow and deep rooted species, respectively, whether or not the differences of belowground biomass between natural and planted trees are related to root characters of tree species still needs further study. The dummy variable model approach was also an effective method for developing origin-specific biomass models. According to the available study conclusions (Wang et al. 2008; Zeng et al. 2011; Fu et al. 2012), in the case of large sample size, it does not matter much to use dummy model or mixed model; but in the case of small sample size, the mixed model method is recommended. The results of this study showed that the differences of aboveground biomass estimates from mixed model and dummy model (the sample sizes were both 302 for Chinese fir and Masson pine) between natural and planted trees were less than 2 %, while the differences of belowground biomass estimates from mixed model and dummy model (the sample sizes were 108 and 104 respectively for Chinese fir and Masson pine) between natural and planted trees were 7–8 % and 9–10 %, respectively for Chinese fir and Masson pine. These results were completely consistent to the conclusions aforementioned. In fact, the mixed model
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might be regarded as a compromise between the dummy model in which the specific parameters were fixed and the population average (PA) model (or generalized model) in which the specific parameter was zero. It can be expected that the smaller the sample sizes, the greater the random effects, the closer to the PA model the mixed model will be; and vice versa, the larger the sample sizes, the smaller the random effects, the closer to the dummy model the mixed model will be. From the results of this study, it was found that the mixed model performed better than dummy variable model. Therefore, no matter how the sample size, it is the best choice to use the mixed model approach. The focus of this paper was to analyze the effect of forest origin on aboveground biomass and belowground biomass. The development of biomass models had not considered the coordination between above- and belowground biomass, and the compatibility between aboveground biomass and stem volume. About these issues, there were many literature to be referenced (Zeng and Tang 2010b, 2011c, 2012; Wang et al. 2012; Zeng et al. 2013). If necessary, the nonlinear mixed model, dummy model and error-in-variable simultaneous equations could be utilized comprehensively to construct an integrated system including origin-specific above- and below-ground biomass equations, and compatible biomass conversion factor functions and root-to-shoot ratio models. Author contribution statement The author made substantial contributions to conception and design, model development, and analysis and discussion of results; and drafted the manuscript and gave final approval of the version to be submitted and any revised version. Acknowledgments The author acknowledges the Forest Biomass Modeling Project of the National Forest Inventory and Monitoring Program (No: 2030208), which was funded by the State Forestry Administration of China, for providing biomass mensuration data of C. lanceolata and P. massoniana, and thanks the project staff of East China Forest Inventory and Planning Institute and Central South Forest Inventory and Planning Institute for biomass data collection. Conflict of interest interest.
The author declares that he has no conflict of
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