Biodiv Sci ›› 2018, Vol. 26 ›› Issue (7): 690-700. DOI: 10.17520/biods.2018092
Special Issue: 生物多样性与生态系统功能
• Original Papers: Plant Diversity • Previous Articles Next Articles
Received:
2018-03-27
Accepted:
2018-06-03
Online:
2018-07-20
Published:
2018-09-11
Contact:
Huang Xiaorong
About author:
# Co-first authors
Xiaorong Huang. Relationship between plant functional diversity and productivity of Pinus massoniana plantations in Guangxi[J]. Biodiv Sci, 2018, 26(7): 690-700.
编号 No. | 地区 Site | 林龄 Age (yr) | 地上生物量 Above- ground biomass (t·ha-1) | 生产力 Produc- tivity (t·ha-1·yr-1) | 属名优势值 CWM_ genus | 叶面积 优势值 CWM_ leafsize | 比叶面积优势值 CWM_ sla (mm2·mg-1) | 高度优势值 CWM_ height (m) | 生长型 优势值 CWM_ form | 功能团 个数Functional group richness (FGR) | 乔木多度加和值 Sum of tree abundance | 灌木多度加和值 Sum of shrub abundance | 草本多度加和值 Sum of herb abundance |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 老虎岭 Laohuling | 18 | 128 | 7.11 | 木姜子属 Litsea | 大 Large | 12 | 30 | 灌木 Shrub | 6 | 25 | 37 | 15 |
2 | 老虎岭 Laohuling | 18 | 127 | 7.06 | 蜜茱萸属 Melicope | 大 Large | 12 | 30 | 灌木 Shrub | 6 | 30 | 37 | 8 |
3 | 老虎岭 Laohuling | 29 | 161 | 5.55 | 松属 Pinus | 大 Large | 12 | 7 | 乔木 Tree | 6 | 49 | 10 | 12 |
4 | 老虎岭 Laohuling | 29 | 156 | 5.38 | 锥属 Castanopsis | 大 Large | 11 | 10 | 乔木 Tree | 6 | 47 | 16 | 11 |
5 | 老虎岭 Laohuling | 29 | 196 | 6.76 | 锥属 Castanopsis | 大 Large | 11 | 10 | 乔木 Tree | 5 | 43 | 10 | 11 |
6 | 老虎岭 Laohuling | 28 | 125 | 4.46 | 柯属 Lithocarpus | 大 Large | 9.7 | 20 | 乔木 Tree | 3 | 21 | 5 | 13 |
7 | 老虎岭 Laohuling | 28 | 162 | 5.79 | 柯属 Lithocarpus | 大 Large | 9.7 | 20 | 乔木 Tree | 5 | 29 | 6 | 14 |
8 | 老虎岭 Laohuling | 28 | 187 | 6.68 | 柯属 Lithocarpus | 大 Large | 9.7 | 14.5 | 乔木 Tree | 5 | 37 | 11 | 11 |
9 | 老虎岭 Laohuling | 28 | 127 | 4.54 | 柯属 Lithocarpus | 大 Large | 9.7 | 20 | 乔木 Tree | 4 | 24 | 16 | 6 |
10 | 老虎岭Laohuling | 28 | 133 | 4.75 | 柯属 Lithocarpus | 大 Large | 9.7 | 20 | 乔木 Tree | 6 | 29 | 9 | 11 |
15 | 三门江 Sanmenjiang | 57 | 253 | 4.44 | 紫金牛属 Ardisia | 大 Large | 9.7 | 20 | 乔木 Tree | 4 | 35 | 14 | 7 |
16 | 三门江 Sanmenjiang | 57 | 126 | 2.21 | 紫金牛属 Ardisia | 大 Large | 9.7 | 20 | 乔木 Tree | 5 | 39 | 13 | 7 |
17 | 三门江 Sanmenjiang | 57 | 214 | 3.75 | 松属 Pinus | 大 Large | 9.7 | 30 | 乔木 Tree | 4 | 44 | 13 | 13 |
18 | 三门江 Sanmenjiang | 57 | 218 | 3.82 | 柯属 Lithocarpus | 大 Large | 9.7 | 30 | 乔木 Tree | 6 | 37 | 24 | 12 |
19 | 三门江 Sanmenjiang | 57 | 249 | 4.37 | 柯属 Lithocarpus | 大 Large | 9.7 | 30 | 乔木 Tree | 5 | 40 | 15 | 15 |
23 | 苍梧 Cangwu | 11 | 96 | 8.73 | 松属 Pinus | 中 Middle | 15 | 30 | 灌木 Shrub | 6 | 35 | 37 | 22 |
24 | 苍梧 Cangwu | 11 | 97 | 8.82 | 松属 Pinus | 大 Large | 11 | 30 | 乔木 Tree | 6 | 41 | 29 | 28 |
25 | 苍梧 Cangwu | 11 | 83 | 7.55 | 松属 Pinus | 小 Small | 11 | 30 | 乔木 Tree | 6 | 41 | 21 | 32 |
26 | 全州 Quanzhou | 22 | 114 | 5.18 | 松属 Pinus | 中 Middle | 12 | 30 | 草本 Herb | 4 | 20 | 15 | 22 |
27 | 全州 Quanzhou | 22 | 76 | 3.45 | 松属 Pinus | 小 Small | 12 | 30 | 草本 Herb | 5 | 13 | 8 | 26 |
28 | 全州 Quanzhou | 22 | 77 | 3.50 | 松属 Pinus | 小 Small | 12 | 30 | 草本 Herb | 5 | 13 | 13 | 21 |
29 | 全州 Quanzhou | 22 | 54 | 2.45 | 松属 Pinus | 中 Middle | 12 | 30 | 草本 Herb | 5 | 14 | 14 | 20 |
30 | 全州 Quanzhou | 22 | 95 | 4.32 | 松属 Pinus | 中 Middle | 12 | 30 | 草本 Herb | 5 | 17 | 20 | 32 |
31 | 老虎岭 Laohuling | 22 | 151 | 6.86 | 锥属 Castanopsis | 大 Large | 12 | 30 | 乔木 Tree | 5 | 47 | 6 | 7 |
32 | 老虎岭 Laohuling | 22 | 124 | 5.64 | 松属 Pinus | 大 Large | 7.5 | 30 | 乔木 Tree | 6 | 29 | 7 | 10 |
Table 1 Forest characteristics and functional dominance parameters of the plots included in this study
编号 No. | 地区 Site | 林龄 Age (yr) | 地上生物量 Above- ground biomass (t·ha-1) | 生产力 Produc- tivity (t·ha-1·yr-1) | 属名优势值 CWM_ genus | 叶面积 优势值 CWM_ leafsize | 比叶面积优势值 CWM_ sla (mm2·mg-1) | 高度优势值 CWM_ height (m) | 生长型 优势值 CWM_ form | 功能团 个数Functional group richness (FGR) | 乔木多度加和值 Sum of tree abundance | 灌木多度加和值 Sum of shrub abundance | 草本多度加和值 Sum of herb abundance |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 老虎岭 Laohuling | 18 | 128 | 7.11 | 木姜子属 Litsea | 大 Large | 12 | 30 | 灌木 Shrub | 6 | 25 | 37 | 15 |
2 | 老虎岭 Laohuling | 18 | 127 | 7.06 | 蜜茱萸属 Melicope | 大 Large | 12 | 30 | 灌木 Shrub | 6 | 30 | 37 | 8 |
3 | 老虎岭 Laohuling | 29 | 161 | 5.55 | 松属 Pinus | 大 Large | 12 | 7 | 乔木 Tree | 6 | 49 | 10 | 12 |
4 | 老虎岭 Laohuling | 29 | 156 | 5.38 | 锥属 Castanopsis | 大 Large | 11 | 10 | 乔木 Tree | 6 | 47 | 16 | 11 |
5 | 老虎岭 Laohuling | 29 | 196 | 6.76 | 锥属 Castanopsis | 大 Large | 11 | 10 | 乔木 Tree | 5 | 43 | 10 | 11 |
6 | 老虎岭 Laohuling | 28 | 125 | 4.46 | 柯属 Lithocarpus | 大 Large | 9.7 | 20 | 乔木 Tree | 3 | 21 | 5 | 13 |
7 | 老虎岭 Laohuling | 28 | 162 | 5.79 | 柯属 Lithocarpus | 大 Large | 9.7 | 20 | 乔木 Tree | 5 | 29 | 6 | 14 |
8 | 老虎岭 Laohuling | 28 | 187 | 6.68 | 柯属 Lithocarpus | 大 Large | 9.7 | 14.5 | 乔木 Tree | 5 | 37 | 11 | 11 |
9 | 老虎岭 Laohuling | 28 | 127 | 4.54 | 柯属 Lithocarpus | 大 Large | 9.7 | 20 | 乔木 Tree | 4 | 24 | 16 | 6 |
10 | 老虎岭Laohuling | 28 | 133 | 4.75 | 柯属 Lithocarpus | 大 Large | 9.7 | 20 | 乔木 Tree | 6 | 29 | 9 | 11 |
15 | 三门江 Sanmenjiang | 57 | 253 | 4.44 | 紫金牛属 Ardisia | 大 Large | 9.7 | 20 | 乔木 Tree | 4 | 35 | 14 | 7 |
16 | 三门江 Sanmenjiang | 57 | 126 | 2.21 | 紫金牛属 Ardisia | 大 Large | 9.7 | 20 | 乔木 Tree | 5 | 39 | 13 | 7 |
17 | 三门江 Sanmenjiang | 57 | 214 | 3.75 | 松属 Pinus | 大 Large | 9.7 | 30 | 乔木 Tree | 4 | 44 | 13 | 13 |
18 | 三门江 Sanmenjiang | 57 | 218 | 3.82 | 柯属 Lithocarpus | 大 Large | 9.7 | 30 | 乔木 Tree | 6 | 37 | 24 | 12 |
19 | 三门江 Sanmenjiang | 57 | 249 | 4.37 | 柯属 Lithocarpus | 大 Large | 9.7 | 30 | 乔木 Tree | 5 | 40 | 15 | 15 |
23 | 苍梧 Cangwu | 11 | 96 | 8.73 | 松属 Pinus | 中 Middle | 15 | 30 | 灌木 Shrub | 6 | 35 | 37 | 22 |
24 | 苍梧 Cangwu | 11 | 97 | 8.82 | 松属 Pinus | 大 Large | 11 | 30 | 乔木 Tree | 6 | 41 | 29 | 28 |
25 | 苍梧 Cangwu | 11 | 83 | 7.55 | 松属 Pinus | 小 Small | 11 | 30 | 乔木 Tree | 6 | 41 | 21 | 32 |
26 | 全州 Quanzhou | 22 | 114 | 5.18 | 松属 Pinus | 中 Middle | 12 | 30 | 草本 Herb | 4 | 20 | 15 | 22 |
27 | 全州 Quanzhou | 22 | 76 | 3.45 | 松属 Pinus | 小 Small | 12 | 30 | 草本 Herb | 5 | 13 | 8 | 26 |
28 | 全州 Quanzhou | 22 | 77 | 3.50 | 松属 Pinus | 小 Small | 12 | 30 | 草本 Herb | 5 | 13 | 13 | 21 |
29 | 全州 Quanzhou | 22 | 54 | 2.45 | 松属 Pinus | 中 Middle | 12 | 30 | 草本 Herb | 5 | 14 | 14 | 20 |
30 | 全州 Quanzhou | 22 | 95 | 4.32 | 松属 Pinus | 中 Middle | 12 | 30 | 草本 Herb | 5 | 17 | 20 | 32 |
31 | 老虎岭 Laohuling | 22 | 151 | 6.86 | 锥属 Castanopsis | 大 Large | 12 | 30 | 乔木 Tree | 5 | 47 | 6 | 7 |
32 | 老虎岭 Laohuling | 22 | 124 | 5.64 | 松属 Pinus | 大 Large | 7.5 | 30 | 乔木 Tree | 6 | 29 | 7 | 10 |
名称 Name | R代码Argument | 公式 Formula | 说明 Note | 参考文献Reference |
---|---|---|---|---|
功能优势值Community-level weighted means | functcomp (X, comm) $CWM | $CWM=\sum\limits_{i=1}^{n}{{{p}_{i}}}\times trai{{t}_{i}}$ | 式中pi是物种i的多度, traiti为物种i的性状值, n为物种个数。 In formula, pi is the abundance of species i and traiti is the trait value of species i. | et al, 2008 |
功能离散度Functional dispersion | dbFD (X, comm) $FDis | $Fdis=\frac{\sum{{{a}_{j}}{{z}_{j}}}}{\sum{{{a}_{j}}}}$ | 式中aj为物种j的多度, zj为物种j到加权质心的距离。 Here aj is the abundance of species j, zj is the distance of species j to the centroid. | |
功能均匀度Functional evenness | dbFD (X, comm) $FEve | $E{{W}_{l}}=\frac{dist\,(i,j)}{{{w}_{i}}+{{w}_{j}}}$ $PE{{W}_{l}}=\frac{E{{W}_{l}}}{\sum\limits_{l=1}^{S-1}{E{{W}_{l}}}}$ $Feve=\frac{\sum\limits_{l=1}^{S-1}{\min \left( PE{{W}_{l}},\frac{1}{S-1} \right)-\frac{1}{S-1}}}{1-\frac{1}{S-1}}$ | Feve为功能均匀度; EWl为加权均匀度; dist (i, j)是物种i和物种j的欧氏距离; PEWl为偏加权均匀度; S是物种数。 Feve is functional evenness; EWl is weighted evenness, dist (i, j) is the Euclidean distance between species i and j, the species involved is branch l in minimum spanning tree, and wi is the relative abundance of species i; PEWl is the partial weighted evenness of branch l; S is species in the community. | et al, 2008 |
功能团个数 A posteriori functional group richness | dbFD (X, comm, calc.FGR = TRUE) | $FG{{R}_{i}}=Grou{{p}_{present\,in\,plot\,i}}$ | FGRi是样地i包含的功能团个数; 本研究指定按功能团总数为6个来分组; dbFD函数默认不计算FGR, 需指定calc.FGR = TRUE。 FGRi is the number of groups present in plot i; and in this study, total functional group was designated as 6. Default dbFD function has set FGR = FALSE and addition is needed in the argument. | |
功能丰富度Functional richness | dbFD (X, comm) $FRic | $\begin{align} & Fri{{c}_{i}}=\text{Number}\,\text{of}\,\text{unique} \\ & \text{trait}\,\text{combination}\,\text{in}\,\text{plot} \\ \end{align}$ | 纯数值性状情况下默认使用凸壳体算法计算功能丰富度。如果有一个性状为类型变量, 则全部性状都作为类型变量, 样地i的功能丰富度为其包含的独特性状组合的个数。 The default convex hull volume algorithm for quantitative data is suppressed as categorical traits present in ‘X’. Fric is measured as the number of unique trait combinations in this study. | et al, 2008 |
功能多样性Rao’s quadratic entropy | dbFD (X, comm) $RaoQ | $RaoQ=\sum\limits_{i=1}^{S-1}{\sum\limits_{j=i+1}^{S}{{{d}_{ij}}{{p}_{i}}{{p}_{i}}}}$${{d}_{ij}}=\frac{{{u}_{ij}}}{n}$ | 式中dij为物种i和j的距离, pi为物种i的多度, n为研究的性状总数, uij为物种i和j性状值不同的性状数量。 Here dij is the difference between the i-th and j-th species, and pi is abundance of species i; n = total number of traits considered, uij= number of traits with different values in species i and j. |
Table 2 List of functional metrics in this study
名称 Name | R代码Argument | 公式 Formula | 说明 Note | 参考文献Reference |
---|---|---|---|---|
功能优势值Community-level weighted means | functcomp (X, comm) $CWM | $CWM=\sum\limits_{i=1}^{n}{{{p}_{i}}}\times trai{{t}_{i}}$ | 式中pi是物种i的多度, traiti为物种i的性状值, n为物种个数。 In formula, pi is the abundance of species i and traiti is the trait value of species i. | et al, 2008 |
功能离散度Functional dispersion | dbFD (X, comm) $FDis | $Fdis=\frac{\sum{{{a}_{j}}{{z}_{j}}}}{\sum{{{a}_{j}}}}$ | 式中aj为物种j的多度, zj为物种j到加权质心的距离。 Here aj is the abundance of species j, zj is the distance of species j to the centroid. | |
功能均匀度Functional evenness | dbFD (X, comm) $FEve | $E{{W}_{l}}=\frac{dist\,(i,j)}{{{w}_{i}}+{{w}_{j}}}$ $PE{{W}_{l}}=\frac{E{{W}_{l}}}{\sum\limits_{l=1}^{S-1}{E{{W}_{l}}}}$ $Feve=\frac{\sum\limits_{l=1}^{S-1}{\min \left( PE{{W}_{l}},\frac{1}{S-1} \right)-\frac{1}{S-1}}}{1-\frac{1}{S-1}}$ | Feve为功能均匀度; EWl为加权均匀度; dist (i, j)是物种i和物种j的欧氏距离; PEWl为偏加权均匀度; S是物种数。 Feve is functional evenness; EWl is weighted evenness, dist (i, j) is the Euclidean distance between species i and j, the species involved is branch l in minimum spanning tree, and wi is the relative abundance of species i; PEWl is the partial weighted evenness of branch l; S is species in the community. | et al, 2008 |
功能团个数 A posteriori functional group richness | dbFD (X, comm, calc.FGR = TRUE) | $FG{{R}_{i}}=Grou{{p}_{present\,in\,plot\,i}}$ | FGRi是样地i包含的功能团个数; 本研究指定按功能团总数为6个来分组; dbFD函数默认不计算FGR, 需指定calc.FGR = TRUE。 FGRi is the number of groups present in plot i; and in this study, total functional group was designated as 6. Default dbFD function has set FGR = FALSE and addition is needed in the argument. | |
功能丰富度Functional richness | dbFD (X, comm) $FRic | $\begin{align} & Fri{{c}_{i}}=\text{Number}\,\text{of}\,\text{unique} \\ & \text{trait}\,\text{combination}\,\text{in}\,\text{plot} \\ \end{align}$ | 纯数值性状情况下默认使用凸壳体算法计算功能丰富度。如果有一个性状为类型变量, 则全部性状都作为类型变量, 样地i的功能丰富度为其包含的独特性状组合的个数。 The default convex hull volume algorithm for quantitative data is suppressed as categorical traits present in ‘X’. Fric is measured as the number of unique trait combinations in this study. | et al, 2008 |
功能多样性Rao’s quadratic entropy | dbFD (X, comm) $RaoQ | $RaoQ=\sum\limits_{i=1}^{S-1}{\sum\limits_{j=i+1}^{S}{{{d}_{ij}}{{p}_{i}}{{p}_{i}}}}$${{d}_{ij}}=\frac{{{u}_{ij}}}{n}$ | 式中dij为物种i和j的距离, pi为物种i的多度, n为研究的性状总数, uij为物种i和j性状值不同的性状数量。 Here dij is the difference between the i-th and j-th species, and pi is abundance of species i; n = total number of traits considered, uij= number of traits with different values in species i and j. |
生产力Produc- tivity | 林龄 Age | 坡向 Aspect | 功能丰富度 Functional richness (Fric) | 功能均匀度 Functional evenness (Feve) | 功能离散度 Functional dispersion (Fdis) | 功能多样性 Rao’s quadratic entropy (RaoQ) | 功能团个数 Functional group richness (FGR) | Shannon指数 Shannon index (H) | Simpson指数Simpson index (D) | 物种丰富度 Species richness (S) | |
---|---|---|---|---|---|---|---|---|---|---|---|
Age | -0.601** | ||||||||||
Aspect | 0.505* | -0.691** | |||||||||
Fric | 0.761** | -0.342 | 0.333 | ||||||||
Feve | 0.577** | -0.360 | 0.277 | 0.426* | |||||||
Fdis | 0.442* | -0.367 | 0.422* | 0.723** | 0.544** | ||||||
RaoQ | 0.459* | -0.340 | 0.404* | 0.750** | 0.545** | 0.997** | |||||
FGR | 0.449* | -0.336 | 0.177 | 0.615** | 0.231 | 0.597** | 0.611** | ||||
H | 0.608** | -0.442* | 0.536** | 0.814** | 0.626** | 0.899** | 0.900** | 0.529** | |||
D | 0.395 | -0.359 | 0.504* | 0.614** | 0.603** | 0.863** | 0.849** | 0.389 | 0.948** | ||
S | 0.722** | -0.388 | 0.371 | 0.974** | 0.433* | 0.806** | 0.828** | 0.654** | 0.856** | 0.670** | |
均匀度Evenness | 0.441* | -0.408* | 0.568** | 0.596** | 0.659** | 0.830** | 0.815** | 0.348 | 0.943** | 0.990** | 0.644** |
Table 3 Pearson correlation coefficients between productivity and diversity parameters, forest age and aspect
生产力Produc- tivity | 林龄 Age | 坡向 Aspect | 功能丰富度 Functional richness (Fric) | 功能均匀度 Functional evenness (Feve) | 功能离散度 Functional dispersion (Fdis) | 功能多样性 Rao’s quadratic entropy (RaoQ) | 功能团个数 Functional group richness (FGR) | Shannon指数 Shannon index (H) | Simpson指数Simpson index (D) | 物种丰富度 Species richness (S) | |
---|---|---|---|---|---|---|---|---|---|---|---|
Age | -0.601** | ||||||||||
Aspect | 0.505* | -0.691** | |||||||||
Fric | 0.761** | -0.342 | 0.333 | ||||||||
Feve | 0.577** | -0.360 | 0.277 | 0.426* | |||||||
Fdis | 0.442* | -0.367 | 0.422* | 0.723** | 0.544** | ||||||
RaoQ | 0.459* | -0.340 | 0.404* | 0.750** | 0.545** | 0.997** | |||||
FGR | 0.449* | -0.336 | 0.177 | 0.615** | 0.231 | 0.597** | 0.611** | ||||
H | 0.608** | -0.442* | 0.536** | 0.814** | 0.626** | 0.899** | 0.900** | 0.529** | |||
D | 0.395 | -0.359 | 0.504* | 0.614** | 0.603** | 0.863** | 0.849** | 0.389 | 0.948** | ||
S | 0.722** | -0.388 | 0.371 | 0.974** | 0.433* | 0.806** | 0.828** | 0.654** | 0.856** | 0.670** | |
均匀度Evenness | 0.441* | -0.408* | 0.568** | 0.596** | 0.659** | 0.830** | 0.815** | 0.348 | 0.943** | 0.990** | 0.644** |
Fig. 1 Effect of forest age on biomass, productivity and functional richness (means and 95% confidence intervals, varied letters indicating significant difference)
Fig. 2 Relationship between growth form CWM (community weighted means) and productivity, functional richness and functional group richness (means and 95% confidence intervals, varied letters indicating significant difference)
全块分量 Full fractions | 解释率 Adjusted R2 | 单块分量 Individual fractions | 解释率 Adjusted R2 | 偏分量 Controlling 1 matrix | 解释率 Adjusted R2 |
---|---|---|---|---|---|
X1 | 0.33 | X1|X2+X3 | 0.22 | X1|X3 | 0.12 |
X2 | 0.43 | X2|X1+X3 | 0.14 | X1|X2 | 0.31 |
X3 | 0.56 | X3|X1+X2 | 0.08 | X2|X3 | 0.04 |
X1+X2 | 0.74 | X1*X2 | -0.10 | X2|X1 | 0.41 |
X1+X3 | 0.68 | X2*X3 | 0.27 | X3|X1 | 0.35 |
X2+X3 | 0.60 | X3*X1 | 0.09 | X3|X2 | 0.17 |
X1+X2+X3 | 0.83 | X1*X2*X3 | 0.12 | ||
残差Residual | 0.17 |
Table 4 Contributions of explanatory matrices to variance of productivity, partitioning by best-fit varpart model
全块分量 Full fractions | 解释率 Adjusted R2 | 单块分量 Individual fractions | 解释率 Adjusted R2 | 偏分量 Controlling 1 matrix | 解释率 Adjusted R2 |
---|---|---|---|---|---|
X1 | 0.33 | X1|X2+X3 | 0.22 | X1|X3 | 0.12 |
X2 | 0.43 | X2|X1+X3 | 0.14 | X1|X2 | 0.31 |
X3 | 0.56 | X3|X1+X2 | 0.08 | X2|X3 | 0.04 |
X1+X2 | 0.74 | X1*X2 | -0.10 | X2|X1 | 0.41 |
X1+X3 | 0.68 | X2*X3 | 0.27 | X3|X1 | 0.35 |
X2+X3 | 0.60 | X3*X1 | 0.09 | X3|X2 | 0.17 |
X1+X2+X3 | 0.83 | X1*X2*X3 | 0.12 | ||
残差Residual | 0.17 |
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