# Allometries for Widely Spaced Populus ssp. and Betula ssp. in Nurse Crop Systems

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area and Forests

#### 2.2. Biomass Sampling

#### 2.3. Supportive Information from the Literature

**Table 1.**Allometric biomass equations and parameters (a, b, c) compiled from the literature as used in this study.

Publication | Compartment | Species | Allometric equation | a | b | c |
---|---|---|---|---|---|---|

André (2010) et al. [39] | TotalAboveground | Q. petraea | $a\times {(\pi \times dbh)}^{b}$ | 0.009 | 2.428 | n.a. |

Fatemi (2011) et al. [40] | TotalAboveground | B. papyrifera | ${10}^{(a+b\times {log}_{10}\left(dbh\right))}$ | 1.99 | 2.538 | n.a. |

Fatemi (2011) et al. [40] | StemWood | B. papyrifera | ${10}^{(a+b\times {log}_{10}\left(dbh\right))}$ | 1.739 | 2.638 | n.a. |

Fatemi (2011) et al. [40] | StemBark | B. papyrifera | ${10}^{(a+b\times {log}_{10}\left(dbh\right))}$ | 0.823 | 2.711 | n.a. |

Fatemi (2011) et al. [40] | Branch | B. papyrifera | ${10}^{(a+b\times {log}_{10}\left(dbh\right))}$ | 1.476 | 2.195 | n.a. |

Fatemi (2011) et al. [40] | Leaves | B. papyrifera | ${10}^{(a+b\times {log}_{10}\left(dbh\right))}$ | 0.622 | 2.485 | n.a. |

Grote (2003) et al. [22] | TotalAboveground | Q. petraea | $a\times {((\pi /4)\times \left(db{h}^{2}\right))}^{b}$ | 0.131 | 1.316 | n.a. |

Johansson (1999) [41] | TotalAboveground | P. tremula | $a\times db{h}^{b}$ | 0.000146 | 2.604 | n.a. |

Johansson (1999) [41] | Stem | P. tremula | $a\times db{h}^{b}$ | 0.000065 | 2.74 | n.a. |

Johansson (1999) [41] | Branch | P. tremula | $a\times db{h}^{b}$ | 0.000515 | 1.873 | n.a. |

Johansson (1999) [41] | Leaves | P. tremula | $a\times db{h}^{b}$ | 0.000847 | 1.416 | n.a. |

Johansson & Karačić (2011) [42] | TotalAboveground | P. nigra × P. doltoides | $a\times db{h}^{b}$ | 0.00028 | 2.459 | n.a. |

Johansson & Karačić (2011) [42] | Stem | P. nigra × P. doltoides | $a\times db{h}^{b}$ | 0.00021 | 2.462 | n.a. |

Johansson & Karačić (2011) [42] | Branch | P. nigra × P. doltoides | $a\times db{h}^{b}$ | 0.00001 | 2.709 | n.a. |

Johansson & Karačić (2011) [42] | Leaves | P. nigra × P. doltoides | $a\times db{h}^{b}$ | 0.00042 | 1.926 | n.a. |

Johansson (1999) [43] | TotalAboveground | B. pendula | $a\times db{h}^{b}$ | 0.00087 | 2.286 | n.a. |

Johansson (1999) [43] | Stem | B. pendula | $a\times db{h}^{b}$ | 0.0008 | 2.282 | n.a. |

Johansson (1999) [43] | Branch | B. pendula | $a\times db{h}^{b}$ | 0.00002 | 2.63 | n.a. |

Johansson (1999) [43] | Leaves | B. pendula | $a\times db{h}^{b}$ | 0.004 | 1.12 | n.a. |

Johansson (1999) [43] | TotalAboveground | B. pubescens | $a\times db{h}^{b}$ | 0.00004 | 2.5 | n.a. |

Johansson (1999) [43] | Branch | B. pubescens | $a\times db{h}^{b}$ | 0.00029 | 2.53 | n.a. |

Johansson (1999) [43] | Leaves | B. pubescens | $a\times db{h}^{b}$ | 0.0009 | 1.477 | n.a. |

Johansson (1999) [43] | Stem | B. pubescens | $a\times db{h}^{b}$ | 0.0002 | 2.543 | n.a. |

Muukkonen (2007) [44] | TotalAboveground | Q. spp. | $exp(a+((b\times dbh)/(dbh+c)\left)\right)$ | −0.604 | 10.677 | 15.9 |

Pastor et al. (1984) [45] | TotalAboveground | P. tremuloides | $a\times db{h}^{b}$ | 0.086 | 2.449 | n.a. |

Pastor et al. (1984) [45] | Stem | P. tremuloides | $a\times db{h}^{b}$ | 0.07 | 2.423 | n.a. |

Pastor et al. (1984) [45] | Branch | P. tremuloides | $a\times db{h}^{b}$ | 0.012 | 2.349 | n.a. |

Rock (2007) [34] | Stem | P. tremula × P. tremuloides | $a\times db{h}^{b}$ | 0.0197 | 2.764 | n.a. |

Rock (2007) [34] | Branch | P. tremula × P. tremuloides | $a\times db{h}^{b}$ | 0.064 | 2.001 | n.a. |

Rock (2007) [34] | TotalAboveground | P. tremula × P. tremuloides | $a\times db{h}^{b}$ | 0.052 | 2.545 | n.a. |

Ruark & Bockheim (1988) [46] | StemWood | P. tremoloides | $exp(a+b\times log(dbh\left)\right)$ | −3.202 | 2.606 | n.a. |

Ruark & Bockheim (1988) [46] | StemBark | P. tremoloides | $exp(a+b\times log(dbh\left)\right)$ | −4.532 | 2.552 | n.a. |

Ruark & Bockheim (1988) [46] | Branch | P. tremoloides | $exp(a+b\times log(dbh\left)\right)$ | −5.04 | 2.695 | n.a. |

Ruark & Bockheim (1988) [46] | Twig | P. tremoloides | $exp(a+b\times log(dbh\left)\right)$ | −5.701 | 1.73 | n.a. |

this study | TotalAboveground | P. tremula × P. tremuloides | $a\times db{h}^{b}\times {h}^{c}$ | 0.021 | 2.084 | 0.936 |

this study | StemWood | P. tremula × P. tremuloides | $a\times db{h}^{b}\times {h}^{c}$ | 0.006 | 1.557 | 1.743 |

this study | StemBark | P. tremula × P. tremuloides | $a\times db{h}^{b}\times {h}^{c}$ | 0.007 | 1.763 | 0.818 |

this study | Branch | P. tremula × P. tremuloides | $a\times db{h}^{b}\times {h}^{c}$ | 0.015 | 3.301 | −0.684 |

this study | TotalAboveground | B. pendula × B. pubscenes | $a\times db{h}^{b}\times {h}^{c}$ | 0.019 | 1.944 | 1.154 |

this study | StemWood | B. pendula × B. pubscenes | $a\times db{h}^{b}\times {h}^{c}$ | 0.012 | 1.432 | 1.708 |

this study | StemBark | B. pendula × B. pubscenes | $a\times db{h}^{b}\times {h}^{c}$ | 0.098 | 2.088 | −0.486 |

this study | Branch | B. pendula × B. pubscenes | $a\times db{h}^{b}\times {h}^{c}$ | 0.001 | 2.862 | 0.779 |

this study | TotalAboveground | Q. spp. | $a\times db{h}^{b}\times {h}^{c}$ | 0.161 | 2.122 | 0.21 |

Suchomel et al. (2012) [28] | TotalAboveground | Q. petraea | $a\times db{h}^{b}$ | 0.093 | 2.51 | n.a. |

Telenius (1999) [47] | TotalAboveground | P. tremula × P. tremoloides | $a+b\times db{h}^{c}$ | −718.281 | 3.565 | 1.738 |

Telenius (1999) [47] | TotalAboveground | B. pendula | $a+b\times db{h}^{c}$ | 32.317 | 0.329 | 2.328 |

Tullus et al. (2009) [48] | TotalAboveground | P. tremula × P. tremuloides | $a\times db{h}^{b}$ | 107.719 | 2.237 | n.a. |

Tullus et al. (2009) [48] | Stem | P. tremula × P. tremuloides | $a\times db{h}^{b}$ | 61.208 | 2.386 | n.a. |

Tullus et al. (2009) [48] | Branch | P. tremula × P. tremuloides | $a\times db{h}^{b}$ | 23.374 | 2.161 | n.a. |

Tullus et al. (2009) [48] | BranchNew | P. tremula × P. tremuloides | $a\times db{h}^{b}$ | 18.819 | 1.651 | n.a. |

Uri et al. (2007) [36] | TotalAboveground | B. pendula | $a\times db{h}^{b}$ | 142.19 | 2.25 | n.a. |

Uri et al. (2007) [36] | Stem | B. pendula | $a\times db{h}^{b}$ | 118.74 | 2.19 | n.a. |

Uri et al. (2007) [36] | BranchOld | B. pendula | $a\times db{h}^{b}$ | 12.68 | 2.33 | n.a. |

Uri et al. (2007) [36] | BranchNew | B. pendula | $a\times db{h}^{b}$ | 0.93 | 3.25 | n.a. |

Uri et al. (2007) [36] | Leaves | B. pendula | $a\times db{h}^{b}$ | 7.54 | 2.58 | n.a. |

Wang et al. (2002) [29] | StemWood | P. tremoloides | $a\times db{h}^{b}$ | 0.042 | 2.64 | n.a. |

Wang et al. (2002) [29] | StemBark | P. tremoloides | $a\times db{h}^{b}$ | 0.003 | 3.033 | n.a. |

Wang et al. (2002) [29] | Branch | P. tremoloides | $a\times db{h}^{b}$ | 0.001 | 3.161 | n.a. |

Wang (2006) [49] | Stem | P. davidiana | ${10}^{(a+b\times log10(dbh\left)\right)}$ | 1.836 | 2.471 | n.a. |

Wang (2006) [49] | Branch | P. davidiana | ${10}^{(a+b\times log10(dbh\left)\right)}$ | 0.129 | 3.224 | n.a. |

Wang et al. (1996) [50] | StemWood | B. papyrifera | $a\times db{h}^{b}$ | 0.028 | 2.64 | n.a. |

Wang et al. (1996) [50] | StemBark | B. papyrifera | $a\times db{h}^{b}$ | 0.037 | 2.164 | n.a. |

Wang et al. (1996) [50] | Branch | B. papyrifera | $a\times db{h}^{b}$ | 0.002 | 2.913 | n.a. |

Wang (2006) [49] | Stem | B. platyphylla | ${10}^{(a+b\times {log}_{10}\left(dbh\right))}$ | 2.141 | 2.278 | n.a. |

Wang (2006) [49] | Branch | B. platyphylla | ${10}^{(a+b\times {log}_{10}\left(dbh\right))}$ | 0.952 | 2.783 | n.a. |

Zabek & Prescott (2006) [51] | Stem | P. trichocarpa × P. deltoides | $a\times db{h}^{b}\times {h}^{c}$ | 0.008 | 1.247 | 1.827 |

Zabek & Prescott (2006) [51] | Branch | P. trichocarpa × P. deltoides | $a\times db{h}^{b}\times {h}^{c}$ | 0.01 | 1.492 | 1.023 |

Zell (2008) [52] | TotalAboveground | Q. spp. | $a\times db{h}^{b}$ | 0.121 | 2.435 | n.a. |

#### 2.4. Stand Density Effects on Tree Height-to-Diameter Ratio in Aspen and Birch Stands

#### 2.5. Stand Density Effects on Allocation of Branch Biomass in Aspen and Birch Stands

#### 2.6. Allometric Biomass Equations

#### 2.7. Performance of Allometric Models and Comparison with Literature Allometries

#### 2.8. Statistical Analysis

## 3. Results

#### 3.1. Study Forests

Site | Species | Basal Area | Stand Density | dbh | Height | |||||
---|---|---|---|---|---|---|---|---|---|---|

Mean | Min. | Max. | Mean | Min. | Max. | |||||

m^{2}/ha | N/ha | cm | cm | cm | m | m | m | |||

K | Aspen | 17.9 | 541.0 | 19.4 | 4.0 | 30.5 | 15.5 | 12.0 | 18.8 | |

Birch | 13.3 | 481.3 | 17.9 | 2.5 | 31.0 | 12.9 | 9.7 | 15.7 | ||

Oak mono | 22.1 | 4219.3 | 7.5 | 3.0 | 16.0 | 9.0 | 7.1 | 10.3 | ||

Oak under Aspen | 1.5 | 2497.0 | 2.5 | 0.4 | 6.2 | 3.9 | 1.5 | 6.4 | ||

Oak under Birch | 1.5 | 2499.2 | 2.5 | 0.4 | 7.9 | 3.6 | 1.3 | 7.9 | ||

S | Aspen | 10.6 | 445.9 | 16.9 | 7.3 | 23.2 | 13.8 | 10.4 | 16.4 | |

Birch | 12.8 | 499.8 | 17.4 | 6.0 | 28.0 | 10.9 | 9.2 | 13.0 | ||

Oak mono | 11.8 | 3841.6 | 5.8 | 2.0 | 13.8 | 7.7 | 6.1 | 8.7 | ||

Oak under Aspen | 0.9 | 1664.7 | 2.4 | 0.8 | 5.4 | n.a. | n.a. | n.a. | ||

Oak under Birch | 0.9 | 1665.0 | 2.5 | 0.6 | 5.5 | n.a. | n.a. | n.a. |

#### 3.2. Stand Density Effects

**Figure 1.**Relationship between height-to-diameter (h/d) ratio and stand density (N/ha) for a selection of stand ages according to data compiled from the literature [Equation (1)].

**Figure 2.**Relationship between allocation of biomass and diameter at breast height (dbh, top), stand density (N/ha, middle), or tree age (bottom) [Equation (2)].

#### 3.3. Allometric Biomass Equations and Analysis of Model Performance

**Table 3.**Parameter estimates, p-values, residual standard errors (ResSE), and ${R}^{2}$ (calculated as one minus residual sum of squares divided by total sum of squares) for allometric biomass equations using diameter at breast height as explanatory variable [Equation (4)].

Species | Compartment | ${\beta}_{1}^{\left(3\right)}$ | ${\beta}_{2}^{\left(3\right)}$ | ${\beta}_{3}^{\left(3\right)}$ | n | ResSE | ps.${R}^{2}$ | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Est. | St.Err. | p-value | Est. | St.Err. | p-value | Est. | St.Err. | p-value | |||||

Aspen | stem wood | 0.197 | 0.102 | 0.070 | 2.032 | 0.173 | 0.0 | n.a. | n.a. | n.a. | 19 | 9.638 | 0.94 |

stem bark | 0.035 | 0.011 | 0.005 | 1.985 | 0.103 | 0.0 | 0.031 | 0.014 | 0.046 | 19 | 0.938 | 0.96 | |

branch | 0.004 | 0.004 | 0.352 | 3.182 | 0.342 | 0.0 | −0.081 | 0.033 | 0.026 | 19 | 6.843 | 0.87 | |

aboveground woody | 0.132 | 0.059 | 0.040 | 2.339 | 0.149 | 0.0 | n.a. | n.a. | n.a. | 19 | 12.527 | 0.97 | |

Birch | stem wood | 0.138 | 0.061 | 0.036 | 2.029 | 0.144 | 0.0 | 0.104 | 0.020 | 0.0 | 20 | 7.841 | 0.86 |

stem bark | 0.053 | 0.022 | 0.025 | 1.872 | 0.133 | 0.0 | n.a. | n.a. | n.a. | 20 | 1.578 | 0.96 | |

branch | 0.002 | 0.002 | 0.159 | 3.282 | 0.215 | 0.0 | n.a. | n.a. | n.a. | 20 | 5.840 | 0.97 | |

aboveground woody | 0.093 | 0.041 | 0.037 | 2.385 | 0.144 | 0.0 | 0.061 | 0.017 | 0.003 | 20 | 13.097 | 0.94 | |

Oak mono | stem wood | 0.097 | 0.023 | 0.0 | 2.236 | 0.099 | 0.0 | 0.060 | 0.022 | 0.011 | 35 | 2.622 | 0.95 |

stem bark | 0.052 | 0.012 | 0.0 | 1.874 | 0.091 | 0.0 | n.a. | n.a. | n.a. | 35 | 0.581 | 0.93 | |

branch | 0.102 | 0.031 | 0.002 | 2.135 | 0.129 | 0.0 | −0.117 | 0.027 | 0.0 | 40 | 2.275 | 0.84 | |

aboveground woody | 0.23 | 0.034 | 0.0 | 2.169 | 0.058 | 0.0 | n.a. | n.a. | n.a. | 40 | 3.334 | 0.98 | |

Oak under nurse crops | aboveground woody | 0.138 | 0.025 | 0.0 | 2.341 | 0.092 | 0.0 | n.a. | n.a. | n.a. | 16 | 0.655 | 0.98 |

Oak overall | aboveground woody | 0.212 | 0.026 | 0.0 | 2.199 | 0.048 | 0.0 | n.a. | n.a. | n.a. | 56 | 2.9 | 0.98 |

**Figure 3.**Allometric biomass equations for aspen, birch, and monoculture oak using diameter at breast height as explanatory variable; models with site effect (K & S) [Equation (4)] were plotted separately. Pointwise 95% credibility intervals (ci) were calculated from bootstrap resampling.

**Table 4.**Parameter estimates, p-values, residual standard errors (ResSE), and ${R}^{2}$ (calculated as one minus residual sum of squares divided by total sum of squares) for allometric biomass equations using diameter at breast height and tree height as explanatory variables [Equation (5)].

Species | Compartment | ${\beta}_{1}^{\left(4\right)}$ | ${\beta}_{2}^{\left(4\right)}$ | ${\beta}_{3}^{\left(4\right)}$ | n | ResSE | ps.${R}^{2}$ | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Est. | St.Err. | p-value | Est. | St.Err. | p-value | Est. | St.Err. | p-value | |||||

Aspen | stem wood | 0.006 | 0.004 | 0.106 | 1.557 | 0.112 | 0.0 | 1.743 | 0.247 | 0.0 | 19 | 5.146 | 0.98 |

stem bark | 0.007 | 0.004 | 0.117 | 1.763 | 0.119 | 0.0 | 0.818 | 0.268 | 0.008 | 19 | 0.854 | 0.98 | |

branch | 0.015 | 0.033 | 0.652 | 3.301 | 0.447 | 0.0 | −0.684 | 0.908 | 0.462 | 19 | 7.948 | 0.91 | |

aboveground woody | 0.021 | 0.016 | 0.211 | 2.084 | 0.152 | 0.0 | 0.936 | 0.326 | 0.011 | 19 | 10.587 | 0.98 | |

Birch | stem wood | 0.012 | 0.006 | 0.069 | 1.432 | 0.164 | 0.0 | 1.708 | 0.264 | 0.0 | 20 | 6.841 | 0.98 |

stem bark | 0.098 | 0.05 | 0.066 | 2.088 | 0.179 | 0.0 | −0.486 | 0.272 | 0.092 | 20 | 1.49 | 0.96 | |

branch | 0.001 | 0.001 | 0.149 | 2.862 | 0.237 | 0.0 | 0.779 | 0.301 | 0.019 | 20 | 5.063 | 0.98 | |

aboveground woody | 0.019 | 0.008 | 0.036 | 1.944 | 0.147 | 0.0 | 1.154 | 0.217 | 0.0 | 20 | 10.521 | 0.98 | |

Oak mono | stem wood | 0.010 | 0.005 | 0.043 | 2.135 | 0.083 | 0.0 | 1.167 | 0.24 | 0.0 | 34 | 2.175 | 0.97 |

stem bark | 0.036 | 0.02 | 0.081 | 1.833 | 0.108 | 0.0 | 0.204 | 0.289 | 0.486 | 34 | 0.585 | 0.93 | |

branch | 0.957 | 0.599 | 0.118 | 2.147 | 0.147 | 0.0 | −1.098 | 0.349 | 0.003 | 40 | 2.444 | 0.89 | |

aboveground woody | 0.161 | 0.056 | 0.007 | 2.122 | 0.069 | 0.0 | 0.21 | 0.183 | 0.258 | 40 | 3.319 | 0.98 | |

Oak under nurse crops | aboveground woody | 0.081 | 0.164 | 0.629 | 2.119 | 0.848 | 0.027 | 0.508 | 1.924 | 0.796 | 16 | 0.678 | 0.98 |

**Figure 4.**The behaviour of allometric biomass equations for aboveground woody biomass using diameter at breast height (dbh) and tree height (h) as explanatory variables [Equation (5)]. (

**Left**) Predictions of aboveground woody biomass [kg] plotted versus diameter at breast height [cm] at a selection of fixed heights [m]; (

**Right**) Predictions of aboveground woody biomass plotted versus height at a selection of fixed diameters at breast height. Blue line sections indicate the data range, orange parts indicate the extrapolation range. Points represent empirical aboveground woody biomass data.

**Table 5.**Performance of our new allometric biomass equations using diameter at breast height as sole explanatory variable [Equation (4)]; absolute (RMSE) and relative (rel.RMSE) root mean squared errors were calculated for all models from jackknife resampling.

Species | Compartment | RMSE | rel. RMSE [%] |
---|---|---|---|

Aspen | stem wood | 10.4 | 20.0 |

stem bark | 1.1 | 13.6 | |

branch | 8.6 | 36.6 | |

aboveground woody | 13.9 | 16.7 | |

Birch | stem wood | 9.5 | 19.7 |

stem bark | 1.6 | 16.7 | |

branch | 6.8 | 23.3 | |

aboveground woody | 16.8 | 19.3 | |

Oak | stem wood | 2.7 | 18.4 |

stem bark | 0.6 | 18.9 | |

branch | 2.9 | 32.9 | |

aboveground woody | 3.8 | 15.6 | |

Oak under nurse crop | aboveground woody | 1.0 | 20.8 |

Oak overall | aboveground woody | 1.0 | 20.8 |

**Table 6.**Performance of our new allometric biomass equations using diameter at breast height and tree height as explanatory variables [Equation (5)]; absolute (RMSE) and relative (rel.RMSE) root mean squared errors were calculated for all models by means of jackknife resampling.

Species | Compartment | RMSE | rel. RMSE [%] |
---|---|---|---|

Aspen | stem wood | 6.0 | 11.6 |

stem bark | 1.0 | 12.2 | |

branch | 9.7 | 41.3 | |

aboveground woody | 12.4 | 14.8 | |

Birch | stem wood | 8.8 | 18.2 |

stem bark | 1.8 | 18.3 | |

branch | 6.2 | 21.3 | |

aboveground woody | 13.6 | 15.5 | |

Oak mono | stem wood | 2.3 | 15.5 |

stem bark | 0.6 | 20.5 | |

branch | 3.1 | 35.2 | |

aboveground woody | 4.0 | 16.5 | |

Oak under nurse crop | aboveground woody | 2.7 | 57.5 |

**Figure 5.**Allocation of biomass across a range of diameters at breast height (dbh) and specified for the biomass compartments stem wood, stem bark, and branches as a fraction of total aboveground woody biomass. Data were estimated using the allometric biomass equations fitted to our sample tree data.

#### 3.4. Comparison with Other Studies

**Table 7.**Bias and absolute (RMSE) and relative (rel.RMSE) root mean squared errors produced when predicting the aboveground woody biomass and branch biomass of our

**sample trees**using our new allometric biomass equations or those from the literature. The RMSE ratio denotes the RMSE produced by allometric biomass equations from the literature divided by the RMSE produced by the corresponding allometric biomass equations fitted in this study, respectively.

Publication | Species | Aboveground woody biomass | Branch biomass | ||||||
---|---|---|---|---|---|---|---|---|---|

bias | RMSE | rel.RMSE | RMSE ratio | bias | RMSE | rel.RMSE | RMSE ratio | ||

[kg/tree] | [kg/tree] | [%] | [kg/tree] | [kg/tree] | [%] | ||||

this study | Populus tremula × P. tremuloides | −1.4 | 13.1 | 13.6 | 1.0 | 0.2 | 7.4 | 27.4 | 1.0 |

Wang et al. (2002) [29] | Populus tremoloides | 0.3 | 18.1 | 18.7 | 1.4 | −18.9 | 28.2 | 104.4 | 3.8 |

Ruark & Bockheim (1988) [46] | Populus tremoloides | −5.6 | 20.0 | 20.7 | 1.5 | −13.5 | 22.1 | 81.8 | 3.0 |

Johansson (1999) [41] | Populus tremula | −7.1 | 20.3 | 21.0 | 1.6 | −20.0 | 31.4 | 116.2 | 4.2 |

Wang (2006) [49] | Populus davidiana | −8.0 | 21.5 | 22.3 | 1.6 | −11.5 | 18.2 | 67.3 | 2.5 |

Pastor et al. (1984) [45] | Populus tremuloides | −12.4 | 27.1 | 28.1 | 2.1 | −18.3 | 28.5 | 105.5 | 3.9 |

Johansson & Karačić (2011) [42] | Populus nigra L. × P. doltoides | −23.9 | 38.4 | 39.8 | 2.9 | −16.2 | 25.3 | 93.6 | 3.4 |

Rock (2007) [34] | Populus tremula × P. tremuloides | −29.2 | 44.0 | 45.6 | 3.4 | −10.1 | 20.2 | 74.7 | 2.7 |

Tullus et al. (2009) [48] | Populus tremula × P. tremuloides | −40.1 | 60.3 | 62.5 | 4.6 | −15.4 | 25.8 | 95.5 | 3.5 |

Zabek & Prescott (2006) [51] | P. trichocarpa × P. deltoides | −49.7 | 72.9 | 75.5 | 5.6 | −16.6 | 27.5 | 101.8 | 3.7 |

Telenius (1999) [47] | Populus tremula × P. tremoloides | −73.3 | 102.3 | 106.0 | 7.8 | n.a. | n.a. | n.a. | |

this study | Betula pendula × B. pubscenes | −0.9 | 9.7 | 11.1 | 1.0 | −0.7 | 4.7 | 16.0 | 1.0 |

Wang et al. (1996) [50] | Betula papyrifera | −12.0 | 20.8 | 23.8 | 2.1 | −21.1 | 30.9 | 105.4 | 6.6 |

Uri et al. (2007) [36] | Betula pendula | −11.9 | 22.8 | 26.1 | 2.4 | −9.7 | 15.8 | 53.9 | 3.4 |

Johansson (1999) [43] | Betula pendula | 22.4 | 33.0 | 37.8 | 3.4 | −14.4 | 22.5 | 76.8 | 4.8 |

Wang (2006) [49] | Betula platyphylla | 25.7 | 37.8 | 43.3 | 3.9 | −2.2 | 7.6 | 25.9 | 1.6 |

Johansson (1999) [43] | Betula pubescens | 24.1 | 38.5 | 44.1 | 4.0 | −11.8 | 19.5 | 66.5 | 4.2 |

Telenius (1999) [47] | Betula pendula | −37.8 | 52.7 | 60.3 | 5.4 | ||||

Fatemi et al. (2011) [40] | Betula papyrifera | 40.6 | 60.6 | 69.4 | 6.3 | −14.9 | 24.5 | 83.6 | 5.2 |

this study | Quercus spp. | 0.3 | 3.2 | 13.3 | 1.0 | n.a. | n.a. | n.a. | n.a. |

Zell (2008) [52] | Quercus spp. | −0.3 | 4.2 | 17.4 | 1.3 | n.a. | n.a. | n.a. | n.a. |

Suchomel et al. (2012) [28] | Quercus petraea | −2.4 | 4.6 | 19.1 | 1.4 | n.a. | n.a. | n.a. | n.a. |

Muukkonen (2007) [44] | Quercus spp. | 1.2 | 6.3 | 26.1 | 2.0 | n.a. | n.a. | n.a. | n.a. |

André et al. (2010) [39] | Quercus petraea | 4.3 | 8.6 | 35.7 | 2.7 | n.a. | n.a. | n.a. | n.a. |

Grote (2003) [22] | Quercus petraea | 5.7 | 12.8 | 53.1 | 4.0 | n.a. | n.a. | n.a. | n.a. |

**Table 8.**Bias and absolute (RMSE) and relative (rel.RMSE) root mean squared errors produced when predicting the aboveground woody biomass and branch biomass of our sample data at

**stand level**using our new allometric biomass equations or those from the literature. The RMSE ratio denotes the RMSE produced by allometric biomass equations from the literature divided by the RMSE produced by the corresponding allometric biomass equations fitted in this study, respectively.

Publication | Species | Aboveground woody biomass | Branch biomass | ||||||
---|---|---|---|---|---|---|---|---|---|

bias | RMSE | rel.RMSE | RMSE ratio | bias | RMSE | rel.RMSE | RMSE ratio | ||

(Mg/ha) | (Mg/ha) | (%) | (Mg/ha) | (Mg/ha) | (%) | ||||

this study | Populus tremula × P. tremuloides | −1.4 | 1.4 | 1.8 | 1.0 | −0.3 | 0.3 | 1.6 | 1.0 |

Wang et al. (2002) [29] | Populus tremoloides | 0.9 | 1.0 | 1.3 | 1.4 | −15.7 | 15.7 | 70.8 | 3.8 |

Ruark & Bockheim (1988) [46] | Populus tremoloides | −4.0 | 4.0 | 5.3 | 1.5 | −11.4 | 11.4 | 51.6 | 3.0 |

Johansson (1999) [41] | Populus tremula | −5.1 | 5.1 | 6.7 | 1.6 | −16.7 | 16.7 | 75.4 | 4.2 |

Wang (2006) [49] | Populus davidiana | −5.8 | 5.8 | 7.7 | 1.6 | −9.7 | 9.7 | 44.0 | 2.5 |

Pastor et al. (1984) [45] | Populus tremuloides | −9.5 | 9.5 | 12.4 | 2.1 | −15.2 | 15.2 | 68.6 | 3.9 |

Johansson & Karačić (2011) [42] | Populus nigra L. × P. doltoides | −18.5 | 18.5 | 24.3 | 2.9 | −13.5 | 13.5 | 61.2 | 3.4 |

Rock (2007) [34] | Populus tremula × P. tremuloides | −22.8 | 22.8 | 29.9 | 3.4 | −8.9 | 8.9 | 40.1 | 2.7 |

Tullus et al. (2009) [48] | Populus tremula × P. tremuloides | −31.7 | 31.7 | 41.5 | 4.6 | −13.1 | 13.1 | 59.0 | 3.5 |

Zabek & Prescott (2006) [51] | P. trichocarpa × P. deltoides | −40.1 | 40.1 | 52.6 | 5.6 | −14.1 | 14.1 | 63.6 | 3.7 |

Telenius (1999) [47] | Populus tremula × P. tremoloides | −57.9 | 58.0 | 76.2 | 7.8 | n.a. | n.a. | n.a. | n.a. |

this study | Betula pendula × B. pubscenes | −0.1 | 0.3 | 0.5 | 1.0 | −0.2 | 0.3 | 1.2 | 1.0 |

Wang et al. (1996) [50] | Betula papyrifera | −8.0 | 8.0 | 12.4 | 2.1 | −15.0 | 15.0 | 71.2 | 6.6 |

Uri et al. (2007) [36] | Betula pendula | −7.7 | 7.8 | 12.0 | 2.4 | −6.5 | 6.5 | 30.9 | 3.4 |

Johansson (1999) [43] | Betula pendula | 18.2 | 18.2 | 28.2 | 3.4 | −9.9 | 9.9 | 47.0 | 4.8 |

Wang (2006) [49] | Betula platyphylla | 20.6 | 20.6 | 31.9 | 3.9 | −0.8 | 0.8 | 4.0 | 1.6 |

Johansson (1999) [43] | Betula pubescens | 19.0 | 19.0 | 29.5 | 4.0 | −7.9 | 7.9 | 37.5 | 4.2 |

Telenius (1999) [47] | Betula pendula | −27.2 | 27.2 | 42.1 | 5.4 | ||||

Fatemi et al. (2011) [40] | Betula papyrifera | 31.4 | 31.5 | 48.7 | 6.3 | −10.1 | 10.1 | 48.1 | 5.2 |

this study | Quercus spp. | −0.1 | 0.1 | 0.4 | 1.0 | n.a. | n.a. | n.a. | n.a. |

Zell (2008) [52] | Quercus spp. | 0.8 | 0.8 | 2.9 | 1.3 | n.a. | n.a. | n.a. | n.a. |

Suchomel et al. (2012) [28] | Quercus petraea | −1.4 | 1.4 | 4.7 | 1.4 | n.a. | n.a. | n.a. | n.a. |

Muukkonen (2007) [44] | Quercus spp. | 3.0 | 3.0 | 10.5 | 2.0 | n.a. | n.a. | n.a. | n.a. |

André et al. (2010) [39] | Quercus petraea | 6.6 | 6.6 | 22.7 | 2.7 | n.a. | n.a. | n.a. | n.a. |

Grote (2003) [22] | Quercus petraea | 9.8 | 9.8 | 33.8 | 4.0 | n.a. | n.a. | n.a. | n.a. |

## 4. Discussion and Conclusions

#### 4.1. Effects of Stand Density and Tree Age on Allometric Relationships of Trees

#### 4.2. Allometric Biomass Equations

#### 4.3. General Conclusion

## Acknowledgments

## Conflicts of Interest

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Stark, H.; Nothdurft, A.; Bauhus, J.
Allometries for Widely Spaced *Populus* ssp. and *Betula* ssp. in Nurse Crop Systems. *Forests* **2013**, *4*, 1003-1031.
https://doi.org/10.3390/f4041003

**AMA Style**

Stark H, Nothdurft A, Bauhus J.
Allometries for Widely Spaced *Populus* ssp. and *Betula* ssp. in Nurse Crop Systems. *Forests*. 2013; 4(4):1003-1031.
https://doi.org/10.3390/f4041003

**Chicago/Turabian Style**

Stark, Hendrik, Arne Nothdurft, and Jürgen Bauhus.
2013. "Allometries for Widely Spaced *Populus* ssp. and *Betula* ssp. in Nurse Crop Systems" *Forests* 4, no. 4: 1003-1031.
https://doi.org/10.3390/f4041003