^{1}

^{*}

^{2}

Allometric relationships for estimating stem volumes of ^{2} values were used to compare the strength of the relationships. Although the allometric equations were highly significant (P<0.01) there was considerable variation among them as indicated by the R^{2} values. Our results suggested that tree volume is more correlated with basal area than with simple D (stem diameter at 1.3 m height above the ground). The allometric relationships of stem volume to the tree diameter at 10% of tree height (D_{0.1}) did not improve the allometric strength in comparison with simple D as reported in case of some other tree species. The multiplication of tree height H with D in the allometric equation gives a little improvement in the degree of fitness of the allometric equations. However, for the Sissoo plantations studied the stem dbh alone showed a very strong accuracy of estimation (R^{2} = 0.997) especially when used as D^{2}. It is concluded that the use of tree height in the allometric equation can be neglected for the species, as far as the present study area is concerned. Therefore, for estimating the stem volume of Sissoo, the use of D^{2} as an independent variable in the allometric equation with a linear or quadratic equation is recommended. The paper describes details of tree volume allometry, which is important in silviculture and forest management.

Sissoo is known as a premier timber species of the rosewood genus with the common name sissoo in Bangladesh. It is native to Sub-Himalayan zone including India, Pakistan and Afghanistan (

There are various independent variables in the allometric relationships to estimate biomass. In most studies, ^{2}_{0.1}^{2}_{0.1}, diameter at one-tenth of ^{2}_{B} (stem diameter at a height of clear bole length) provides better results in estimating the weight of branch and leaf, and leaf area per tree, as described by the pipe model theory of Shinozaki et al. (

In this paper, we seek to establish the allometric relationships of the stem volume of individual trees to different dimensions, such as ^{2}, ^{2}_{0.1}, _{0.1}^{2} and _{0.1}^{2}

The study was carried out in block plantations at Khulna located in the southern part of Bangladesh (

The species is a strong-light demander and shows good coppicing ability (

All the studies were carried out in May 2006 in a monoculture plantation of _{0.1} -

The simple allometric equation is generally written using the power curve (

where

where ln ^{2}, ^{2}_{0.1}, _{0.1}^{2} and _{0.1}^{2}

The coefficient of determination ^{2} was calculated using the following equation (based on the real data before logarithmic transformation - eqn. 8):

where _{i} is the observed value, _{ei} is the corresponding values calculated from the regression line, and _{mi} is the mean of the observed values (^{2} value (coefficient of determination) is a measure of the goodness-of-fit between the observed and calculated values (

Various allometric equations were developed for data fitting. The allometric relationships of stem volume of sissoo trees to ^{2} are illustrated in ^{2} is used (^{2} = 0.970) shows better fitting than linear equation (^{2} = 0.944). When ^{2} = 0.983) than power equation (^{2} = 0.970 - ^{2} = 0.997) and ^{2} (^{2} = 0.996) with a very close estimate by the quadratic equation for ^{2} = 0.993) and ^{2} (^{2} = 0.996).

_{0.1} and _{0.1}^{2}. As observed with the variable _{0.1 } alsoshowed strong data fitting (^{2} = 0.925) in the allometry (^{2} = 0.964) when the _{0.1} value is squared. The power equation for both the variables _{0.1} and _{0.1}^{2} showed the same coefficient of determination (^{2} = 0.961). For both the variables _{0.1} and _{0.1}^{2} the polynomial cubic and quadratic equations showed a slight stronger fitting (

As illustrated in ^{2}^{2} = 0.995) and _{0.1}^{2}^{2} = 0.995). The polynomial cubic along with the quadratic equation showed a very close fit in comparison with the linear equation for both variables ^{2}_{0.1}^{2}

Although the allometric equations were highly significant (^{2} values (^{2}. This indicates that tree volume is more correlated with basal area than with simple dbh (^{2} = 0.997) with a very close estimate by the quadratic equation (^{2} = 0.993). However, there were low differences in the goodness-of-fit among the polynomial, power and linear equations. As the quadratic and cubic equations consist of several coefficients, for practical applications in stand volume estimation, because of simplicity, the linear or power equations the use of ^{2} as an independent variable should be preferred (

Like the commonly known variable _{0.1 } also showed strong linear data fitting (^{2} = 0.925) in the allometry (^{2} = 0.964) when _{0.1}^{2} value is used instead of _{0.1} (_{0.1} (^{2} = 0.989) and _{0.1}^{2} (^{2} = 0.988). The next strong fit is also from the quadratic equation for _{0.1} (^{2} = 0.981) and _{0.1}^{2} (^{2} = 0.987). Overall, it may be remarked that the allometric relationships of stem volume to the tree diameter at 10% of tree height (_{0.1}) did not improve the allometric strength in

The multiplication of tree height ^{2} ^{2} = 0.995) and _{0.1}^{2}^{2} = 0.995) in the allometric estimation. This suggests that biologically tree diameter and height change proportionality with the change of tree size (^{2}_{0.1}^{2}^{2} = 0.995).

For predicting timber yield (^{2} = 0.983 to 0.997) especially when used as ^{2}. Thus, it is concluded that the use of tree height in the allometric equation (^{2} as an independent variable in the allometric equation with a linear or quadratic equation is recommended.

The findings of this study indicate that there is a variation in the use of independent variables in allometric equations for estimating the stem volume of the species. The allometric relationships described in this paper may not be appropriate in mixed or open forest stands, because the present study was carried out under monospecific and closed canopy conditions. For estimation stem volume of trees outside the size range of this investigation, care should be taken in extrapolating the present allometric relationships. Therefore, users of these allometric equations are recommended to check some individual trees outside the present size class.

We are grateful to Forestry and Wood Technology Discipline, Khulna University, Bangladesh for providing logistic support for the field data collection. The data analysis and manuscript preparation were performed in the Institute of Forest Growth and Forest Computer Sciences, Technische Universität Dresden, Germany, which was supported by the Alexander von Humboldt Stiftung / Foundation, Germany.

^{2}. American Statistics 39: 279-285.

Location map of the study site.

Relationships of stem volume to ^{2} in

Relationships of stem volume to _{0.1} and _{0.1}^{2} in

Relationships of stem volume to ^{2}_{0.1}^{2}

Description of sissoo sample trees used for this study. _{0.1}: stem diameter at a height of

Tree No. | | _{0.1} (cm) | | ^{3}) |
---|---|---|---|---|

1 | 9.549 | 10.027 | 9.01 | 10403.4 |

2 | 9.708 | 10.504 | 8.01 | 17653.9 |

3 | 10.134 | 11.141 | 8.02 | 25678.3 |

4 | 10.663 | 10.982 | 9.01 | 20521.2 |

5 | 10.759 | 11.459 | 8.07 | 27829.2 |

6 | 11.141 | 11.937 | 9.03 | 14610.4 |

7 | 11.513 | 12.414 | 7.50 | 36859.9 |

8 | 11.678 | 13.051 | 8.02 | 37520.3 |

9 | 11.937 | 11.937 | 9.75 | 38089.3 |

10 | 12.321 | 12.573 | 8.50 | 41628.1 |

11 | 12.614 | 12.892 | 8.50 | 46894.1 |

12 | 12.984 | 12.796 | 12.01 | 51629.2 |

13 | 13.210 | 13.528 | 11.03 | 62953.1 |

14 | 13.242 | 13.210 | 11.02 | 56349.9 |

15 | 13.687 | 13.433 | 10.25 | 57361.4 |

16 | 13.866 | 14.006 | 10.25 | 36131.8 |

17 | 14.006 | 14.324 | 8.50 | 60054.8 |

18 | 14.961 | 14.801 | 14.01 | 89369.7 |

19 | 15.597 | 15.756 | 14.04 | 101757.4 |

20 | 16.470 | 16.870 | 14.02 | 128149.9 |

21 | 16.999 | 17.666 | 11.01 | 139271.9 |

22 | 17.189 | 17.507 | 10.75 | 122993.6 |

23 | 21.963 | 22.282 | 12.50 | 206910.6 |

24 | 26.897 | 26.420 | 15.10 | 411254.8 |

25 | 27.056 | 26.420 | 15.00 | 390567.9 |

26 | 27.693 | 27.693 | 14.75 | 437078.1 |

27 | 29.155 | 28.254 | 20.05 | 569421.1 |

28 | 31.210 | 29.155 | 20.02 | 665874.1 |

29 | 32.675 | 30.152 | 20.50 | 759421.1 |

30 | 33.423 | 31.831 | 21.75 | 819421.1 |

Summarized coefficients of the relationships between individual tree volumes of Sissoo to different independent variables. _{0.1}: stem diameter at a height of _{0.1} = [cm],

Variable | Equation | a | b | c | d | R^{2} | F | Sign. |
---|---|---|---|---|---|---|---|---|

D | LIN | -342298 | 30629.2 | - | - | 0.944 | 474.4 | < 0.01 |

LOG | -1E+06 | 561873 | - | - | 0.869 | 186.3 | < 0.01 | |

QUA | 145717 | -24827 | 1322.63 | - | 0.993 | 1925.9 | < 0.01 | |

CUB | -203182 | 34316.7 | -1754.7 | 49.327 | 0.997 | 2588.8 | < 0.01 | |

POW | 15.91 | 3.108 | - | - | 0.97 | 902.6 | < 0.01 | |

EXP | 5528 | 0.159 | - | - | 0.928 | 361.7 | < 0.01 | |

D^{2} | LIN | -75972 | 739.7 | - | - | 0.983 | 1660.3 | < 0.01 |

LOG | -1E+06 | 280937 | - | - | 0.869 | 186.3 | < 0.01 | |

QUA | -13315 | 317.6 | 0.3825 | - | 0.996 | 3517 | < 0.01 | |

CUB | -31764 | 487.7 | 0.0288 | 0.0002 | 0.996 | 2462.9 | < 0.01 | |

POW | 15.91 | 1.554 | - | - | 0.97 | 902.6 | < 0.01 | |

EXP | 23664 | 0.0036 | - | - | 0.867 | 182.3 | < 0.01 | |

D_{0.1} | LIN | -390344 | 33385.1 | - | - | 0.925 | 343 | < 0.01 |

LOG | -2E+06 | 611406 | - | - | 0.86 | 172.4 | < 0.01 | |

QUA | 275457 | -42005 | 1844.01 | - | 0.981 | 696.3 | < 0.01 | |

CUB | -445256 | 80012.7 | -4601.5 | 106.354 | 0.989 | 782.3 | < 0.01 | |

POW | 7.04 | 3.385 | - | - | 0.961 | 695.9 | < 0.01 | |

EXP | 4172 | 0.1752 | - | - | 0.928 | 362.9 | < 0.01 | |

D_{0.1}^{2} | LIN | -99651 | 828.7 | - | - | 0.964 | 742.6 | < 0.01 |

LOG | -2E+06 | 305703 | - | - | 0.86 | 172.4 | < 0.01 | |

QUA | 7859 | 104.7 | 0.7173 | - | 0.987 | 1043.7 | < 0.01 | |

CUB | -30223 | 453.3 | -0.0564 | 0.0005 | 0.988 | 721.3 | < 0.01 | |

POW | 7.04 | 1.693 | - | - | 0.961 | 695.9 | < 0.01 | |

EXP | 20529 | 0.0042 | - | - | 0.881 | 207.6 | < 0.01 | |

D_{2}H | LIN | -5209 | 34.9 | - | - | 0.995 | 5738.1 | < 0.01 |

LOG | -1E+06 | 205386 | - | - | 0.877 | 199 | < 0.01 | |

QUA | -15721 | 40.2 | -0.0002 | - | 0.997 | 4000.6 | < 0.01 | |

CUB | -17734 | 41.7 | -0.0004 | 4.90E-09 | 0.997 | 2584.4 | < 0.01 | |

POW | 11 | 1.125 | - | - | 0.959 | 656.2 | < 0.01 | |

EXP | 35224 | 0.0002 | - | - | 0.785 | 102.3 | < 0.01 | |

D_{0.1}^{2} H | LIN | -18747 | 39.3 | - | - | 0.995 | 5791.8 | < 0.01 |

LOG | -2E+06 | 219854 | - | - | 0.877 | 199.2 | < 0.01 | |

QUA | -20488 | 40.2 | -5.00E-05 | - | 0.995 | 2811.9 | < 0.01 | |

CUB | -10661 | 33 | 0.0008 | -3.00E-08 | 0.996 | 1959.7 | < 0.01 | |

POW | 5.65 | 1.204 | - | - | 0.959 | 654.2 | < 0.01 | |

EXP | 32624 | 0.0002 | - | - | 0.808 | 118.1 | < 0.01 |