Weller??s allometric model assumes that the allometric relationships of mean area occupied by a tree
$ \bar{s} $ , i.e., the reciprocal of population density
$ \rho $ ,
$ \bar{s}\left( { = {1 \mathord{\left/ {\vphantom {1 {\rho = g_{\varphi } \cdot \bar{w}^{\varphi } }}} \right. \kern-0em} {\rho = g_{\varphi } \cdot \bar{w}^{\varphi } }}} \right) $ , mean tree height
$ \bar{H}\left( { = g_{\theta } \cdot \bar{w}^{\theta } } \right) $ , and mean aboveground mass density
$ \bar{d}\left( { = g_{\delta } \cdot \bar{w}^{\delta } } \right) $ to mean aboveground mass
$ \bar{w} $ hold. Using the model, the self-thinning line
$ \left( {\bar{w} = K \cdot \rho^{ - \alpha } } \right) $ of overcrowded
Kandelia obovata stands in Okinawa, Japan, was studied over 8?years. Mean tree height increased with increasing
$ \bar{w} $ . The values of the allometric constant
$ \theta $ and the multiplying factor
$ g_{\theta } $ are 0.3857 and 2.157?m?kg
???, respectively. The allometric constant
$ \delta $ and the multiplying factor
$ g_{\delta } $ are ?0.01673 and 2.685?m
?3?kg
1???, respectively. The
$ \delta $ value was not significantly different from zero, showing that
$ \bar{d} $ remains constant regardless of any increase in
$ \bar{w} $ . The average of
$ \bar{d} $ , i.e., biomass density
$ \left( {{{\bar{w} \cdot \rho } \mathord{\left/ {\vphantom {{\bar{w} \cdot \rho } {\bar{H}}}} \right. \kern-0em} {\bar{H}}}} \right) $ , was 2.641?±?0.022?kg?m
?3, which was considerably higher than 1.3?C1.5?kg?m
?3 of most terrestrial forests. The self-thinning exponent
$ \alpha \left( { = {1 \mathord{\left/ {\vphantom {1 {\varphi = }}} \right. \kern-0em} {\varphi = }}{1 \mathord{\left/ {\vphantom {1 {\left\{ {1 - \left( {\theta + \delta } \right)} \right\}}}} \right. \kern-0em} {\left\{ {1 - \left( {\theta + \delta } \right)} \right\}}}} \right) $ and the multiplying factor
$ K\left( { = \left( {g_{\theta } \cdot g_{\delta } } \right)^{\alpha } } \right) $ were estimated to be 1.585 and 16.18?kg?m
?2??, respectively. The estimators
$ \theta $ and
$ \delta $ are dependent on each other. Therefore, the observed value of
$ \theta + \delta $ cannot be used for the test of the hypothesis that the expectation of the estimator
$ \theta + \delta $ equals 1/3, i.e.,
$ \alpha = {3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-0em} 2} $ , or 1/4, i.e.,
$ \alpha = {4 \mathord{\left/ {\vphantom {4 3}} \right. \kern-0em} 3} $ . The
$ \varphi $ value was 0.6310, which is the same as the reciprocal of the self-thinning exponent of 1.585, and was not significantly different from 2/3 (
t?=?1.860,
df?=?191,
p?=?0.06429), i.e.,
$ \alpha = {3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-0em} 2} $ . Thus the self-thinning exponent is not significantly different from 3/2 based on the simple geometric model. On the other hand, the self-thinning exponent was significantly different from 3/4 (
t?=?6.213,
df?=?191,
p?=?3.182?×?10
?9), i.e.,
$ \alpha = {4 \mathord{\left/ {\vphantom {4 3}} \right. \kern-0em} 3} $ . Therefore, the self-thinning exponent is significantly different from 4/3 based on the metabolic model.
相似文献