The self-thinning exponent in overcrowded stands of the mangrove, Kandelia obovata, on Okinawa Island, Japan

Abstract

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 $\rho$, $\bar{s}\left( { = {1 \mathord{\left/ {\vphantom {1 {\rho = g_{\varphi } \cdot \bar{w}^{\varphi } }}} \right. \kern-\nulldelimiterspace} {\rho = g_{\varphi } \cdot \bar{w}^{\varphi } }}} \right)$, 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^−θ, respectively. The allometric constant $\delta$ and the multiplying factor $g_{\delta }$ are −0.01673 and 2.685 m⁻³ kg^1−δ, 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 $\left( {{{\bar{w} \cdot \rho } \mathord{\left/ {\vphantom {{\bar{w} \cdot \rho } {\bar{H}}}} \right. \kern-\nulldelimiterspace} {\bar{H}}}} \right)$, was 2.641 ± 0.022 kg m⁻³, which was considerably higher than 1.3–1.5 kg m⁻³ of most terrestrial forests. The self-thinning exponent $\alpha \left( { = {1 \mathord{\left/ {\vphantom {1 {\varphi = }}} \right. \kern-\nulldelimiterspace} {\varphi = }}{1 \mathord{\left/ {\vphantom {1 {\left\{ {1 - \left( {\theta + \delta } \right)} \right\}}}} \right. \kern-\nulldelimiterspace} {\left\{ {1 - \left( {\theta + \delta } \right)} \right\}}}} \right)$ 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^−2α, 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., $\alpha = {3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2}$, or 1/4, i.e., $\alpha = {4 \mathord{\left/ {\vphantom {4 3}} \right. \kern-\nulldelimiterspace} 3}$. 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., $\alpha = {3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2}$. 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., $\alpha = {4 \mathord{\left/ {\vphantom {4 3}} \right. \kern-\nulldelimiterspace} 3}$. Therefore, the self-thinning exponent is significantly different from 4/3 based on the metabolic model.