Table 4 Formulations of the distance-dependent indices, size distance (SD) and point density (PD) in both traditional and unilateral competition versions (_U) and the combined search radius criteria for the selection of the competitors (j) among the neighbouring trees (i)
Type | Index | Formula1 | Type | Search radius criteria | Formula1 |
|---|---|---|---|---|---|
SD | H | \( H=\sum\limits_{{i\ne j}} {\left( {\frac{{{d_j}}}{{{d_i}\left( {{dis}{{{t}}_{ij }}+1} \right)}}} \right)} \) | SD | D1 | \( {dis}{{{t}}_{ij }} < \frac{{{d_i}+{d_j}}}{8} \) |
H_U a | Unilateral version | DC | \( {dis}{{{t}}_{ij }} < {c}{{{w}}_i}+{c}{{{w}}_j} \) | ||
CC | \( {CC}=\sum\limits_{{i\ne j}} {\left( {\frac{{{c}{{{w}}_j}}}{{{c}{{{w}}_i}\left( {{dis}{{{t}}_{ij }}+1} \right)}}} \right)} \) | H1 | \( {dis}{{{t}}_{ij }} < \frac{{{h_i}+{h_j}}}{8} \) | ||
CC_U a | Unilateral version | H2 | \( {dis}{{{t}}_{ij }} < \frac{{{h_j}-{h}{{{c}}_i}}}{1.19 } \) | ||
CCU | \( {CCU}=\sum\limits_{{i\ne j}} {\left( {\frac{{{c}{{{w}}_j}}}{{{c}{{{w}}_i}}}} \right)} \) | H3 | \( {dis}{{{t}}_{ij }} < \frac{{{h_j}-{h}{{{c}}_i}}}{2} \) | ||
CCU_U a | Unilateral version | H4 | \( {dis}{{{t}}_{ij }} < 0.25{h_j} \) | ||
PD | PD | \( {PD}=\frac{2,500 }{n}\left( {\sum\limits_{j=1}^n {\left( {j-0.5} \right)}\,{{{\left( {\frac{{{d_j}}}{{{dis}{{{t}}_{ij }}}}} \right)}}^2}} \right) \) | T | All sample trees | |
PD_U a | Unilateral version | PD | F4 | \( {dis}{{{t}}_{ij }} < 0.25{h_j} \) with BAF = 4 m2 ha−1 |