Table 2 Tested distance-independent and distance-dependent competition indices

Distance-independent competition indices

Diameter squared ratio (DRS)

\( \mathrm{CI}=\frac{D_i^2}{{\overset{-}{D}}^2} \)

Glover and Hool (1979)

Standardized stand density (SSD)

\( \mathrm{CI}=\frac{1}{500}\bullet N\bullet {\left[\frac{\overset{-}{D}}{10}\right]}^{1.605} \)

Reineke (1933)

Basal area of larger trees (BAL)

\( \mathrm{CI}={\sum}_j\left[\pi \bullet {\left(\frac{D_j}{200}\right)}^2\right]\bullet \frac{10\ 000}{\mathrm{Plot}\ \mathrm{area}} \)

For D _j   ≥ D _i

Wykoff et al. (1982)

Distance-dependent competition indices

Hegyi’s competition index (HI1)

\( \mathrm{CI}=\sum_{i\ne j}\frac{D_j}{D_i\bullet {\mathrm{Dist}}_{i j}} \)

Hegyi (1974)

Hegyi’s competition index (HI2)

\( \mathrm{CI}=\sum_{i\ne j}\frac{D_j}{D_i\bullet \left({\mathrm{Dist}}_{i j}+1\right)} \)

Hegyi (1974)

Martin-Ek index (MEI)

\( \mathrm{CI}=\sum_{\mathrm{i}\ne \mathrm{j}}\left[\frac{D_j}{D_i}\bullet {e}^{\left(\frac{{16\bullet \mathrm{Dist}}_{i j}}{D_i+{D}_j}\right)}\right] \)

Martin and Ek (1984)

Spurr’s point density index (SPDI)

\( \mathrm{CI}=\frac{75.625}{\mathrm{n}}\bullet \sum_{i\ne j}\left[\left(\mathrm{j}+\frac{1}{2}\right)\frac{{\mathrm{D}}_{\mathrm{j}}^2}{{\mathrm{D}\mathrm{i}\mathrm{st}}_{\mathrm{j}\mathrm{i}}^2}\right] \)

Spurr (1962)