Objective  Considering stand density, diameter structure and tree species structure, the optimal model for stand mean height and mean DBH relationship was constructed using algebraic difference approach. It may provide a theoretical basis for site productivity estimation and sustainable management of natural mixed forests.

  Method  Base algebraic difference approaches were modeled with 4 different data structure types, i.e. typeC, typeD, typeE and typeF based on Richards model using 4 inventory data of permanent sample plots in natural Quercus spp. broadleaved mixed stands. The 4 different base algebraic difference approaches were comparatively analyzed to get the optimal data structure type. Algebraic difference approach of diversity indices was constructed based on the optimal data structure type using 5 different stand density indices, including tree number (N), stand basal area (BA), stand density index (SDIr), additive stand density index (SDIa) and canopy density (CD), and the 5 different diameter diversity indices including Shannon evenness index (ShaI), Simpson index (SimI), McIntosh evenness index (MceI), Gini coefficient (GinI) and Berger-Parker index (BerI), and the 4 different species diversity indices including ShaI, SimI, MceI and BerI. The algebraic difference approach of diversity indices was comparatively analyzed to obtain the optimize algebraic difference approaches, i.e. the optimize stand mean height and mean DBH relationship.

  Result  Model fitting effects of calibration data in different data structure types were sorted from best to worst, and the ranking was: typeD > typeC > typeF > typeE. Except for typeC, model coefficients b and r of the other three data structure types were significant (P < 0.01), indicating that the model fitting effects of typeD were the best. Model fitting effects of SDIr were the best. Model coefficients b₀, r and cSD were significant (P < 0.01), regardless of which stand density index was used, indicating that model fitting effects of the 5 different stand density indices were reasonable. Model fitting effect of ShaI was the best. Except for GinI, model coefficients b₀, r, cSDIr and cDI of the other 4 diameter diversity indices were significant (P < 0.01), indicating that model fitting effects of ShaI, SimI, MceI and BerI were reasonable. Model fitting and validation effects had little difference among the 4 species diversity indices. Model coefficients b₀, r, cSDIr, cShaI and cSP of BerI were significant (P < 0.01), indicating that BerI was reasonable. However, model coefficients b₀, r, cSDIr, cShaI and cSP of ShaI, SimI and MceI were not significant at the level of 0.05, indicating that ShaI, SimI and MceI were not reasonable.

  Conclusion  TypeD is the best data structure type, stand density, diameter diversity and species diversity were significant for algebraic difference approach. Moreover, the model fitting effects of algebraic difference approach within SDIr, ShaI and BerI are the best, which is served as the optimize stand mean height and mean DBH relationship in natural Quercus spp. broadleaved mixed stands.