Can an Exponential Function Be Applied to the Asymptotic Density–Size Relationship? Two New Stand-Density Indices in Mixed-Species Forests
Abstract: This study presents two stand-density indices (SDIs) based on exponential density decline
as a function of quadratic mean diameter for all species combined in mixed-species forests with 22
species mix grouped in four species groups. The exponential-based density–diameter relationship,
as well the density index corresponding to the slope or instantaneous mortality rate parameters,
was compared with those based on power-law density–diameter relationship. A dataset of 202 fully
stocked circular plots at maximum density was used for fitting the models, and a dataset of 122
circular plots was used for validation stand density index for all species combined of mixed-species
stands. The dataset for validation was independent of dataset for model development. The first
stand-density index showed a density management graphic (DMG) with a variable intercept and
common instantaneous mortality rate, and the second index showed a DMG with common intercept
and variable mortality rate. Additionally, the value of the initial density of the fitted line was
more realistic than those generated by the potential model for all species combined. Moreover,
the density management diagrams showed a curvilinear trend based on the maximum stand density
index in graphical log–log scale. The DMGs could be interpreted as forest scenarios based on
variable initial density and common management objectives or the same density and different
management objectives for forest-rotation periods involving all species combined in mixed-species
stands. The fitting of exponential and potential equations for species or species groups showed that
the density–size relationships in mixed-species forests should be modeled for all species combined
because the disaggregation of mixture species represented a weak tendency for each species or species
group and the resultant fitted equations were unrealistic.