A random-parameter model was used to relate total height to diameter at breast height (dbh) for cherrybark oak (Quercus pagoda Raf.). Data were obtained from 561 trees located in 50 stands occurring on bottomland hardwood sites in East Texas, near the western extent of the cherrybarkoak natural range. Mixed-model estimation techniques were used to fit fixed-effects parameters to the height-dbh relationship for cherrybark oak, with random-effects parameters representing sample stands from which tree data were obtained. The fixed-effect parameter estimates can be used topredict average cherrybark oak height for a given dbh in the region from which the data were obtained. Because random parameters associated with stands were used in the data-fitting process, the models can be calibrated to fit new stands by obtaining measurements to fit appropriate randomparameters for that stand. This calibration improves height predictions for individual stands while requiring less data than would the development of a completely new height prediction model for that stand. South. J. Appl. For. 29(1):22–26.
A linear relationship between the logarithm of Lorey's mean height and the logarithm of number of trees per hectare at maximum density can be derived from well known maximum size-density relationships associated with Reineke's stand density index and the power self-thinning principle. This leads to a system of three mathematically interrelated maximum size-density equations relating the three classically most important measures of tree size to density at its maximum. Given any two of these three equations, the third can be derived. Data obtained from unthinned control plots in a shortleaf pine (Pinus echinata Mill.) thinning study from Oklahoma are used to demonstrate these relationships. Slope estimates for the Reineke and Lorey maximum size-density lines are fitted simultaneously using three-stage least-squares with parameter constraints. First-difference models were used in the estimation procedure to reduce autocorrelation among remeasured plot data.
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