Maximum Size-Density Relationship between Lorey's Mean Height and Trees per Hectare

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.