DIAMETER DISTRIBUTION GROWTH AND YIELD MODELS FOR MIXED SPECIES FOREST STANDS (MICHIGAN)
Abstract
A general method for modeling growth and yield in mixed species, uneven-aged forest stands by using systems of differential equations was proposed. Recovery of diameter distribution parameters for each species from values of forest yields at any particular time was discussed. Equations for diameter distribution change rates were derived by using moment relationships together with systems of differential equations in forest yields. The utility of the modeling technique proposed was demonstrated by an application to mixed species uneven-aged permanent plot data from the upper peninsula of Michigan. Hardwood and softwood were the two species groups used. For each species group, equations which predicted change rates in basal area per acre, sum of diameters per acre, and number of trees per acre were developed by using the first two measurements taken on the permanent plots. These equations were taken to be a system of first order ordinary differential equations. Given a set of initial conditions (that is, initial values of number of trees per acre, sum of diameters per acre, and basal area per acre), yield predictions for future times may be obtained by numerical integration of the system. Future values of diameter distribution parameters may then be obtained by solving the system of equations formed by equating each yield type to the product of number of trees and the expected value of the yield per tree with respect to the diameter distribution parameters. Alternatively, the relationship mentioned above may be used to obtain differential equations for the diameter distribution parameters. When these equations are included with the system of differential equations in forest yields, predictions for diameter distribution parameters may be obtained as solutions to the resulting system of differential equations. The yield projection technique was tested by using the differential equation system to predict conditions at the third measurement period for those permanent plots on which a third measurement was taken.
Degree
Ph.D.
Subject Area
Forestry
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