Stand models for lodgepole pine and limits to their application

Intensive study of the growth of individual trees in the open and in stands, and of the growth of stands themselves, has provided the basic biological assumptions and equations, which then are used in simulation of stand growth. Simulation, emerging as a research technique since the advent of electronic computers, has helped solve many forestry problems previously considered unmanageable. Simulation is almost essential in building stand growth models. Stand growth models for lodgepole pine (Pinus contorta Doug.)¹, are needed to illustrate some economic consequences of alternative methods of management. Such analyses can provide guidelines for improved stand management. These better approaches are desirable because lodgepole pine is required to supply increasing demands of a rapidly developing pulp industry in British Columbia and in Alberta. Newnham's stand models are critically examined and fully described. A revised simulation model is built and the methods used are described. Principles and assumptions basic to the development of stand models in general are also outlined. The revised model is initiated with a 30 x 30 tree matrix. The dbh frequency distribution of these 900 trees is normal. A mean dbh of 1.2 inches at 15 years, with a standard deviation of 0.4 inches, is assumed to represent site index 70 feet at 80 years. The dbh growth of each of the 900 trees is predicted by 5-year periods using a regression of dbh on age for open-grown lodgepole pine, with appropriate reductions for crown competition. The crown width of each of the 900 trees is calculated from the regression of crown width on dbh for open-grown lodgepole pine trees. A factor is introduced to reduce the calculated crown width, as trees grow from open-grown initially to forest-grown conditions. Tree height is calculated from the multiple regression equation of height on dbh and basal area per acre. Individual tree volumes are calculated from ratios of volume to basal area for various heights. Techniques of testing confidence in the prediction of stand parameters are illustrated for the revised model. Combined standard errors of estimate (in per cent) are used to indicate the error estimates for the simulation model. These are large but, by comparison with all available data on tree growth and stand yield, the revised simulation model satisfactorily describes the growth of lodgepole pine stands in all four spacings tested. Moreover, much of the information calculated for each 5-year period cannot be obtained from conventional yield tables. In order to analyze the economic consequences of harvesting various kinds of products, yields of 8-foot logs and ratios of section volume to tree volume are calculated for ages 20 to 100. Maximum gross yields will come from 3.3 ft. x 3.3 ft. initial spacings. However many small trees included in gross yield estimates will be less than 6 inches in dbh and therefore not merchantable. The full range of influence of tree size on costs and values per tree is illustrated. Ratios of lineal feet per acre to cubic volume per acre are used to adjust logging and milling costs for tree size, based on the average cost per cunit which applies to lodgepole pine trees averaging about 11 inches in dbh. In all cases tested, initial spacings of 13.2 ft. x 13.2 ft. give the best net return per acre from plywood and lumber. Production of lumber is next best. Poles and piling are less attractive, under the present assumptions. Production of pulp chips alone would create a loss at present market value. Results are summarized in two comprehensive wood and product value yield tables (Tables 5A and 55). These tables may improve decision-making concerning initial spacing. The revised simulation model also can be used to simulate, in a few minutes, the growth of many other kinds of lodgepole pine stands from age 15 to age 100, or more. Economic consequences of many approaches to managing lodgepole pine can be illustrated now. Although greatly improved economic and biological data are desirable, the revised model can provide good preliminary answers to many important questions about management of lodgepole pine.

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