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UBC Theses and Dissertations

The development of a stand model for Douglas fir Newnham, R. M.


A mathematical model has been developed to describe the growth of trees in stands of Douglas fir (Pseudotsuga menziesii (Mirb.) Franco) from age ten to age 100 years. An initial square pattern of spacing was assumed. At age ten years the trees were assumed to be open-grown, that is, growing in diameter at breast height at a maximum rate. A regression of d.b.h. on age was obtained from eighteen open-grown, Douglas fir trees measured on the Saanich Peninsula, Vancouver Island. The relationship derived from these data agreed with further data collected elsewhere in the coastal regions of British Columbia and Washington and in the interior of British Columbia. The d.b.h. growth of individual trees was predicted by five-year periods. Relationships between crown width and d.b.h. were calculated from data on 426 open-grown, Douglas fir trees. There was a close correlation between crown width and root spread for open-grown trees. A multiple regression equation was obtained for height of 869 trees on d.b.h. and basal area per acre. All regression equations calculated for use in the model, were highly significant statistically. The model is initiated with a matrix of 15 x 15 trees (or tree "locations”). The initial d.b.h. of each tree is specified and, from the crown width/d.b.h. regressions, the crown width of each tree is calculated. As long as the tree remains free of competition, this calculated crown width is reduced by 40 per cent by the reduction factor "REDFAC", to give the "competitive" crown width. This was because it was found that, in young Douglas fir plantations, there could be considerable overlapping of the crowns before d.b.h. growth was reduced. As soon as competition sets in the original 40 per cent reduction is systematically reduced. The proportion of the circumference of each tree that is occupied by the crowns of surrounding competitors is then calculated. This proportion indicates the amount of competition to which the tree is being subjected and varies between zero, if the tree is open-grown, and one or more, if the tree is completely enclosed by the surrounding competitors. If the reduction is sufficiently great, continued survival of the tree is considered unlikely, and the tree is assumed to have died. The periodic d.b.h. growth of the surviving trees is calculated at five-year intervals to age 100 years. All calculations are performed using am I.B.M. 7090 electronic computer. A summary of the structure of the stand can be printed out at the end of each five-year period if required. Height growth can be described by modifying the stand model by including an appropriate regression equation. Similarly, volume growth can be estimated by modifying the basic stand model. The mathematical model developed here satisfactorily describes the growth of Douglas fir stands on an individual tree basis, over a wide range of site conditions, stand densities, amounts and distributions of mortality and thinning regimes. Field data cannot be secured to evaluate the accuracy of all the tests made. However, there are no gross errors in absolute values and results are accurate proportionately. The model described here can aid the forester in managing Douglas fir stands in the Pacific Northwest. By simulating the growth of his stands from age ten to age 100 years in a few minutes he can study questions that would otherwise require several human generations to evaluate.

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