Tree dimensions: Maximizing the rate of height growth in dense stands

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Abstract
To determine the effect of tree dimensions on the rate of height growth a model was constructed relating tree weight to total height and R, the ratio of crown weight to trunk weight. The model is based on the assumption that the trunk buckling safety factor is constant. If trees also maintain a constant R as they grow then the rate of height growth is maximized by R=0.17. In addition, the height growth rate increases as the buckling safety factor decreases. These predictions of optimal form for height growth are appropriate for shade intolerant, successional species growing in dense stands. Dimensional measurements of self thinning Populus tremuloides indicate near optimal dimensions for height growth. Trees ranging from 7 to 19 m in height had trunks which were only 50% thicker than the minimum required to prevent them from buckling under their own weight, and had a mean R of 0.13. This ratio of crown weight to trunk weight is significantly lower than the optimal value, but the predicted height growth rate for R=0.13 is 99% of that predicted for R=0.17.

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