Functional relation of the whole-tree CO_2 exchange to tree size

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The whole-tree CO_2 gas-exchange was measured on five sample trees in a 19-year-old hinoki (Chamaecyparis obtusa) stand, using an open gas-exchange system. The measurement for each sample tree was kept on a 10-day run a month.The annual gross photosynthetic production by a tree, p, decreased with decreasing stem volume, v. The relationship was successfully expressed in the following generalized power function :*where g, h, and v_<min> are coefficients. Equation 1 implies that p decreases abruptly near the critical tree size, v_<min>, below which trees can not survive. In the light of the fact that the value of the exponent h was about 2/3, p is approximately proportional to the surface area in larger-sized trees.On the other hand, the annual respiratory consumption by a tree, r, was proportional to p, i.e.,*where the proportional constant k of 0.38 meant that r accounts for about 40% of p, regardless of tree size.Assuming Eqs.1 and 2 results in the following equation :*where g' is equal to k^.g. The observed data were well fitted with Eq.3.