Scaling of tree height and trunk diameter as a function of ring number

Abstract

Phipps (1967) showed, in suppressed maples and oaks, that on average the cross-sectional area of successive tree rings is independent of ring number. From that empirical result I argued that mean ring width and mean ring diameter scale as the inverse square root and square root, respectively, of ring number (Prothero 1997). Here I give an illustrative argument as to how macroscopic trunk variables may be related quantitatively to microscopic ring variables. First, evidence is presented consistent with the theory of Greenhill (1881) and the empirical evidence of McMahon (1973) that tree height in a diversity of species scales as about the two-thirds power of trunk diameter. Here I report further evidence bearing on the same question. From these combined results I suggest that tree height, and by implication trunk height, and other parameters governing macroscopic tree trunk proportions, can all be expressed as powers of a microscopic variable, namely ring number, where the scaling exponents are all proper fractions. I suggest that at least one of these relationships is, in principle, non-adaptive.