Inverse relationship of crown fractal dimension to self-thinning exponent of tree populations: a hypothesis

The self-thinning rule describes in overcrowded even-aged plant monocultures a consistent relationship of mean mass to the approximately −3/2 power of plant density. Recent analyses revealed cases of statistically significant departures of the exponent from −3/2, confirming earlier suggestions. Shade tolerance, crown structure, and stand conditions have been suggested to influence variation in the self-thinning exponent; however, quantitative relationships of the species' traits to thinning exponent have been unclear. I examined patterns of crown fractal dimension, a quantitative measure of crown structure, and their relationship to the self-thinning exponent in four tree species, Nothofagussolandri var. cliffortioides (Hook. f.) Poole, Pinusbanksiana Lamb., Pinusdensiflora Sieb. et Zucc., and Cryptomeriajaponica (Linn. fil.) D. Don. Only stands at maximum crowding were used for analysis. Crown fractal dimension of monocultures is hypothesized to be a factor determining the species-specific variation in the self-thinning exponent of tree populations and is inversely proportional to the thinning exponent. Species-specific change in foliage packing through development of overcrowded populations is suggested to be closely related to variation in crown fractal dimension and the self-thinning exponent. Implications to possible effects of leaf shape and structural characteristics of crowns to crown fractal dimensions are discussed.