Spatial leaf distribution and self-thinning exponent of Pinus banksiana and Populus tremuloides

Abstract

A hypothesis that the pattern of spatial leaf distribution in forest canopies is numerically related to the exponent of the self-thinning relationship in even-aged monocultures was tested by evaluating the crown fractal dimension of Pinus banksiana (jack pine) and Populus tremuloides (quaking aspen) in Wood Buffalo National Park, Canada. Pure species stands that were considered the most dense for a given mean tree size were measured to establish the empirical self-thinning relationships. The value of the self-thinning exponent was estimated as –1.42 with 95% Confidence Interval (CI) (−1.47, −1.36) for Pinus banksiana, and –1.29 with 95% CI (−1.45, −1.14) for Populus tremuloides. For each species the box dimension of spatial leaf distribution was estimated from unit cylinders described by sequentially lowering in forest canopies, horizontal “flaps” of one of various diameters attached to the top of a height-measuring pole. The box dimension appeared as 1.95 (1.84, 2.06) for Pinus banksiana, and 2.24 (2.05, 2.43) for Populus tremuloides. By assuming that the box dimension is equivalent to the fractal dimension at the inter-population level, the self-thinning exponent was predicted to be –1.53 (−1.62, −1.45) for Pinus banksiana, and –1.33 (−1.45, −1.23) for Populus tremuloides. The empirical exponent was equivalent to that predicted from the box fractal dimension, as judged by the 95% CI of the dimensions. We conclude that spatial patterns of leaf distribution in forest canopies, as being characterized by the box fractal dimension, are closely related to the value of the self-thinning exponent in the dense monocultures of the species we examined.