Enquist and Niklas propose that trees in natural forests have invariant size-density distributions (SDDs) that scale as a -2 power of stem diameter, although early studies described such distributions using negative exponential functions. Using New Zealand and 'global' data sets, we demonstrate that neither type of function accurately describes the SDD over the entire diameter range. Instead, scaling functions provide the best fit to smaller stems, while negative exponential functions provide the best fit to larger stems. We argue that these patterns are consistent with competition shaping the small-stem phase and exogenous disturbance shaping the large-stem phase. Mortality rates, estimated from repeat measurements on 1546 New Zealand plots, fell precipitously with stem size until 18 cm but remained constant after that, consistent with our arguments. Even in the small-stem phase, where SDDs were best described by scaling functions, the scaling exponents were not invariantly -2, but differed significantly from this value in both the 'global' and New Zealand data sets, and varied through time in the New Zealand data set.