Diameter distributions and structural sustainability in forests

For over a century, the negative exponential relationship of tree density to diameter has been observed and considered an indicator of equilibrium forest structure, especially at the stand level. More recent studies have suggested that other forms of diameter distributions should be considered “balanced”. Some of these seemingly contradictory findings can be resolved by understanding the impacts of scale and sampling area on the possibility of observing a negative exponential distribution. We calculated the minimum area required to sample the smallest number of trees necessary to produce hypothetical negative exponential distributions. The minimum area is influenced greatly by the maximum diameter and the exponential decrease rate of the distribution. It is also influenced by the width of diameter classes used to summarize the data, and the basal area per hectare of the sample. These differences in minimum required sampling area are important considerations because some recent studies that suggest a rotated sigmoid distribution, rather than negative exponential, is more characteristic of old-growth forests may have used sampling schemes that were insufficient to observe a negative exponential distribution even if one existed. Others have used criteria in selecting sampling locations that ensure a high density of large trees, thereby precluding them from observing a negative exponential distribution even if one existed. Our review suggests that within-stand sampling areas for testing diameter distribution in temperate forests typically need to exceed 1 ha, especially in mature to old-growth stages, though mortality rate, diameter class width, and total stand basal area all affect the area or number of prism points needed. Diameter distributions have rarely been assessed at the landscape scale. Nonetheless, it is reasonable to expect that landscape distributions may generally be negative exponential and the slope of the line (i.e. the mortality rate) may be an important measure of landscape dynamics. Old-growth landscapes where natural disturbances are typically small patches will have a lower mortality rate than those where disturbances are more frequent and widespread.