Stephenson et al.'s ecological fallacy

After more than a century of research the typical growth pattern of a tree was thought to be fairly well understood. Following germination height growth accelerates for some time, then increment peaks and the added height each year becomes less and less. The cross sectional area (basal area) of the tree follows a similar pattern, but the maximum basal area increment occurs at some time after the maximum height increment. An increase in basal area in a tall tree will add more volume to the stem than the same increase in a short tree, so the increment in stem volume (or mass) peaks very late. Stephenson et al. challenge this paradigm, and suggest that mass increment increases continuously. Their analysis methods however are a textbook example of the 'ecological fallacy', and their conclusions therefore unsupported. The ecological fallacy 1 was most famously described by the sociologist William Robinson (1913-1996) 1 , who pointed out that correlations present in aggregated data do not imply that the same correlations are present in the individuals 3. In the context of the Stephenson et al. paper 4 , this means that the fact that large trees of a species tend to have higher mass increment than small trees in no way implies that increment in individuals is a monotonic function of tree size. Robinson gave a mathematical proof of the fallacy, but we can demonstrate the effect here using tree measurements pertinent to Stephenson et al.'s study. Adolf Ritter von Guttenberg (1839-1917) compiled one of the classic datasets of forestry science 5,6. In 95 stands of Norway Spruce (Picea abies [L] Karst) across the Austrian Alps he felled 107 average trees and cut the stems into sections of between 1.0 and 4.0 metres length. The volume of each section was calculated individually and summed to give a total stem volume. By counting and measuring the annual growth rings in each section he was able to record a quite detailed growth history for each tree. We use here the data from the Hinterberg forest region in Styria, and select the six trees taken from Site Class 1 plots (the most productive). Tree ages at felling were 140 and 150 years. Aboveground biomass (including branches and foliage) is derived from the volume, diameter and height data using relationships from the standard Austrian biomass functions 7. When we aggregate the data for these six trees and fit …