REPORT Disturbances prevent stem size-density distributions in natural forests from following scaling relationships David A. Coomes 1,2 *, Richard P. Duncan 3 , Robert B. Allen 2 and James Truscott 1 1 Department of Plant Sciences, Cambridge University, Downing Street, Cambridge, CB2 3EA, UK 2 Landcare Research, PO Box 69, Lincoln, Canterbury, New Zealand 3 Ecology and Entomology Group, PO Box 84, Lincoln University, Canterbury, New Zealand *Correspondence: E-mail: dac18@cam.ac.uk Abstract 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 ÔglobalÕ 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 ÔglobalÕ and New Zealand data sets, and varied through time in the New Zealand data set. Keywords Community ecology, demographic modelling, diffusion equation, disturbance, equilib- rium, forest dynamics, herbivory, Kolmogorov, scaling rules. Ecology Letters (2003) 6: 980–989 INTRODUCTION There are a few general ecological theories that link the properties of individual organisms with the functioning of communities and ecosystems, so a recent series of scaling rules that report such links have been heralded with great interest (Enquist et al. 1998; Enquist & Niklas 2001; Midgley 2001; Whitfield 2001). The theories use the physical laws of fluid dynamics to predict the ways in which vessels should change in dimension along vascular systems, plants should allocate carbon, and even how ecological communities should be structured (Enquist et al. 1998). Building on this theory, Enquist & Niklas (2001) propose that size-density distributions (henceforth SDDs) of natural forests should scale as the )2 power of stem diameter. As the forestry literature abounds with size-density analyses but has lacked an overarching theory, a general theory explaining the shape of SDDs would represent a substantial breakthrough (Midgley 2001). Enquist and Niklas support their argument with an analysis of stem-diameter data from 226 transects located in forests throughout the world. In every case they consider, scaling relationships seem to fit the empirical SDDs with scaling exponents close to )2. Many studies have shown that competition can lead to scaling relationships in SDDs, at least in even-aged, self- thinning stands (reviewed by Begon et al. 1996; Enquist et al. 1998). Such relationships generally arise when the probab- ility of mortality depends on stem size, such that the smallest stems have the highest probability of mortality, with that probability declining in progressively larger stems (Begon et al. 1996; Table 1a). Such an outcome is expected under size-asymmetric competition for a limiting resource such as light. Enquist & Niklas (2001) have extended this concept to mixed-species mixed-aged forests, assuming that competi- tion is the dominant process affecting SDDs, and that competition in mixed forests operates in a similar manner to that observed in even-aged, self-thinning stands. In contrast, many studies have shown that exogenous disturbances are a major source of stem mortality in natural forests (Bormann & Likens 1979; Wells et al. 2001). If disturbances were equally likely to kill stems regardless of their size, and if disturbances were the major source of stem mortality, then the annual rate of mortality in a given size class would be proportional to the number of stems in that size class. The resulting SDD would then be negative exponential, assuming that growth rate is constant in all size Ecology Letters, (2003) 6: 980–989 doi: 10.1046/j.1461-0248.2003.00520.x Ó2003 Blackwell Publishing Ltd/CNRS