On the challenge of fitting tree size distributions in ecology
Abstract
Patterns that resemble strongly skewed size distributions are frequently observed in ecology. A typical example represents tree size distributions of stem diameters. Empirical tests of ecological theories predicting their parameters have been conducted, but the results are difficult to interpret because the statistical methods that are applied to fit such decaying size distributions vary. In addition, binning of field data as well as measurement errors might potentially bias parameter estimates. Here, we compare three different methods for parameter estimation – the common maximum likelihood estimation (MLE) and two modified types of MLE correcting for binning of observations or random measurement errors. We test whether three typical frequency distributions, namely the power-law, negative exponential and Weibull distribution, can be precisely identified, and how parameter estimates are biased when observations are additionally either binned or contain measurement error. We show that uncorrected MLE already loses the ability to discern functional form and parameters at relatively small levels of uncertainties, while the modified MLE methods that consider such uncertainties are comparatively much more robust. We conclude that it is important to reduce binning of observations, if possible, and to quantify observation accuracy in empirical studies for fitting strongly skewed size distributions.
What the paper shows and why it matters (AI-generated)
Ecology is full of strongly skewed size distributions — tree diameters being the classic example — but the statistical methods used to fit them vary study to study, making results hard to compare. Testing three estimation methods against binned and noisy data, the authors find standard maximum likelihood loses its ability to tell a power-law from an exponential or Weibull distribution surprisingly quickly, while methods that explicitly correct for binning and measurement error stay robust. The distinction keeps mattering in later work on canopy structure atlases and tree-size demographic theory that leans on exactly these distributional fits.