Artifactions in the Log-Transformation of Species Abundance Distributions

One of the most frequently studied pattern in ecology is the Species Abundance Distribution (SAD) that represents the frequency distribution of species abundances in an assemblage. Two main approaches to displaying such information have been employed: histograms constructed using exponentially increasing bin widths as pioneered by Preston (1948), and plots of ranked species abundances. While both techniques have been extensively used in the investigation of community ecology hypotheses, the Preston-style species-abundance histogram has become central to current debates concerning appropriate characterization of the SAD and the processes generating it. Here we point out an important issue in the Preston approach that has profound implications to this debate: by employing bins of exponentially increasing size, the resultant histogram may display a hump-shaped pattern that is not congruent with the shape of the untransformed distribution. Moreover, any distribution constructed from log-transformed abundances will necessarily reveal at least one internal mode, even when the non-transformed probability density function is strictly decreasing. We warn against misinterpretation of such transformed datasets, and suggest that rank-abundance plots, which are equivalent to the cumulative distribution functions extensively used in other branches of science, represent a more informative approach as they allow for better discrimination between a number of probability distributions. Ecologists should be aware that logarithmic transformation often generates a log-normal-like shape, and are encouraged to use rank abundance curves to visualize and analyze species-abundance patterns.