Importance of Power-law Distributions in Ecology: Power-law Distributions: Physicists’ Fancy or Ecologists’ Imperative?

Abstract

Nature abounds in variation, especially in biological systems-whether in lifespans, sizes, weights, colour patterns, or any other characteristic of organisms. Often, these variations are assumed to have a normal or Gaussian distribution as the underlying probability distribution. The assumption of a normal distribution is fine in most cases, as it leads to decent explanations and predictions. However, there are crucial exceptions, especially if data follow a so-called power-law distribution, which fundamentally differs from the normal distribution. In this article, we introduce power-law distributions in a way accessible to biology students, give examples of systems where they are found, explain some of their key properties, and emphasise how they differ from the normal distribution. We compare normal, exponential, and power-law distributions and, in particular, illustrate that the chance of an extreme event is much higher in systems with an underlying power-law distribution. Because the mean and variance of power-law distributions do not converge, we explain how our ability to obtain reliable estimates of simple statistics like the mean and variance of biological variables becomes severely limited. Finally, we explain the implications of these results in the context of animal foraging, ecosystem self-organisation, and resilience.