Towards a seascape typology. I. Zipf versus Pareto laws

Two data analysis methods, referred to as the Zipf and Pareto methods, initially introduced in economics and linguistics two centuries ago and subsequently used in a wide range of fields (word frequency in languages and literature, human demographics, finance, city formation, genomics and physics), are described and proposed here as a potential tool to classify space–time patterns in marine ecology. The aim of this paper is, first, to present the theoretical bases of Zipf and Pareto laws, and to demonstrate that they are strictly equivalent. In that way, we provide a one-to-one correspondence between their characteristic exponents and argue that the choice of technique is a matter of convenience. Second, we argue that the appeal of this technique is that it is assumption-free for the distribution of the data and regularity of sampling interval, as well as being extremely easy to implement. Finally, in order to allow marine ecologists to identify and classify any structure in their data sets, we provide a step by step overview of the characteristic shapes expected for Zipf's law for the cases of randomness, power law behavior, power law behavior contaminated by internal and external noise, and competing power laws illustrated on the basis of typical ecological situations such as mixing processes involving non-interacting and interacting species, phytoplankton growth processes and differential grazing by zooplankton.