Bayesian hierarchical modelling of size spectra

A fundamental pattern in ecology is that smaller organisms are more abundant than larger organisms. This pattern is known as the individual size distribution (ISD), which is the frequency distribution of all individual body sizes in an ecosystem.

The ISD is described by a power law and a major goal of size spectra analyses is to estimate the exponent of the power law, λ. However, while numerous methods have been developed to do this, they have focused almost exclusively on estimating λ from single samples.

Here, we develop an extension of the truncated Pareto distribution within the probabilistic modelling language Stan. We use it to estimate multiple λs simultaneously in a hierarchical modelling approach.

The most important result is the ability to examine hypotheses related to size spectra, including the assessment of fixed and random effects, within a single Bayesian generalized mixed model. While the example here uses size spectra, the technique can also be generalized to any data that follow a power law distribution.