Comparing colours using visual models

TL;DR: This work formalizes the two questions that must be answered to establish both the statistical presence and theoretical magnitude of colour differences, and proposes a two-step, permutation-based approach that achieves this goal.

Abstract: Colour in nature presents a striking dimension of variation, though understanding its function and evolution largely depends on our ability to capture the perspective of relevant viewers. This goal has been radically advanced by the development and widespread adoption of perceptual colour spaces, which allow for the viewer-subjective estimation of colour appearance. Most studies of colour in camouflage, aposematism, sexual selection, and other signalling contexts draw on these colour spaces, with the shared analytical objective of estimating how similar (or dissimilar) colour samples are to a given viewer. We summarise popular approaches for estimating the separation of samples in colour space, and use a simulation-based approach to test their efficacy with common data structures. We show that these methods largely fail to estimate the separation of colour samples by neglecting (i) the statistical distribution and within-group variation of the data, and/or (ii) the perceptual separation of groups relative to the observer9s visual capabilities. Instead, we formalize the two questions that must be answered to establish both the statistical presence and perceptual magnitude of colour differences, and propose a two-step, permutation-based approach that achieves this goal. Unlike previous methods, our suggested approach accounts for the multidimensional nature of visual model data, and is robust against common colour-data features such as heterogeneity and outliers. We demonstrate the pitfalls of current methods and the flexibility of our suggested framework using heuristic examples drawn from the literature, with recommendations for future inquiry.