Comparing colors using visual models

Color 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 color spaces, which allow for the viewer-subjective estimation of color appearance. Most studies of color in camouflage, aposematism, sexual selection, and other signaling contexts draw on these models, with the shared analytical objective of estimating how similar (or dissimilar) color samples are to a given viewer. We summarize popular approaches for estimating the separation of samples in color 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 color samples by neglecting 1) the statistical distribution and within-group variation of the data and/or 2) the discriminability of groups relative to the observer's visual capabilities. Instead, we formalize the 2 questions that must be answered to establish both the statistical presence and theoretical magnitude of color differences, and propose a 2-step, permutationbased 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 color-data features such as heterogeneity and outliers. We demonstrate the pitfalls of current methods and the flexibility of our suggested framework using an example from the literature, with recommendations for future inquiry.