Distance transform: a tool for the study of animal colour patterns

Summary The information in animal colour patterns plays a key role in many ecological interactions; quantification would help us to study them, but this is problematic. Comparing patterns using human judgement is subjective and inconsistent. Traditional shape analysis is unsuitable as patterns do not usually contain conserved landmarks. Alternative statistical approaches also have weaknesses, particularly as they are generally based on summary measures that discard most or all of the spatial information in a pattern. We present a method for quantifying the similarity of a pair of patterns based on the distance transform of a binary image. The method compares the whole pattern, pixel by pixel, while being robust to small spatial variations among images. We demonstrate the utility of the distance transform method using three ecological examples. We generate a measure of mimetic accuracy between hoverflies ( D iptera: S yrphidae) and wasps ( H ymenoptera) based on abdominal pattern and show that this correlates strongly with the perception of a model predator (humans). We calculate similarity values within a group of mimetic butterflies and compare this with proposed pairings of M üllerian comimics. Finally, we characterise variation in clypeal badges of a paper wasp ( P olistes dominula ) and compare this with previous measures of variation. While our results generally support the findings of existing studies that have used simpler ad hoc methods for measuring differences between patterns, our method is able to detect more subtle variation and hence reveal previously overlooked trends.