To be effective, animal colour signals must attract attention—and therefore need to be conspicuous. To understand the signal function, it is useful to evaluate their conspicuousness to relevant viewers under various environmental conditions, including when visual scenes are cluttered by objects of varying colour. A widely used metric of colour difference (Δ S ) is based on the receptor noise limited (RNL) model, which was originally proposed to determine when two similar colours appear different from one another, termed the discrimination threshold (or just noticeable difference). Estimates of the perceptual distances between colours that exceed this threshold—termed ‘suprathreshold’ colour differences—often assume that a colour's conspicuousness scales linearly with colour distance, and that this scale is independent of the direction in colour space. Currently, there is little behavioural evidence to support these assumptions. This study evaluated the relationship between Δ S and conspicuousness in suprathreshold colours using an Ishihara-style test with a coral reef fish, Rhinecanthus aculeatus . As our measure of conspicuousness, we tested whether fish, when presented with two colourful targets, preferred to peck at the one with a greater Δ S ­ from the average distractor colour. We found the relationship between Δ S and conspicuousness followed­­ a sigmoidal function, with high Δ S colours perceived as equally conspicuous. We found that the relationship between Δ S and conspicuousness varied across colour space (i.e. for different hues). The sigmoidal detectability curve was little affected by colour variation in the background or when colour distance was calculated using a model that does not incorporate receptor noise. These results suggest that the RNL model may provide accurate estimates for perceptual distance for small suprathreshold distance colours, even in complex viewing environments, but must be used with caution with perceptual distances exceeding­ ­10 Δ S .

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