A generalized equation for the calculation of receptor noise limited colour distances in n-chromatic visual systems

Researchers must assess similarities and differences in colour from an animal's eye view when investigating hypotheses in ecology, evolution and behaviour. Nervous systems generate colour perceptions by comparing the responses of different spectral classes of photoreceptor through colour opponent mechanisms, and the performance of these mechanisms is limited by photoreceptor noise. Accordingly, the receptor noise limited (RNL) colour distance model of Vorobyev and Osorio (Vorobyev & Osorio 1998 Proc. R. Soc. Lond. B265, 351-358 (doi:10.1098/rspb.1998.0302)) generates predictions about the discriminability of colours that agree with behavioural data, and consequently it has found wide application in studies of animal colour vision. Vorobyev and Osorio (1998) provide equations to calculate RNL colour distances for animals with di-, tri- and tetrachromatic vision, which is adequate for many species. However, researchers may sometimes wish to compute RNL colour distances for potentially more complex colour visual systems. Thus, we derive a simple, single formula for the computation of RNL distance between two measurements of colour, equivalent to the published di-, tri- and tetrachromatic equations of Vorobyev and Osorio (1998), and valid for colour visual systems with any number of types of noisy photoreceptors. This formula will allow the easy application of this important colour visual model across the fields of ecology, evolution and behaviour.