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(A) Diagram of a four-stage model of colour discrimination by a trichromatic eye (modified from Brandt & Vorobyev, 1997). Stage 1 : responses of receptors (r, rh) sensitive to short (S), medium (M) and long (L) wavelengths of light, to reference and test stimuli. Stage 2 : achromatic and\or chromatic interactions between signals . Three mechanisms are needed to represent all the information (x " , x # , x $ , for the reference and x " , x # , x $ , for the test stimulus) encoded by three receptor types. Stage 3: ∆S represents the distance of the two stimuli in colour space, this distance depends on the metrics (see Figs 3, 4). At stage 4, either the test or the reference stimulus is selected with a probability P corr . (B) Model that does not include stage 2 mechanisms ; many models are of this type, see Figs 3B, C, 4C, and 5A, ii and iii.  

(A) Diagram of a four-stage model of colour discrimination by a trichromatic eye (modified from Brandt & Vorobyev, 1997). Stage 1 : responses of receptors (r, rh) sensitive to short (S), medium (M) and long (L) wavelengths of light, to reference and test stimuli. Stage 2 : achromatic and\or chromatic interactions between signals . Three mechanisms are needed to represent all the information (x " , x # , x $ , for the reference and x " , x # , x $ , for the test stimulus) encoded by three receptor types. Stage 3: ∆S represents the distance of the two stimuli in colour space, this distance depends on the metrics (see Figs 3, 4). At stage 4, either the test or the reference stimulus is selected with a probability P corr . (B) Model that does not include stage 2 mechanisms ; many models are of this type, see Figs 3B, C, 4C, and 5A, ii and iii.  

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Over a century ago workers such as J. Lubbock and K. von Frisch developed behavioural criteria for establishing that non-human animals see colour. Many animals in most phyla have since then been shown to have colour vision. Colour is used for specific behaviours, such as phototaxis and object recognition, while other behaviours such as motion detec...

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... mammals, although there was also important work on honeybees (Daumer, 1956 ;von Helversen, 1972). Work on non-mammalian species is now becoming easier thanks to increasing numbers of measurements of photoreceptor spectral sensitivities (Table 1). The history of human colour vision can be reversed ; once spectral inputs to the receptors are known (Fig. 1, stage 1) it is possible to study neural processing of signals arising from a single stimulus (Fig. 1, stage 2), and the mechanisms comparing signals from different stimuli (Fig. 1, stage ...
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... on non-mammalian species is now becoming easier thanks to increasing numbers of measurements of photoreceptor spectral sensitivities (Table 1). The history of human colour vision can be reversed ; once spectral inputs to the receptors are known (Fig. 1, stage 1) it is possible to study neural processing of signals arising from a single stimulus (Fig. 1, stage 2), and the mechanisms comparing signals from different stimuli (Fig. 1, stage ...
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... of measurements of photoreceptor spectral sensitivities (Table 1). The history of human colour vision can be reversed ; once spectral inputs to the receptors are known (Fig. 1, stage 1) it is possible to study neural processing of signals arising from a single stimulus (Fig. 1, stage 2), and the mechanisms comparing signals from different stimuli (Fig. 1, stage ...
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... existence of multiple spectral types of photoreceptor is not sufficient for colour vision. Subsequent neural stages ( Fig. 1, stages 2 and 3) are necessary, and we are generally interested in the behavioural manifestations of these neural mechanisms ( Fig. 1, stage 4). In the simplest arrangement, behaviour is directly driven by the response of one or more receptors to a stimulus (Fig. 1B). When only one receptor is involved, behaviour is colour blind, and ...
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... existence of multiple spectral types of photoreceptor is not sufficient for colour vision. Subsequent neural stages ( Fig. 1, stages 2 and 3) are necessary, and we are generally interested in the behavioural manifestations of these neural mechanisms ( Fig. 1, stage 4). In the simplest arrangement, behaviour is directly driven by the response of one or more receptors to a stimulus (Fig. 1B). When only one receptor is involved, behaviour is colour blind, and the corresponding channel is called achromatic. When signals of several receptors are directly used to discriminate stimuli behaviour is no ...
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... of photoreceptor is not sufficient for colour vision. Subsequent neural stages ( Fig. 1, stages 2 and 3) are necessary, and we are generally interested in the behavioural manifestations of these neural mechanisms ( Fig. 1, stage 4). In the simplest arrangement, behaviour is directly driven by the response of one or more receptors to a stimulus (Fig. 1B). When only one receptor is involved, behaviour is colour blind, and the corresponding channel is called achromatic. When signals of several receptors are directly used to discriminate stimuli behaviour is no longer colour blind -even if no chromatic interaction occurs. Alternatively, receptor signals may interact ( Fig. 1A ; stage 2). ...
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... to a stimulus (Fig. 1B). When only one receptor is involved, behaviour is colour blind, and the corresponding channel is called achromatic. When signals of several receptors are directly used to discriminate stimuli behaviour is no longer colour blind -even if no chromatic interaction occurs. Alternatively, receptor signals may interact ( Fig. 1A ; stage 2). Visual neurons may either sum photoreceptor signals, or compare them by some type of inhibitory interaction to give the ratio or difference of receptor signals. Chromatic mechanisms involve the comparison of receptor outputs, while achromatic mechanisms involve only additive Fig. 2. Relative sensitivities of photoreceptors ...
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... and many subsequent models of colour vision implement his hypothesis. Hering (1878), on the other hand, argued that interactions are essential, and that two opponent channels -yellow-blue and red-greenunderlie human colour sensations. Helmholtz and Hering models can be reconciled by recognizing that colour vision is a multistage process ( Fig. 1 ; see 91 ...
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... discrimination (∆λ\λ function) is defined as the smallest wavelength difference that can be discriminated using two monochromatic stimuli. Monochromatic stimuli might be discriminated by both chromatic and achromatic signals, but studies of wavelength discrimination are generally intended to isolate chromatic mechanisms, in which case stimulus intensities are adjusted to remove achromatic signals, although this adjustment is difficult (Section V.1b). ...
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... well as identifying receptor types, behavioural spectral sensitivities (without quantitative modelling) can implicate neural interactions between receptor outputs. The simplest possibility is that receptor signals from two stimuli (Fig. 1, stage 3) are compared without opponency (Fig. 1B). This predicts that peaks of the behavioural spectral sensitivity curves should be at least as broad as the receptor Fig. 3. Diagrams of contours of equal colour discriminability in trichromatic receptor space. Different contours are predicted by three models that have been used to fit ...
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... well as identifying receptor types, behavioural spectral sensitivities (without quantitative modelling) can implicate neural interactions between receptor outputs. The simplest possibility is that receptor signals from two stimuli (Fig. 1, stage 3) are compared without opponency (Fig. 1B). This predicts that peaks of the behavioural spectral sensitivity curves should be at least as broad as the receptor Fig. 3. Diagrams of contours of equal colour discriminability in trichromatic receptor space. Different contours are predicted by three models that have been used to fit experimental data (Fig. 5 ;Brandt & Vorobyev, ...
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... be deduced by fitting the model to experimental data (see Fig. 5). The dotted line indicates the axis in the colour space corresponding to this mechanism. The two planes orthogonal to the mechanism's axis give contours of equal discriminability. (B) Discrimination is limited by noise in the three receptor mechanisms, with stage 2 mechanisms (see Fig. 1) absent or not adding noise. This is a Helmholtz line element. Distance in this colour space is given by ∆S # l g SS ∆q# S jg MM ∆q# M jg LL ∆q# L . The three peaks. Neumeyer (1984) found that peaks of the behavioural spectral sensitivity curve of goldfish were in fact narrower than those of its photoreceptors, and deduced that there ...
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... line element. Distance in this colour space is given by ∆S # l g SS ∆q# S jg MM ∆q# M jg LL ∆q# L . The three peaks. Neumeyer (1984) found that peaks of the behavioural spectral sensitivity curve of goldfish were in fact narrower than those of its photoreceptors, and deduced that there are inhibitory interactions between receptor signals (Fig. 1A, stage ...
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... (1896) introduced quantitative modelling of thresholds (Wyszecki & Stiles, 1982). The theory assumes that discriminability of any two colours is given by their separation in some colour space, ∆S, and that the behavioural response, P corr (Fig. 1, stage 4), depends on ∆S alone. Where ∆S is below a threshold value, colours are assumed to be indistinguishable. In two-alternative forced-choice tests P corr can vary from 0n5 (random choice) to 1 (100 % reliable choice), and threshold is usually assumed to correspond to P corr l 0n75. It is important to note that distances (∆S ) refer to ...
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... to note that distances (∆S ) refer to discriminability of stimuli, and say nothing about perceptual similarity of stimuli that are 100 % discriminable. In a given space, the rule for calculating distance between points is called the ' metric ' of the space. Different metrics make different assumptions about the processing of receptor signals (Fig. 1, stage 2), and about the comparison of neural signals corresponding to two colours (stage 3). Many models have been developed to explain human colour discrimination, some of which have been applied to ...
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... key question is whether limits to colour discrimination are imposed at the receptor stage (Fig. 1, stage 1), or by subsequent neural stages (stages 2, 3). When noise originating in the receptors limits the discriminability, the shape of threshold contours says nothing about the receptor inputs to stage 2 mechanisms. For the models where discrimination thresholds are described by polygonal contours (dominance metric and city block metric ...
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... models (Riemann metric) make very general assumptions about neural mechanisms of colour discrimination. They are valid if : (i ) postreceptoral neural interactions (Fig. 1, stages 2 and 3) are smooth functions, and threshold stimuli are reasonably close together in receptor space (Brandt and Vorobyev, 1997, Appendix A) ; or (ii ) behavioural thresholds are set by noise in neural mechanisms (Vorobyev & Osorio, 1998, Appendix ...
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... the polygonal models, the dominance metric is one of the earliest models of colour vision, postulating that the receptors do not interact (stage 2 is absent ; Fig. 1B). Colour vision can then be described without assuming opponent interactions. This model proposes that the most sensitive receptor mechanism is used for detection of any given stimulus. The upper envelope of the receptor sensitivities then describes behavioural spectral sensitivity (Pirenne, 1962). The dominance metric -with or without ...
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... models fit the thresholds for both humans (Poirson & Wandell, 1990) and bees (Brandt & Vorobyev, 1997) almost as well as polygonal models (Fig. 5). Brandt & Vorobyev (1997) tested a number of models on von Helversen's (1972) measurements of honeybee spectral sensitivity (Fig. 5). Models that assume that receptor signals do not interact (Fig. 1B) fail to explain the data. This implies that receptor signals are integrated by some neural mechanism (Fig. 1, stage 2) before responses to different stimuli are compared (stage 3). Likewise, single-mechanism models -such as those described in Section V.2.cdo not fit the data. To explain honeybee spectral sensitivity one needs to assume ...
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... almost as well as polygonal models (Fig. 5). Brandt & Vorobyev (1997) tested a number of models on von Helversen's (1972) measurements of honeybee spectral sensitivity (Fig. 5). Models that assume that receptor signals do not interact (Fig. 1B) fail to explain the data. This implies that receptor signals are integrated by some neural mechanism (Fig. 1, stage 2) before responses to different stimuli are compared (stage 3). Likewise, single-mechanism models -such as those described in Section V.2.cdo not fit the data. To explain honeybee spectral sensitivity one needs to assume at least two stage 2 mechanisms, which must be insensitive to intensity variation, and involve chromatic interactions ...

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... A combination of physiological or genetic and computational methods is typically employed to determine what colors are discriminable to animal eyes (Kelber et al. 2003). Physiological methods include microspectrophotometry and electrophysiology, both of which involve stimulating photoreceptors with different colors of light to determine the wavelengths of their peak sensitivities. ...
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... I then averaged the colour distance (ΔS) for each comparison and compared the resulting values to a standard colour discriminability threshold of ΔS = 1. This threshold represents when two colours become just distinct enough to tell apart by the modelled viewer, also known as a 'just-noticeable-difference' (JND; Kelber et al., 2003;Vorobyev et al., 2001). I did not test for statistical differences in the mean ΔS values of artificial versus live prey, as differences in values greater than one are difficult to interpret without further behavioural data from the relevant receiver(s) (Santiago et al., 2020). ...
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