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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 detection are colour blind. Having established the existence of colour vision, research focussed on the question of how many spectral types of photoreceptors are involved. Recently, data on photoreceptor spectral sensitivities have been combined with behavioural experiments and physiological models to study systematically the next logical question: 'what neural interactions underlie colour vision?' This review gives an overview of the methods used to study animal colour vision, and discusses how quantitative modelling can suggest how photoreceptor signals are combined and compared to allow for the discrimination of biologically relevant stimuli.
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Biol.Rev. (2003), 78, pp. 81–118 "Cambridge Philosophical Society
DOI: 10.1017\S1464793102005985 Printed in the United Kingdom 81
Animal colour vision – behavioural tests and
physiological concepts
"Department of Cell and Organism Biology,Vision Group,Lund University,HelgonavaWgen 3, S-22362 Lund,Sweden
#Department of Biological Sciences,University of Maryland Baltimore County, 1000 Hilltop Circle,Baltimore,MD 21250, USA
$School of Biological Sciences,University of Sussex,Falmer,Brighton BN1 9QG, UK
(Received 3September 2001; revised 15 April 2002)
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 detection are colour blind. Having established the existence of colour vision,
research focussed on the question of how many spectral types of photoreceptors are involved. Recently, data
on photoreceptor spectral sensitivities have been combined with behavioural experiments and physiological
models to study systematically the next logical question: ‘what neural interactions underlie colour vision?
This review gives an overview of the methods used to study animal colour vision, and discusses how
quantitative modelling can suggest how photoreceptor signals are combined and compared to allow for the
discrimination of biologically relevant stimuli.
Key words: colour, vision, model, behaviour, photoreceptor, threshold.
I. Introduction ............................................................................................................................ 82
II. Photoreceptor signals ............................................................................................................... 83
(1) Diversity of receptors........................................................................................................ 83
(2) Spectral tuning of receptors.............................................................................................. 86
(a) Measurement of receptor sensitivities......................................................................... 86
(b) Visual pigments .......................................................................................................... 86
(c) Filters ......................................................................................................................... 87
(3) Modelling receptor signals................................................................................................ 87
III. Colour vision concepts ............................................................................................................. 88
(1) What is colour vision ? ....................................................................................................... 88
(2) Colour spaces, and the number of receptor types used for colour vision .......................... 89
(3) Achromatic and chromatic signals .................................................................................... 89
IV. Uses of chromatic signals ......................................................................................................... 91
V. Tests of colour vision............................................................................................................... 100
(1) Evidence for colour vision ................................................................................................. 100
(a) Grey card experiments............................................................................................... 100
(b) Monochromatic stimuli .............................................................................................. 101
(c) Broadband stimuli at different intensities ................................................................... 102
* Author for correspondence: e-mail: almut.kelber!
Present address: Vision Touch and Hearing Research Centre, University of Queensland, Brisbane, Queensland,
4072, Australia.
82 Almut Kelber, Misha Vorobyev and Daniel Osorio
(2) Tests of visual mechanisms ................................................................................................ 102
(a) Colour matching........................................................................................................ 102
(b) Discrimination of specially adjusted stimuli ............................................................... 103
(c) Receptor-based models of colour choices ................................................................... 103
VI. Modelling thresholds for colour discrimination....................................................................... 103
(1) Measuring thresholds ........................................................................................................ 104
(2) Interpretations of the shapes of threshold sensitivity curves............................................. 104
(3) Metric spaces and quantitative analysis of threshold data................................................ 105
(a) Inferring neural mechanisms from threshold data ..................................................... 106
(b) Receptor noise and colour thresholds ......................................................................... 108
(4) Threshold models as a tool to study the biological relevance of colour vision.................. 109
VII. Conclusions.............................................................................................................................. 109
VIII. Acknowledgements .................................................................................................................. 109
IX. Appendix A : Colour spaces ..................................................................................................... 109
X. Appendix B: Receptor-noise-limited colour opponent model.................................................. 111
XI. References................................................................................................................................ 112
Human colour science and psychophysics became
established during the nineteenth century, and
people began to ask whether animals see colour.
Lubbock (1888) in his book On the senses,instincts and
intelligence of animals demonstrated to his satisfaction
that Daphnia sp. see colour, using the fact that they
are both positively phototactic, and prefer yellow to
white light which is more intense across the entire
spectrum (see Section V.1c). Lubbock (1888) also
made a good case that honeybees (Apis mellifera) can
associate colour with food, but did not rule out their
using brightness. It was left to von Frisch (1914) to
confirm honeybee colour vision. At the same time
the problem of equating human colour sensations
with animal behaviour was well recognized. One
critic (Anonymous, 1889) of Lubbock’s book
doubted that one can conclude that animals taste,
see or hear simply because their movement is direc-
ted by sense organs analogous to our own. To this
day doubts persist as to whether animals enjoy the
sensation of, and hence can truly be said to see,
colour (Cogan, 1995; Stoerig, 1998). Nonetheless,
given the behavioural criteria of Lubbock and von
Frisch (see Section III.1) it is evident that many
animals use colour for tasks such as phototaxis where
spectral composition identifies a light source, and for
detecting and discriminating objects (Menzel, 1979 ;
Jacobs, 1981; Mollon, 1989).
This review deals with three main questions,
much as suggested by Menzel (1979): (1) Is colour
vision used for a particular task ? (2) How many
spectral types of photoreceptor are involved ? (3)
What can be said about the post-receptoral neural
mechanisms of colour discrimination, such as chro-
matic opponency?
Concepts in colour vision are mostly derived from
human perception and psychophysics. Human tri-
chromacy was proposed first in the eighteenth
century (Mollon, 1997), and models relating our
colour discrimination to underlying receptor re-
sponses and neural mechanisms are over a century
old (Maxwell, 1860; Hering, 1878 ; Helmholtz,
1896). When human cone spectral sensitivities were
first directly measured (Bowmaker & Dartnall,
1980), they closely matched psychophysical predic-
tions (Smith & Pokorny, 1975). As animals are more
difficult to test than humans, most work has aimed
simply to establish the existence of colour vision,
rather than to determine receptor inputs and neural
When Jacobs (1981) wrote his book Comparative
Color Vision most studies that went beyond dem-
onstrating the existence of colour vision were from
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 dif-
ferent stimuli (Fig. 1, stage 3).
We review two types of tests of colour discrimi-
nation. Firstly, tests of the ability to make a
discrimination (Section V), and secondly measure-
ments of discrimination thresholds (Section VI).
83Animal colour vision
Before looking at experimental data we outline the
diversity of visual photoreceptors that underlie
colour vision (Section II), introduce some ideas
relevant to understanding colour and how it is
studied (Section III), and discuss the roles of
achromatic and chromatic signals (Section IV).
(1) Diversity of receptors
Knowing photoreceptor spectral sensitivities simpli-
fies the study of colour vision, and phylogenetic
comparisons give insight into its evolutionary origins
and function. For example, haplorrhine primates
(i.e. monkeys and apes) often have three spectral
types of cone, compared to two in most other
mammals. Perhaps then trichromacy is an adap-
tation to the primates’ particular diurnal lifestyle
and frugivorous diet (Mollon, 1989). On the other
hand, the fact that many bees and wasps have a
similar set of three photoreceptors to the honeybee
implies that honeybee trichromacy is not a specific
adaptation to its being a generalist pollinator, being
evolutionarily older than the life-style (Peitsch et al.,
1992). Swallowtail butterflies (Papilio sp.) might
have evolved a fourth receptor type (sensitive to very
long wavelengths) as an adaptation to oviposition on
green leaves rather than to flower detection (Kelber,
Data on visual pigment and photoreceptor spec-
tral sensitivities are increasing, especially for verte-
brates. Microspectrophotometry (MSP) can be used
where intracellular recording is difficult. Molecular
genetics shows how opsins (pigment proteins) have
evolved, and how specific aminoacid residues de-
termine spectral tuning (Bowmaker, 1998; Bow-
maker & Hunt, 1999; Nathans, 1999). Table 1
indicates the range in numbers and spectral tuning
of photoreceptors in a selection of molluscs, arthro-
pods and vertebrates.
Photoreceptor nomenclature is complicated, and
potentially confusing. Receptors have been named
either according to the part of the spectrum to which
they are absolutely or relatively most sensitive:
red ’, ‘ green ’, ‘blue ’, ‘ UV ’ etc., or by their
sensitivity relative to other receptors in the eye for
example ‘long ’ (L), ‘ short ’ (S) and ‘medium ’ (M)
wavelength sensitive. This nomenclature is satis-
factory for referring to a given species or closely
related group of species, but is less satisfactory and
potentially confusing for more general comparisons.
Moreover, given that four main gene families of
vertebrate cone opsin have been recognized (His-
atomi et al., 1994; Bowmaker & Hunt, 1999), it
seems desirable to use the terms VS (‘very short ’), S,
M and L to refer to the opsin gene family, and to
specify the spectral sensitivity maximum of the
photopigment (see also Bowmaker & Hunt, 1999).
For invertebrate photopigments we simply specify
the spectral sensitivity maxima of each species’ visual
pigments or photoreceptors (Table 1).
Of invertebrates, Octopus vulgaris like most other
cephalopod molluscs has a single spectral type of
receptor. Some spiders and crustaceans have two
types. Daphnia magna and perhaps jumping spiders
(Salticidae) have four, while stomatopod crustaceans
have up to 16. Among insects, cockroaches (Blatto-
dea) and some ants have two spectral receptor types,
while most bees and wasps have three (Peitsch et al.,
1992). Dragonflies (Odonata) and sawflies (Tenthri-
dinidae) have four spectral types of receptor, and
some flies (Diptera) and butterflies have five or more
(Table 1; reviewed by Briscoe & Chittka, 2001).
In vertebrates, the two main types of visual
photoreceptor cell, rods and cones, are distinguished
by a number of morphological and physiological
features (Cohen, 1972). Normally, rods are active at
low (scotopic) light intensities, and cones at high
(photopic) intensities. Colour vision uses mainly
cone signals, but goldfish (Carassius auratus) may use
rods and red (L) cones in dim light (down to 1 or 2
log units above absolute threshold: Powers & Easter,
1978b), and rods contribute to colour vision in
amphibians (Muntz, 1963) and humans (Wyszecki
& Stiles, 1982).
Of the more primitive vertebrates, lampreys have
one rod and two anatomically distinct types of cone
(Collin, Potter & Braekevelt, 1999), but only two
photopigments have been described (Table 1).
Many teleost fishes, reptiles and birds have one rod
and four cone opsins. These form five families
defined by amino acid sequences and characterized
by the locations of their spectral sensitivity maxima
(Table 1; Hisatomi et al., 1994 ; Bowmaker, 1998 ;
Bowmaker & Hunt, 1999): rod, very short (VS, or
violet\ultraviolet), short (S, or blue), medium (M,
or green) and long (L, or red). Rana spp. frogs also
have up to five receptor types, however two of them
are rods (a ‘red ’ rod and a ‘ green’ rod, Table 1).
Vertebrate lineages often lose visual photopigments,
for example many teleost fish along with most
mammals have only two cone pigments, while
snakes, crocodiles and geckos have three.
Mammals lost two cone opsin families, probably
during an early ‘nocturnal ’ phase of evolution,
84 Almut Kelber, Misha Vorobyev and Daniel Osorio
Table 1. Examples of receptors in different animal classes,other reviews listed give additional information about specific taxa.We give the species names,the
method used to determine sensitivity,and sensitivity maxima.Vertebrate receptors are classified according to the probable gene family of their opsin (see Section
II):VS(very short wavelength or UV receptor), S(short wavelength), M(medium wavelength), L(long wavelength). For invertebrates,sensitivity maxima
are mostly of receptors in vivo, whereas for vertebrates (other than ERG)they are generally sensitivities of isolated receptors,and do not take account of
intraocular filtering.Methods: E,electrophysiological recording,mostly intracellular for invertebrates and suction electrode recordings for vertebrates ; ERG,
electroretinogram; MSP,microspectrophotometry of photoreceptors or (MSP-G)artificially expressed
Animal group Method Sensitivity maxima (nm) Reference
Bivalva (Tridacna sp.) E 360 490 540 Wilkens (1984)
Octopus (Octopus vulgaris) E 470 Messenger (1981)
Firefly squid (Watasenia scintillans) MSP 470 485 500 Matsui et al. (1988)
Jumping spider (Plexippus validus) E 360 520 Blest et al. (1981)
Jumping spider (Menemerus confusus) E 360 490 520 580 Yamashita & Tateda (1976)
Ctenid spider (Cupiennius salei) E 340 480 520 Walla et al. (1996)
Crustaceans Review: Marshall et al. (1999)
Water flea (Daphnia magna) E 348 434 525 608 Smith & Macagno (1990)
Mantis shrimp (Neogonodactylus sp.,
Odontodactylus sp.)
E\MSP 12j(maxima from
315 to 654 nm)
Cronin & Marshall (1989); Marshall & Oberwinkler (1999)
Isopod (Ligia exotica) E 340 470 520 Hariyama et al. (1993)
Crayfish (Procambarus clarkii) 460 560\600 Nosaki (1969)
Insects Reviews: Menzel & Backhaus (1991) ; Briscoe & Chittka (2001)
Cockroach (Periplaneta americana) E 365 510 Mote & Goldsmith (1970)
Dragonfly (Sympetrum rubicundum) E 330 430 490 520 620 Meinertzhagen et al. (1983)
House fly (Musca domestica) E 335 355 460 490 530 Hardie (1986)
Honeybee (Apis mellifera) E 344 436 556 Menzel & Blakers (1976) ; Peitsch et al. (1992)
Butterfly (Papilio xuthus) E 360 400 440 520 600 Arikawa et al. (1987)
Vertebrates Rod VS S M L Reviews: Bowmaker (1995) (fish); Bowmaker (1998)
Lamprey (Lampetra lampetra) MSP 515 555 Govardovskii & Lychakov (1984)
Sturgeon (Acipenser baeri) MSP 549 465 549 613 Govardovskii et al. (1991)
Goldfish (Carrassius auratus)MSP\E 522 356 447 537623Bowmaker et al. (1991); Palacios et al. (1998)
Cichlid (Aequidens pulcher) MSP 500 453 530570Kro
$ger et al. (1999)
Frog (Rana spp.* including
? 431 502 562 Liebman & Entine (1968) ; Govardovsii & Zueva (1974) ;
Koskelainen et al. (1994)
Salamander (Ambystoma tigrinum) E 506 400 444 610 Perry & McNaughton (1991)
85Animal colour vision
Crocodile (Alligator mississippiensis) MSP 501 444 535 566Sillman et al. (1991)
Turtle (Pseudymys scripta ) MSP 360 450 518 620 Baylor & Hodgkin (1973); Loew & Govardovskii (2001)
Lizard (Anolis carolinensis) MSP-G 358 437 495 560 Kawamura & Yokoyama (1998)
Gecko (Gekko gekko) MSP 364 467 521 Loew (1994)
BirdsReviews: Bowmaker et al. 1997 ; Hart 2001
Chicken (Gallus gallus) MSP 506 418 455 507 569 Bowmaker et al. (1997)
Pekin robin (Leiothrix lutea) MSP 500 355 454 499 568 Maier & Bowmaker (1993)
Mammals Review: Jacobs (1993)
Dolphin (Tursiops truncatus) MSP-G 488 524 Fasick et al. (1998)
Squirrel (Spermophilus sp.) ERG 500 436 518 Jacobs (1993)
Human MSP\E 498 437 533564Bowmaker & Dartnall (1980) ; Schnapf et al. (1987)
* Some vertebrates including various fish and amphibia express both retinal and dehydroxyretinal as the chromophore in a single class of photo-
receptor or even a single cell (e.g. Firsov et al., 1994; Partridge & Cummins, 1999). Dehydroxyretinal red-shifts the spectral sensitivity by over 50 nm
for long-wavelength-sensitive opsins. Where receptors may use both types of chromophore we give the value for the retinal-bearing variant.
Bird double cones contain the long-wavelength-sensitive visual pigment and are not thought to contribute to colour vision, fishes can use double
cones for colour vision and the pigments of the principle and accessory cones are given.
Primate M and L receptor pigments are both derived from the mammal L pigment. They are named M and L for convenience.
86 Almut Kelber, Misha Vorobyev and Daniel Osorio
Fig. 1. (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 sig-
nals. Three mechanisms are needed to represent all the
information (x",x#,x$, for the reference and x
$, for
the test stimulus) encoded by three receptor types. Stage
3: Srepresents 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 Pcorr. (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.
leaving them with L and VS opsins ( Jacobs, 1993 ;
Bowmaker, 1998; Bowmaker & Hunt, 1999). Mam-
malian VS photopigment and cones are commonly
called ‘S ’ (i.e. short-wavelength sensitive). This S
cone opsin is probably absent from dolphins and
seals (Peichl, Behrmann & Kro
$ger, 2001) and from
nocturnal species including racoons (Procyon spp.)
and owl monkey (Aotus sp.; Ahnelt & Kolb, 2000) ;
these species are cone monochromats. Conversely,
many primates, including all known Old-World
monkeys (Catarrhini), have recovered three types of
cone pigment by evolving separate ‘ L ’ (red) and
M ’ (green) opsins from the ancestral L opsin gene
(Bowmaker, 1998; Nathans, 1999).
(2) Spectral tuning of receptors
(a)Measurement of receptor sensitivities
A photoreceptor’s spectral sensitivity is given by the
relative likelihood of absorption of a photon incident
on the cornea, as a function of its wavelength. Once
a photon is absorbed, the electrical responses of
visual photoreceptors are (so far as is known)
independent of its wavelength. This ‘ principle of
univariance’ (Rushton, 1965) means that the inten-
sities of two visible spectra can always be adjusted to
give equal responses, so that individual photorecep-
tors are ‘colour blind ’.
Spectral sensitivities can be established in various
ways (Table 1). In invertebrates, the usual and
direct method is by intracellular recording from
photoreceptors in vivo the response to (typically)
monochromatic stimuli of known intensity (Autrum
& von Zwehl, 1964; Peitsch et al., 1992). In
vertebrates, suction electrode recording of isolated
receptors is often more practical (Schnapf, Kraft &
Baylor, 1987). Electroretinograms (ERG) combined
with selective adaptation are widely used with
vertebrates (Jacobs, 1993), but may be difficult to
interpret when there are three or more spectral types
of receptor. Alternatively, absorption spectra of
photopigments, and other visual media can be
measured by spectrophotometry, and receptor spec-
tral sensitivities can be estimated from these spectra.
Spectrophotometry can be performed either in
photoreceptors (Liebman & Entine, 1968 ; Cronin &
Marshall, 1989; Bowmaker et al., 1997), or artificial
expression systems (Asenjo, Rim & Oprian, 1994 ;
Fasick et al., 1998; Nathans, 1999). Finally, spectral
sensitivity of some vertebrate pigments can now be
predicted from the amino acid composition of the
opsin (Asenjo et al., 1994; Nathans, 1999 ; Bowmaker
& Hunt, 1999).
(b)Visual pigments
Visual photopigments are G-protein-coupled recep-
tors, which comprise an opsin protein and a
carotenoid chromophore. When a chromophore
absorbs a photon it isomerizes, and this causes the
opsin to change conformation to activate phototrans-
duction (Aidley, 1998). The visual pigment’s spectral
sensitivity depends both upon the chromophore and
the opsin, but for a given chromophore the shape of
the curve is a predictable function of the peak
wavelength (Dartnall, 1953; Govardovskii et al.,
2000). The commonest chromophore is retinal, the
87Animal colour vision
aldehyde derivative of vitamin A1, but fishes,
amphibians and reptiles sometimes have 3,4-
dehydroxyretinal, the derivative of vitamin A2 (por-
phyropsin; Wald, 1939 ; Provencio, Loew & Foster,
1992), and many insects use 3-hydroxyretinal, a
derivative of xanthophylls (Vogt & Kirschfeld,
1984). Substitution of A2 for A1 red-shifts sensitivity,
and this underlies some variation in fish and
amphibians (Liebman & Entine, 1968). The squid
Watasenia scintillans is remarkable for having three
visual pigments based on one opsin and three types
of chromophore (Matsui et al., 1988). Normally
though, the main source of variability in spectral
sensitivities is the opsin. For A1-based visual pig-
ments, sensitivity maxima range from approximately
310 nm to 570 nm, and for A2-based pigments up to
635 nm (Provencio et al., 1992).
Usually a single photoreceptor cell contains one
type of visual pigment, but there are exceptions, the
best known being the presence of mixtures of A1 and
A2 visual pigments in fish and amphibians (Firsov,
Govardovskii & Donner, 1994). Mouse (Mus mus-
culus), and possibly wallaby (Macropus eugenii) ex-
press two different opsins in the same cone photo-
receptor (Ro
$hlich, van Veen & Szel, 1994 ; Hemmi
$nert, 1999; Neitz & Neitz, 2001). The
swallowtail butterfly (Papilio xuthus) has a complex
set of photoreceptors, some of which co-express two
opsin genes (Kitamoto et al., 1998). Other receptors
in this butterfly express a single opsin, but adopt
different sensitivities depending on the presence of
3-hydroxyretinol, which works as a UV-absorbing
screening pigment (Arikawa et al., 1999). On the
other hand, flies use 3-hydroxyretinol as an antennal
pigment, which broadens spectral sensitivity by
adding a UV peak (Hardie, 1986; Vogt, 1989).
Receptor sensitivities depend primarily on their
visual pigments, but ocular filters often have a
marked effect (Walls, 1942; Douglas & Marshall,
1999). Yellow lenses of diurnal mammals and some
fishes absorb UV and violet light. The coloured oil
droplets in cone inner segments of many diurnal
reptiles and birds are of particular interest (Walls,
1942; Partridge, 1989 ; Goldsmith, 1991 ; Hart,
2001). These droplets vary in colour, and early
workers attributed a variety of functions to them,
most notably as a basis for colour vision in animals
assumed to have only a single visual pigment (e.g.
Walls, 1942; King-Smith, 1969). For vertebrates this
latter theory was doubted by Walls (1942), and now
seems unlikely because, at least in turtles and birds
four types of oil droplets are each associated with a
specific type of single cone photopigment (Bowmaker
et al., 1997; Loew & Govardovskii, 2001). Typically,
oil droplets cut off light of short wavelengths from a
value around the sensitivity maximum of the opsin
(Hart, 2001), and this appreciably sharpens spectral
tuning. Model calculations have recently provided
clear evidence that this sharpening indeed benefits
colour vision (Vorobyev et al., 1998).
In the grasshopper Phaeoba sp., corneal filters over
a single spectral type of photopigment may indeed
provide a basis for colour vision (Kong, Fung &
Wasserman, 1980). Corneal filters are common in
tachinid flies, but it is uncertain how they affect
spectral sensitivities. More generally, invertebrates
have a wide variety of intraocular filters using
photostable pigments (Douglas & Marshall, 1999).
Also, some compound eyes such as those of butterflies
and stomatopods have ‘tiered retinae ’ where light
passes first through ‘ distal ’ receptor cells in an
ommatidium, and so is filtered, before it reaches the
proximal cells (Cronin & Marshall, 1989 ; Douglas
& Marshall, 1999). In compound eyes, there is also
lateral ’ filtering, where several photoreceptor spec-
tral types combine to form a single light-guiding
rhabdom and hence compete for photons (see
Section II.3).
(3) Modelling receptor signals
The physical stimulus for vision is the number of
quanta absorbed by a receptor per unit time (e.g.
receptor integration time). Due to the availability of
cheaper spectrophotometers large numbers of biolo-
gically relevant stimuli have recently been measured
and used for modelling. Where the spectral dis-
tribution of a light stimulus, I(λ) is known, the
quantum catch, Qi, of a receptor type i, with spectral
sensitivity, Ri(λ), is given by:
Qil&I(λ)Ri(λ)dλ, (1)
where integration is over the visible spectrum.
Stimulus intensity can be given either in quantum or
in energy units, but the units of light stimulus and
spectral sensitivity must correspond. Quantum units
are commonly used in animal studies, and are
appropriate since photoreceptors act as quantum
counters. In human psychophysics, energy units are
more often used. If E(λ) is the spectrum of a light
stimulus in energy units, then the spectrum in
quantal units, I(λ), is given by:
88 Almut Kelber, Misha Vorobyev and Daniel Osorio
I(λ)lλ\hc E(λ), (2)
where his Planck’s constant and cthe velocity of
light. Similarly, the relationship of spectral sen-
sitivity in quantum units, Ri(λ), to that in energy
units, RE
i(λ) is given by:
i(λ). (3)
Usually relative rather then absolute sensitivity is
important, in which case the constant hc is omitted,
and spectral sensitivity is transformed from energy to
quantum units by dividing by wavelength. To derive
spectral sensitivity from spectrophotometric measure-
ments, let Fi(λ) be the attenuation of incoming light
by optical filters in the light path to the visual
pigments, and ki(λ) the extinction coefficient (ab-
sorption in a thin layer) of a pigment i, and xthe
length of a photoreceptor. Then the receptor
response, Ri(λ), is given by:
i(λ)o1kexp[kki(λ)x]q. (4)
Cis a proportionality factor that describes the
receptor’s absolute sensitivity. The second term in
eqn (4) describes ‘self-screening ’ by the visual
pigment, which being spectrally selective, removes
the wavelengths to which it most sensitive so that the
long receptor has a broadened spectral sensitivity.
Warrant and Nilsson (1998) give a simplified
expression for this term. When xis small
1kexp(kki(λ)x)%ki(λ)x. For arthropod eyes op-
tical modelling is complicated, because light may be
filtered as it travels along the rhabdom (photorecep-
tors). In fused rhabdoms, the visual pigments of
different receptor types act as filters for each other
thus narrowing the spectral sensitivity of each
receptor type. If sensitivities of the pigments are
known, spectral sensitivities can be calculated (Sny-
der, Menzel & Laughlin, 1973).
(1) What is colour vision ?
Understanding colour starts from our own subjective
experience. Colours have the qualities of hue,
saturation and brightness. Brightness is the value on
the dark to light scale. Saturation describes a colour’s
similarity to a neutral grey or white: a grey object
with a small reddish tint has low saturation, whereas
a red object with little white or grey tint is highly
saturated. Hue refers to colour differences other than
those of brightness and saturation, and is the
attribute denoted by terms such as red, yellow, green
or purple (Wyszecki & Stiles, 1982; Byrne & Hilbert,
1997; Backhaus, Kliegl & Werner, 1998). Brightness
is the achromatic aspect of colour, and hue and
saturation are chromatic aspects. There is no
evidence that animals perceive hue, saturation or
brightness as separate qualities, or that they cat-
egorize colours as yellow, red etc. Indeed some
workers insist that colour perception requires con-
sciousness; what we call colour vision, on be-
havioural criteria, Stoerig (1998) recognizes as
wavelength information processing ’.
A comprehensive definition of colour from the
standard handbook of colour science (Wyszecki &
Stiles, 1982, p. 487) is ‘that aspect of visual
perception by which an observer may distinguish
differences between two structure-free fields of view
of the same size and shape, such as may be caused by
differences in the spectral composition of the radiant
energy … ’. The advantage of this definition is that it
is not based on the human sensation of colour but on
a physical measurement – ‘ the spectral composition
of radiant energy therefore it can be applied to
animals. Paradoxically, by this definition, the ability
to discriminate colours does not entail colour vision.
Humans discriminate colours by means of chro-
matic (hue, saturation) as well as achromatic
(brightness) signals. Colour-blind people (mono-
chromats, including all humans in very dim light
intensities) discriminate many colours by means of
brightness. Colour vision, in humans, therefore
means the ability to discriminate colours by their
chromatic aspect, even though achromatic signals
contribute to human colour perception, i.e. subjects
with colour vision can discriminate colours of equal
brightness. We do not know whether animals
perceive brightness or hue, thus a general working
definition for colour vision needs to be based on a
physical criterion. Brightness relates to the sensitivity
of the achromatic channel in a visual system. A light
of 700 nm wavelength of high intensity might look as
bright as a light of 550 nm at low intensity. Intensity
is measured as the number of quanta incident on the
eye per unit area, angle in space and unit time
interval. For monochromats, it is always possible to
adjust the intensities of two spectral stimuli to yield
equal sensations. For humans with colour vision,
colours with different saturation or hue cannot
be made indiscriminable by adjusting stimulus
When describing animal colour vision we will
refer to intensity-related cues as achromatic cues,
89Animal colour vision
and to the signal they generate in the animal’s visual
system, as the achromatic signal. In humans, this
signal leads to the perception of brightness. We
conclude that an animal has colour vision if it can
discriminate two lights of different spectral com-
position, regardless of their relative intensity (e.g.
DeValois & DeValois, 1997; Menzel, 1979 ; Neu-
meyer, 1991; Goldsmith, 1991; Byrne & Hilbert,
1997). Section V describes experiments required to
test colour vision.
(2) Colour spaces, and the number of
receptor types used for colour vision
As we have just seen, animals with a single spectral
type of photoreceptor are monochromats in that it is
always possible to adjust the relative intensities of
two spectra to give identical responses (Rushton,
1965). If more than one light, or primary, is needed
to match colour the animal has colour vision. Colour
vision is classified as dichromatic, trichromatic,
tetrachromatic etc., according to the number of
lights required to match any spectral light. This
number cannot exceed the number of receptor types
in the eye but may be fewer, and needs to be
established behaviourally. Most vertebrates, for
example, normally do not use rods for colour vision.
Flies have two anatomically separate visual path-
ways; one of these is probably used for colour vision
and receives input from four of their five receptor
types (Troje, 1993).
Normal human observers are trichromats, because
any spectrum can be matched by a unique com-
bination of three primary spectra. Trichromacy was
first proposed in the eighteenth century by Lomo-
nosov, Palmer and Young (Mollon, 1997), and
established experimentally by Maxwell (1860). The
intensities of the three primaries that match a given
light are called ‘tristimulus values ’, and these give a
quantitative description of its colour. Tristimulus
values are linearly related to the quantum catches in
the three types of cone (Fig. 2B; Wyszecki & Stiles,
1982). Hence, for humans colour can be specified
either by the intensities of three known spectra
required for a match, or by the quantum catches Qi
of the three receptor types. A colour can then be
represented geometrically, as a point Qin a colour
space, whose dimensionality is given by the number
of primaries required for a colour match, or by the
number of receptor types involved (Fig. 2, Appendix
A). Colour matching establishes directly the dimen-
sionality of colour vision, and thus the number of
receptors used independently for colour discrimi-
nation (see Section V.2). Colour matching includes
the possibility that one of the primaries is added
negatively – i.e. it is added to the colour that one
tries to match instead of the other primaries.
Otherwise it is not possible to match colours that lie
outside the polygon in the colour space set by the
For humans, spectral sensitivities of the cardinal
axes of commonly used colour spaces (e.g. RGB,
XYZ; Wyszecki & Stiles, 1982) were chosen before
the cone sensitivities were known. Likewise, Daumer
(1956) proposed a trichromatic colour space for
honeybees from colour-matching experiments. But
Daumer’s work is an exception, and in most animal
studies the cardinal axes of colour spaces represent
receptor responses (Appendix 1; Menzel & Back-
haus, 1991; Neumeyer, 1991 ; Goldsmith, 1991 ;
Brandt & Vorobyev, 1997; Vorobyev & Menzel,
1999; Osorio, Miklo
!si & Gonda, 1999a; Osorio,
Vorobyev & Jones, 1999b).
In practice, the dimensionality of colour vision has
been studied in few animals. Many mammals are
dichromats save primates which are often trichro-
mats (Jacobs 1981, 1993), as are bees (Daumer,
1956). Goldfish, turtle (Pseudemys scripta elegans),
pigeon (Columba livia) and chicken (Gallus gallus) are
probably tetrachromats (Arnold & Neumeyer, 1987 ;
Neumeyer, 1992; Palacios et al., 1990 ; Palacios &
Varela, 1992; Osorio et al., 1999 b).
(3) Achromatic and chromatic signals
The existence of multiple spectral types of photo-
receptor is not sufficient for colour vision. Sub-
sequent neural stages (Fig. 1, stages 2 and 3) are
necessary, and we are generally interested in the
behavioural manifestations of these neural mechan-
isms (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). 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 mechan-
isms involve the comparison of receptor outputs,
while achromatic mechanisms involve only additive
90 Almut Kelber, Misha Vorobyev and Daniel Osorio
Fig. 2. Relative sensitivities of photoreceptors (left), receptor spaces (middle), and chromaticity diagrams with mono-
chromatic loci (right) for representative di- (A), tri-(B) and tetrachromatic eyes (C). Colour is represented as a point
Qin the receptor space, where each co-ordinate axis corresponds to the quantum catches of very short- (VS), short-
(S), medium- (M) and long-wavelength-sensitive (L) receptors. Receptor spaces thus have ndimensions for visual
systems with nreceptors; the four-dimensional receptor space can not be visualized. Chromaticity diagrams (right)
where Qil1, are projections of the receptor space to nk1 dimensions. A line (dashed) connecting Qwith the origin
intersects the chromaticity diagram (a line, for dichromats; a plane, for trichromats, and a three-dimensional space,
for tetrachromats) in a point qc. The vertices of chromaticity diagrams (VS, S, M, L) represent colours that are
represented on the axes of the colour spaces (middle). Colour loci of monochromatic lights are represented by the
dashed line, and plotted points every 10 nm (A, B) or 50 nm (C). NP in A indicates the neutral point of a dichromat,
i.e. the wavelength of light that has the same chromaticicty coordinates as white light. See Appendix A for details of
receptor spaces, and the corresponding chromaticity diagrams.
interactions. ndegrees of freedom in post-receptoral
neural signals are required to encode all the
information represented by a retina with nspectral
types of photoreceptor.
Historically, Helmholtz (1896) proposed that
human colour vision did not require interactions
between the three receptor mechanisms, 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-green –
underlie human colour sensations. Helmholtz and
Hering models can be reconciled by recognizing that
colour vision is a multistage process (Fig. 1 ; see
91Animal colour vision
Chapter 8 in Wyszecki & Stiles, 1982). Psycho-
physical evidence indicates that humans combine
their three receptor signals to give one achromatic
(or luminance) signal, and two chromatic signals
(Jameson & Hurvich, 1955 ; Krauskopf, Williams &
Heeley, 1982). The achromatic aspect of colour –
brightness – is mediated by non-opponent mechan-
isms, whereas the chromatic aspects of colour – hue
and saturation – are mediated by opponent mech-
anisms. Regardless of whether animals perceive
saturation, hue and brightness, we can hypothesize
that they have similar chromatic and achromatic
mechanisms. Nonetheless, care is required to in-
terpret behavioural experiments as evidence for
post-receptoral (stage 2) interactions, and we return
to this subject in Section VI.
It should be possible to relate psychophysically
defined mechanisms to neural responses, but even for
primates this is not easy. Macaque (Macaca macaca)
retinal ganglion cells, which transmit signals up the
optic nerve, do fall into three main spectral types:
those coding mainly luminance, yellow-blue op-
ponent cells, and the cells of the parvocellular
pathway, which probably represent the red-green
signal (Dacey, 2000). Ganglion cell spectral sensi-
tivities do not however match psychophysical predic-
tions, for example they fail to predict the redness of
short wavelength (violet) light. There are recordings
for spectral opponent neurons in many other species,
which we cannot review here. However, it is worth
noting that Backhaus (1991) relates electrophysio-
logical recordings from colour opponent neurons in
honeybees to opponent mechanisms proposed from
behavioural studies (see Section V.2c).
Colour vision seems to be useful. Most eyes have
multiple spectral types of photoreceptor (Table 1),
and most animals have colour vision (Table 2), but
it is not easy to specify the costs and benefits. Costs
arise because colour vision compromises absolute
sensitivity and (often) spatial resolution (van
Hateren, 1993; Osorio, Ruderman & Cronin, 1998).
Moreover, many processes such as directional mo-
tion detection are generally colour blind. Various
theoretical studies have considered the consequences
of varying the numbers and tuning of spectral
photoreceptor types (Barlow, 1982; Maloney, 1986 ;
van Hateren, 1993), but no theory accounts well
for the diversity in numbers and spectral tuning
of photoreceptors across the animal kingdom
(Table 1).
Despite the lack of a satisfactory quantitative
model, intuitively it seems reasonable that chromatic
signals are useful for object detection and identifi-
cation. Under shadows and patchy illumination as in
forests or shallow water, variations in light intensity
cause large variations in receptor signals from a
given surface. The ratio of signals from two receptor
types is however comparatively robust with respect
to illumination, and hence a better indicator of
object properties (Rubin & Richards, 1982; Mollon,
1989; Maximov, 2000). According to this argument
chromatic signals should ideally represent this ratio
of receptor responses, making them insensitive to
variations in intensity, but other signals such as the
differences of receptor responses would also be useful.
Even so, variable illumination will affect chromatic
signals, making it necessary to ‘ discount ’ the
illuminant by colour constancy (Hurlbert, 1998).
Many animals have colour constancy but we do not
deal here with this subject, which was reviewed
recently by Neumeyer (1998).
Given the capacity of nervous systems to combine
signals with different weightings, and to perform a
large variety of operations, the coding of colour
should reflect the fact that chromatic and achromatic
signals are useful for different purposes. This means
that when achromatic cues are used, as for motion
detection, chromatic signals are disregarded, and
when chromatic signals are used, as for the recog-
nition of the colour of food sources, achromatic
information may often be disregarded because it is
unreliable. As we have said, one might expect a wide
range of animals to have chromatic mechanisms
whose responses are independent of intensity.
Honeybees are an example of a species with
intensity-independent colour vision (see Section VI).
In his pioneering work, von Frisch (1914) trained
bees to feed from a sugar solution presented on a blue
(or a yellow) card, and found that they could dis-
criminate the training colour from 30 different shades
of grey. Indeed, his bees were unable to learn to
discriminate between greys of different intensity,
which implied that they had learned only chromatic
signals. On the other hand, motion vision in honey-
bees is colour-blind (Lehrer, 1993). Where animals
use either chromatic or achromatic cues in different
behaviours, as bees (von Frisch, 1914) and birds
(Goldsmith, Collins & Perlman, 1981) do, it can be
shown very convincingly that an animal discrimi-
nates colour stimuli regardless of their relative
92 Almut Kelber, Misha Vorobyev and Daniel Osorio
Table 2. Animal species (excluding primates)that have been shown to use colour vision in different behavioural experiments.As in the Introduction,we pose
three questions,is colour vision used for a particual behaviour (q1)? How many spectral types of receptor are involved (q2)? How many chromatic mechanisms
are found (q3)? Only experiments which give an answer (or at least an indication)to one of the questions are listed here.We note whether colour vision has
been proved (yes to q1)or there is only a strong indication (ind.) for colour vision.For example,spectral sensitivity curves per se do not provide proof of
colour vision.The number of receptors and post-receptoral mechanisms (Fig. 1,stage 2)used for colour vision is given if it was determined by behavioural
tests and\or model calculations (q2 and q3). Some experiments gave evidence that a specific receptor (VS,very short wavelength receptor ; S short wavelength
receptor; M medium wavelength receptor ; L,long wavelength receptor)is involved,this is mentioned in the comment.Under method we give the type of
experiment,the behaviour used to test the animal and whether spontaneous or trained behaviour was used.We refer to other review articles for some animal
groups.For detailed descriptions of methods,see Sections V and VI
Animal species Method Reference q1 q2 q3 Comments
Two-spotted spider mite
(Tetranchus urticae)
Monochromatic stimuli,
McEnroe & Dronka (1966) Ind.
Water mite (Unionicola
Monochromatic stimuli,
Dimmock & Davids (1985) Yes
Jumping spider (Hasarius
Grey card experiment, heat
avoidance reaction
Nakamura & Yamashita
Yes First clear evidence for colour
vision in spiders
Common shrimp (Crangon
Grey card experiment,
Koller (1927) Ind.
Hermit crabs (Clibanarius
Grey card experiment,
spontaneous choices of shell
Koller (1928) Yes
Fiddler crab (Uca pugilator) Monochromatic stimuli,
Hyatt (1975) Yes
Water flea (Daphnia magna) Broadband stimuli, phototaxis Lubbock (1888), von Frisch
& Kuppelwieser (1913)
Monochromatic stimuli,
Koehler (1924), Storz & Paul
Mantis shrimp
(Odontodactylus scyllaris)
Grey card experiment, food
Marshall et al. (1996) Yes
Insects Reviews: Mazokhin-
Porshnyakov (1969); Menzel
Grasshopper (Phaeoba sp.) Broadband stimuli, phototaxis Kong et al. (1980) Ind. Eye bands with different
screening pigments
Aphid (Myzodes persicae) Monochromatic stimuli,
Moericke (1950) Yes
93Animal colour vision
Honeybee (Apis mellifera) Grey card experiment von Frisch (1914) Yes
Monochromatic stimuli, food
$hn (1927) Yes First evidence for UV
sensitivity in bees
Grey card experiment, food
Lotmar (1933) Yes
Grey card experiment*, food
Yes *Use of different shades of
colour instead of grey
Spectral sensitivity, food
Helversen (1972) 3 2* *Models: Brandt &
Vorobyev (1997); Vorobyev
& Osorio (1998)
Wavelength discrimination,
food training
Helversen (1972) 3
Colour mixture, food training Daumer (1956) Yes 3
Multidimensional scaling
(MDS)*, Food training
Backhaus (1991) Yes * 3 2 *First colour discrimination
model in bees (see Sections
V2.cand VI.3)
Wasp (Polybia occidentalis) Grey card experiment, food
Shafir (1996) Yes
German wasp (Paravespula
Grey card experiment, food
Beier & Menzel (1972) Yes * *Proof that no L receptor is
Hornet (Vespa rufa) Schremmer (1941b) * * Proof that no L receptor is
Desert ant (Cataglyphis
Monochromatic stimuli, food
Wehner & Toggweiler (1972) Yes
Eight species of
Colour discrimination* Chittka et al. (1992) Yes * 3 * Model: a modification of
the model by Backhaus
Hummingbird hawkmoth
(Macroglossum stellatarum)
Grey card experiment, food
Knoll (1922) Yes
Monochromatic stimuli,
spontaneous choices, feeding
Kelber (1997) Ind.
Monochromatic stimuli, food
Kelber & He
!nique (1999) Yes * * Proof that no L receptor is
Striped hawkmoth (Hyles
Grey card experiment, food
Knoll (1926) Ind. Few observations
Gamma fly (Autographa
Grey card experiment, food
Schremmer (1941a) Yes
Swallowtail butterfly
(Papilio xuthus)
Grey card experiment Kinoshita et al. (1999)
Orchard butterfly (Papilio
Monochromatic stimuli, food
Kelber & Pfaff (1999) Yes * *L receptor used for colour
Paper colours*, spontaneous
choices, oviposition
Kelber (1999) Yes 3 1* * Model calculation
94 Almut Kelber, Misha Vorobyev and Daniel Osorio
Table 2 (cont.)
Animal species Method Reference q1 q2 q3 Comments
Insects (cont.)
Tortoiseshell (Aglais urticae),
peacock butterfly (Inachis
io), fritillary (Argynnis
paphia), cabbage white
(Pieris brassicae), brimstone
(Gonepteryx rhamni)
Grey card experiment,
spontaneous choices, feeding
Ilse (1928) Ind.
Heliconius erato Grey card experiment,
spontaneous choices, feeding
Crane (1955) Yes
Zebra (Heliconius charotonius) Grey card experiment food
Swihart (1971) Yes Colour learning but no
intensity learning
Cabbage white (P.brassicae) Monochromatic stimuli,
spontaneous choices, feeding
and oviposition
Scherer & Kolb (1987) Yes 4 1 * * Model : Kelber 2001
Tortoiseshell caterpillars
(Aglais urticae)
Grey card experiment,
$ffert & Go
$tz (1936) Yes
Blowfly (Lucilia cuprina) Grey card experiment,
spontaneous choices, feeding
Fukushi (1990) Ind.
Wavelength discrimination,
spontaneous choices, feeding
Troje (1993) Yes Model proposed
Olive fruit fly (Dacus oleae) Grey card experiment,
spontaneous choices,
Prokopy et al. (1975) Yes 2 1 * * Model : Kelber 2001
Bee fly (Bombylius fuliginosus) Grey card experiment, feeding Knoll (1921) Yes
Drone fly (Eristalis tenax) Grey card experiment, food
Ilse (1949) Yes
Grey card experiment,
spontaneous choices, feeding
Kugler (1950) Yes
Monochromatic stimuli,
spontaneous choices, feeding
Lunau & Wacht (1994) Yes 2 1* * Model : Kelber 2001
Minnow (Phoxinus laevis) Grey card experiment,
spontanous colour change
von Frisch (1912, 1913a) Yes
Grey card experiment food
von Frisch (1913b) Yes
Wavelength discrimination,
food training
Wolff (1925) Ind. 4 * *Evidence for a VS receptor
95Animal colour vision
Wrasse (Crenilabrus melops) Grey card experiment,
spontaneous colour change
von Frisch (1913a) Ind.
Stickleback (Gasterosteus
Monochromatic stimuli, food
Schiemenz (1923) Yes * * Indication for a VS receptor
Grey card experiment, escape
Schiemenz (1923) Yes
Tench (Tinca tinca), golden
orfe (Idus melanotus)
Grey card experiment Burkamp (1923) Yes
Goldfish (Carassius auratus) Spectral sensitivity, heart rate
conditioning, bright light
Beauchamp & Rowe (1977) Ind. 4* *The high sensitivity in UV
was measured but taken as
Spectral sensitivity,
respiration rate conditioning
in dim light
Powers & Easter (1978a) Ind. 2* *Rod and L cone colour
vision in dim light for
respiration rate conditioning
Monochromatic lights,
respiration rate conditioning
in dim light
Powers & Easter (1978b) Yes 2* *Rod and L cone colour
vision in dim light for the
Spectral sensitivity, food
training, dim light
Neumeyer & Arnold (1989) Ind. 3 * *Only VS, S and M cones
contribute to colour vision
for the task under dim light
Spectral sensitivity, food
training, bright light
Neumeyer (1984) Ind.
Colour matching, food
Neumeyer (1985, 1992) Yes 4* *First direct evidence for
tetrachromatic colour vision
in an animal
Wavelengh discrimination,
food training
Neumeyer (1985, 1986) Yes * 4 *Maxima of discrimination
curve are narrower than
those of receptor curves
Common toad (Bufo bufo) Grey card experiment,
dishabituation of turning
Meng (1958) Yes
Grey card experiment, mate
Gnyubkin et al. (1975)
Kondrashev et al. (1976)
Dimentman et al. (1978)
96 Almut Kelber, Misha Vorobyev and Daniel Osorio
Table 2 (cont.)
Animal species Method Reference q1 q2 q3 Comments
Amphibians (cont.)
Grey toad (Bufo viridis) Grey card experiment, feeding
Falzman & Bastakov (1999) Yes
Grey card experiment, mate
Orlov & Maximov (1982) Yes 3 1* * Model : Losev & Maximov
(1982) (see Section V.2c)
Arrow poison frog
(Dentrobates pumilo)
Broadband stimuli,
spontaneous mate choice
Summers et al. (1999) Ind.
Common frog (Rana
Broadband stimuli, phototaxis Muntz (1962, 1963) Yes
16 species of frog and toad
(Scaphiopus sp., Rana spp.,
Bufo spp., Hyla spp.,
Limnaoedus sp., Pseudacris
sp., Acris sp.)
Broadband stimuli, phototaxis Jaeger & Hailman (1971);
Hailman & Jaeger (1974)
Common frog (Rana
temporaria), Crested newt
(Triturus cristatus), Fire
salamander (Salamandra
Grey card experiment, food
Kasperczyk (1971) Yes
Fire salamander
(S.salamandra), newts
Grey card experiment, prey
Himstedt (1972) Yes * Motion vision involved but
object detection task used
for tests
Fire salamander
Spectral sensitivity, detection
of moving prey dummy
Przyrembel et al. (1995) Ind. 3* *Deduced from the number
of maxima in sensitivity
Caspian terrapin (Clemmys
Wavelength. discrimination,
food training
Wojtusiak (1932) Ind. 4* *Three maxima in
discrimination curve
Grey card experiment, food
Wojtusiak (1932) Yes
Giant turtles (Testudo
Monochromatic lights, food
Quaranta (1952) Yes
Freshwater turtle (Pseudemys
Spectral sensitivity, food
Neumeyer & Ja
$ger (1985) Ind. 3 * *Deduced from four maxima
in the sensitivity curve
Wavelength discrimination,
food training
Arnold & Neumeyer (1987) Yes 4 * *Gap in wavelength
discimination function due
to oil droplet absorption
97Animal colour vision
Sand lizard (Lacerta agilis) Grey card experiment, food
Wagner (1932) Yes
Anole lizard (Anolis
Moving coloured stimuli,
visual fixation reflex
Fleishman & Persons (2001) Yes
Birds Review: Varela et al. (1993)
Columba livia (pigeon) Spectral sensitivity, food
Remy & Emmerton (1989) Yes 4 2* * Model Vorobyev & Osorio
Wavelength discrimination Emmerton & Delius (1980) Ind. 4
Colour mixture Palacios et al. (1990); Palacios
& Varela (1992)
Pekin robin (Leiothrix lutea) Spectral sensitivity, food
Maier (1992) Yes 4 2 * * Model Vorobyev & Osorio
Pied flycatcher (Muscicapa
Grey card experiments, nest
Derim-Oglu et al. (1987);
Derim-Oglu & Maximov
Yes * *Colour discrimination but
generalization over
brightness, VS receptor is
Great tit (Parus major) Tree
sparrow (Passer montanus)
Grey card experiments, nest
Derim-Oglu & Maximov
* *VS receptor is used for
colour discrimination
Budgerigar (Melopsittacus
Grey card experiment, food
Plath (1935) Yes
Chick males (Gallus gallus) Grey card experiment with
adjusted light spectra, food
Osorio et al. (1999) Yes 4 * *Colour discrimination was
possible with each pair of
two receptors (see Section
Jay (Garullus glandarius) Grey card experiment food
Hertz (1928) Yes
Hummingbird (Archilochus
Wavelength discrimination,
food training
Goldsmith et al. (1981) Yes * * VS receptor used for colour
Tawny owl (Strix aluco) Grey card experiment, food
Ferens (1947) Yes
Monochromatic stimuli, food
Martin (1974) Yes
Little owl (Athene noctua) Grey card experiment, food
Meyknecht (1941) Yes
Mammals Review: Jacobs (1993)
Possum (Didelphis virginiana) Monochromatic stimuli, food
Friedman (1967) Yes
Tammar wallaby (Macropus
Monochromatic stimuli, food
Hemmi (1999) Yes
Neutral point, food training Hemmi (1999) Yes 2
98 Almut Kelber, Misha Vorobyev and Daniel Osorio
Table 2 (cont.)
Animal species Method Reference q1 q2 q3 Comments
Mammals (cont.)
Tree shrew (Tupaia
Spectral sensitivity, food
Jacobs & Neitz (1986) Yes 2 1 * * Model Vorobyev & Osorio
Neutral point, food training Jacobs & Neitz (1986) Yes 2
Tree shew (Tupaia glis) Spectral sensitivity, food
Polson (1968) Yes 2
Dog (Canis lupus familiaris)* Grey card experiment, food
Orbeli (1909) Yes *See Rosengren (1969), for
additional references on dog
colour vision
Grey card experiment, food
Rosengren (1969) Yes
Spectral sensitivity, food
Neitz et al. (1989)
Wavelength. discrimination,
food training
Neitz et al. (1989)
Neutral point, food training Neitz et al. (1989) 2
Wolf (Canis lupus) Grey card experiment, food
Eisfeldt (1967) Yes
Cat (Felis sylvestris)* Grey card experiment,
playing behaviour ng
Buchholtz (1952) Yes *See Autrum & Thomas
(1973) and Jacobs (1981),
for more references on cat
colour vision.
Monochromatic stimuli, food
Bonaventure (1961) Yes
Coloured lights, food training Sechzer & Brown (1964) Yes
Coloured lights, food training Mello & Peterson (1964) Yes
Spectral sensitivity, food
Loop et al. (1987) Yes 2** ** Whether cats have two or
three cone types and di- or
trichromatic colour vision is
still an unresolved question
Adjusted spectra, food
Kezeli et al. (1987) Yes 3 **
Mongoose (Mungos
Grey card experiment, food
$cker (1957) Yes
Indian civet (Viverricula
Grey card experiment, food
$cker (1957) Yes
Sciurus vulgaris (Common
Grey card experiment, food
Meyer-Oehme (1957) Yes
Grey squirrel (Sciurus
griseus) Fox squirrel
Wavelength discrimination,
food training
Jacobs (1976) Ind. 2
99Animal colour vision
Antelope ground squirrel
(Ammospermophilus leucurus)
Monochromatic stimuli, food
Crescitelli & Pollack (1972) Yes 2
Ground squirrel
S.lateralis) Prairie dog
(Cynomys ludovicanus)
Spectral sensitivity, white
point, wavelength
discrimination, food training
Jacobs (1978) Yes 2
Ground squirrel
(Spermophilus beecheri)
Spectral sensitivity, food
Jacobs (1993) Yes 2 1 * Model Vorobyev & Osorio
Rat (Rattus norvegicus) Monochromatic stimuli, food
Walton & Bornemeier (1938) Yes
Wavelength discrimination,
food training
Jacobs & Neitz (1985)
Manatee (Trichechus
Grey card experiment, food
Griebel & Schmid (1996) Yes
Sea lion (Zalophus
Grey card experiment, food
Griebel & Schmid (1992) Yes* * Peichl et al. (2001) showed
that sea lions and seals have
only one cone type, the
basis of their colour
discrimination ability
therefore remains uncertain.
Fur seal (Arctocephalus sp.) Grey card experiment, food
Busch & Du
$cker (1987) Yes *
Horse (Equus equus) Grey card experiment, food
Grzimek (1952) Yes
Zebu (Bos indicus) Grey card experiment, food
Hoffmann (1952) Ind.
100 Almut Kelber, Misha Vorobyev and Daniel Osorio
Von Frisch (1914) successfully differentiated the uses
of chromatic and achromatic signals by bees.
Although bees and birds do not usually learn
achromatic signals, mammals usually have com-
paratively poor colour vision, and may prefer to use
achromatic cues (Jacobs, 1981, 1993). For that
reason, many researchers failed to train mammals
like cats or dogs to discriminate colours, and until
the 1960s it was not certain if they could see colour
(Rosengren, 1969; Jacobs, 1981).
An early method of excluding achromatic in-
formation was to present an animal with two stimuli
of different colours that were matched in brightness,
meaning that intensities were adjusted so they
appeared equally bright. Early work used human
brightness, but it was recognized that the animal’s
spectral sensitivity could differ from ours, and needed
to be measured. Stimulus intensities could then be
adjusted appropriately for the test species (see
Section V.2). There are several difficulties with this
approach. First, spectral sensitivity may depend
upon behavioural context (Jacobs 1981 ; Neumeyer,
1991). The spectral sensitivity of goldfish, for
example, differs depending upon whether they are
trained to prefer a coloured target over a dark one,
or a dark target over a coloured one (Neumeyer,
1991). More fundamentally, for light-adapted eyes
behavioural spectral sensitivities often are mediated
by chromatic, not achromatic mechanisms. Adjust-
ing intensities according to these sensitivities does
not then exclude achromatic signals (see Fig. 5 ;
Section VI.3). Finally, where two or more receptor
types contribute to the achromatic mechanism, and
are randomly arranged (as in primates) spectral
differences can locally lead to an achromatic signal
even if the intensities are properly adjusted for the
average. Given the difficulties of excluding achro-
matic signals, a more practical method is to make
intensity unreliable by testing discrimination for a
range of relative intensities, or by adding intensity
Colour vision tests must refer to a specific
behavioural context. In dim light, many vertebrates
lack colour vision, and directional motion vision
is often based on signals from one spectral type
of receptor (Schlieper, 1927; bees : Lehrer, 1993 ;
goldfish: Schaerer & Neumeyer, 1996). Behaviours
tested include feeding, mating, escape, phototaxis,
movement detection, camouflage, nest orientation
and oviposition. Both spontaneous and learned
behaviour can be studied. However, the most usual
way of testing colour vision is by associative learning
with a food reward. Here, we list general methods
according to the stimulus design and give examples
of the behavioural context in which these have been
used. Table 2 gives an extensive, but still incomplete
list, of experiments (for older reviews see Mazokhin-
Porshnyakov, 1969; Autrum & Thomas, 1973 ;
Menzel, 1979; Jacobs, 1981, 1993).
Three related methods for demonstrating colour
vision are described below (Section V.1), all of
which predate the knowledge of receptor sensitivi-
ties: (a) discrimination of a fixed colour from a series
of grey shades; (b) discrimination of monochromatic
colours, which can be changed in intensity ; (c) dis-
crimination of two broadband stimuli that can be
adjusted such that either one or the other emits more
photons over the entire spectrum. If an animal
selects a stimulus according to its wavelength
distribution it must have colour vision.
Section V.2 describes investigations that set out to
study which receptors and neural mechanisms
underlie colour vision. These include: (a) colour-
matching experiments, the only direct test of the
number of receptors; (b) discrimination tests with
stimuli specially adjusted to test hypotheses on
receptors; and (c) models of colour choices based on
discrimination tests.
Knowledge of discrimination thresholds allows
quantitative description of colour vision, and is
discussed in Section VI. In recent years, quantitative
models have emerged as powerful tools for under-
standing the biological relevance of colour dis-
(1) Evidence for colour vision
(a)Grey card experiments
Von Frisch’s (1914) ‘grey-card ’ experiment with
bees is a convincing demonstration of colour vision.
An animal learns to associate a reward with a colour,
and then chooses between this colour and many
shades of grey. It is assumed that at least one grey
gives a sufficiently similar achromatic signal to the
trained colour, so that if all are discriminable from
the colour the animal is not relying on achromatic
cues. Von Frisch (1913b) also tested European
minnows (Phoxinus phoxinus), and his influence led to
many similar studies, especially in Germany during
the 1920s and 30s (Table 2).
There have been some interesting variants on the
grey card method. Swihart (1971) noted that
Heliconius charitonius butterflies cannot associate a
medium shade of grey with food, always choosing
101Animal colour vision
the brightest, but could learn successively two
yellowish colours. Since both yellows could not both
have been the brightest, the butterflies could not
have been using achromatic cues. An alternative
explanation is that the butterflies have a preference
for yellow, and this directs their attention to the
intensity of yellow objects so that they can learn the
achromatic signal; but this too requires colour vision.
Apart from associative learning, spontaneous
preferences have long been used to test colour vision.
Ilse (1928) found that butterflies (various Nym-
phalidae, Papilionidae, Pieridae and Satyridae)
prefer both blue and yellow to any achromatic shade
including white. On the other hand when hermit
crabs (Eupagurus anachoretus) select a new home they
prefer achromatic shells of any intensity from black
to white over blue or yellow alternatives (Koller,
Control of body coloration by fish (von Frisch,
1913a) and crustaceans also uses colour vision. To
match their background brown shrimps (Crangon vul-
garis) selectively dilate red, yellow and sepia-brown
pigmented chromophores. In tanks surrounded by
yellow paper the yellow pigment was more expanded
than with any shade of grey surround (Koller,
1927). In contrast, cuttlefish (Sepia officinalis) seem
to be colour blind when selecting body pattern on
coloured gravels (Marshall & Messenger, 1996).
Amphibians have multiple types of spectral re-
ceptor, but are often difficult to train by operant
conditioning, so alternative methods are needed to
test colour vision. For example, toads (Bufo bufo)
jump towards coloured cards that resemble prey, but
the response habituates. Meng (1958) found that
toads react again if they see a novel colour, but not
a different shade of grey. The urodeles Salamandra-
salamandra and Triturus spp. also respond to moving
prey, and to test them Himstedt (1972) used an
elongated window divided into two fields that
differed in colour or intensity. The border separating
the fields moved sinusoidally. A jump towards the
target indicated that the amphibian saw the border.
The salamanders reacted much more strongly to a
border between a coloured and any grey field than
they did to a border between two similar shades of
grey indicating that they used colour to make the
discrimination. Fleishman & Persons (2001) used a
similar method, testing responses of lizards (Anolis
cristellatus) to movement of coloured cards that
resembled the displays of conspecifics.
A variation of the grey card technique is to add
intensity noise to the training colours, making
brightness an unreliable cue. This technique is
widely used when testing human colour vision, and
is a feature of Ishihara’s (1917) tests. Such patterns
can be displayed on a monitor (which excludes
ultraviolet) or printed out as paper stimuli. Osorio et
al. (1999b) trained chicks to find food in small paper
containers covered with such patterns, and demon-
strated tetrachromatic colour vision in this bird.
(b)Monochromatic stimuli
Monochromatic stimuli can be precisely defined in
physical terms, and thus have long been used in
human psychophysics (e.g. Maxwell, 1860) and with
animals. If changes in relative intensity of two
monochromatic lights do not influence an animal’s
choice, it must be using colour vision. Monochro-
matic (or narrow-band) lights can be produced
with monochromators, interference filters, or light-
emitting diodes (LEDs). There are three basic
(i) If the spectral sensitivity of a species is known,
the intensities of the stimuli can be adjusted to give
equal achromatic signals, but other than with
humans this is not easy. In a careful study, Powers &
Easter (1978b) classically conditioned goldfish (con-
ditioned stimulus: respiration rate; unconditioned
stimulus: electric shock) to discriminate lights of
532 nm and 636 nm whose intensities were adjusted
according to a previously determined detection
threshold (using separate curves for photopic and
scotopic sensitivities). To ensure that discrimination
was not made by achromatic cues, both lights were
varied over 0n5 log units. Goldsmith et al. (1981)
used a similar method to test spectral discrimination
by black-chinned hummingbirds (Archilochus alex-
andri), with stimulus intensities adjusted for the
photopic sensitivity of the pigeon. This study
demonstrated hummingbird colour vision, because
they did not discriminate stimuli differing only in
(ii) When spectral sensitivity is unknown – as is
usual – training can be done using equal (or arbi-
trarily chosen) physical intensities. After training,
intensities in unrewarded tests have then to be varied
over an (often inconveniently) large range of several
log units (e.g. Quaranta, 1952 for giant tortoises,
Testudo spp.; Kelber & Pfaff, 1999 for the butterfly
Papilio aegeus).
(iii) In operant conditioning, training can involve
intensity variations, and no subsequent unrewarded
tests are needed. This was how Schiemenz (1923)
demonstrated that European minnow and three-
spined stickleback (Gasterosteus aculeatus) see UV light
102 Almut Kelber, Misha Vorobyev and Daniel Osorio
and have colour vision. Operant training with
narrow-band lights is commonly used with mammals
(Table 2; Jacobs 1981, 1993). For the tammar
wallaby (Macropus eugenii), Hemmi (1999) adjusted
stimulus intensities to give equal signals for the
L cone, and went on to vary both rewarded and
unrewarded training intensities widely. It was clear
that the wallabies have colour vision because they
preferred the rewarded colour to black, but black to
the colour that was unrewarded during training.
Spontaneous preferences for food sources or
oviposition substrates have been studied using
monochromatic lights in butterflies (Scherer & Kolb,
1987) and hoverflies (Lunau & Wacht, 1994).
Narrowband spectral stimuli have long been used to
study Daphnia sp. phototaxis with controversial
results (Koehler, 1924), but a recent careful study
(Storz & Paul, 1998) shows that Daphnia magna
phototaxis is specific to wavelength, and indepen-
dent of intensity, over a large intensity range.
(c)Broadband stimuli at different intensities
When Lubbock (1888) studied Daphnia sp. he first
found that they are positively phototactic (up to
some intensity limit), and then that they prefer a
light source filtered with a yellow filter to the
unfiltered alternative. As the unfiltered light had a
higher intensity at all wavelengths, Lubbock (1888)
could conclude that the Daphnia sp. have colour
vision, preferring yellow to white light. He specu-
lated that this preference arises because the algae
that Daphina sp. eat colour water yellow. Subsequent
experiments on phototaxis in frogs (Rana spp.), toads
and grasshoppers (Phaeoba sp.) resembled Lubbock’s,
trading a preference for a particular waveband
against a general preference for high intensities
(Muntz, 1962; Jaeger & Hailman, 1971; Kong et al.,
1980). Unlike Daphnia sp., both grasshoppers and
amphibians preferred short to long wavelengths. For
frogs, Muntz’s (1962) critical test was to present the
more attractive colour together with a mixture of
this light and the less attractive colour. The mixture
then had a higher intensity than the preferred
colour. Since the less intense stimulus was chosen in
these experiments, it was concluded that a chromatic
mechanism overrode the preference for the more
intense stimulus. Jaeger & Hailman (1971), on the
other hand, showed that even when the stimulus
with the less attractive colour was more intense
than the other at all wavelengths it remained
less attractive. A similar stimulus design, but with
operant conditioning, was used successfully to show
that dogs have colour vision (Orbeli, 1909).
(2) Tests of visual mechanisms
We now turn from simple demonstrations of colour
vision to tests of the underlying physiological
mechanisms. Firstly, we discuss colour matching as a
direct test of the number of receptors used for colour
vision, which can be done without knowledge of
receptor spectral sensitivities, and secondly tests of
receptor inputs to visual behaviour based on knowl-
edge of receptor sensitivities.
(a)Colour matching
Colour matching is the direct test for dimensionality
of colour vision. It is based on the principle (see
Section II.2) that if nreceptor signals are compared
in colour vision, any spectral stimulus can be
matched with a specific mixture of nprimaries. For
a dichromat, a mixture of two primary spectra can
match white light, a trichromat requires three and so
Following Maxwell (1860), colour matching has
been used widely with mammals, which are di- or
trichromatic (Jacobs, 1981, 1993). Things are more
complicated with increasing numbers of receptors,
but colour-matching experiments have shown that
honeybees are trichromats (Daumer, 1956), and
goldfish and pigeon tetrachromats (Neumeyer, 1985,
1992; Palacios et al., 1990 ; Palacios & Varela, 1992).
It seems unrealistic to test butterflies for possible
pentachromatic vision (Arikawa, Inokuma &
Eguchi, 1987), and impossible to test a mantis
shrimp with 12 spectral types of photoreceptors
(Cronin & Marshall, 1989 ; Marshall & Ober-
winkler, 1999). Even with goldfish, a two-step
procedure was applied (Neumeyer, 1992). First,
three lights were used to match ‘ human-white ’ light
missing UV and second, it was shown that goldfishes
can discriminate UV-containing white from UV-
missing white.
A special case of colour matching can be used to
demonstrate dichromacy (Fig. 2A; Jacobs, 1981).
For a dichromatic eye all colours are represented by
quantum catches of two receptor types. For any
broadband stimulus, including a white one, it is
possible to find a wavelength and intensity of
monochromatic light, which will match the quantum
catches of both receptors. Thus, a dichromat confuses
light of a specific wavelength – called the neutral
point – with white light ( Jacobs, 1981, 1993 ;
Hemmi, 1999).
103Animal colour vision
(b)Discrimination of specially adjusted stimuli
If photoreceptor spectral sensitivities are known
photoreceptor quantum catches can be calculated
(see Section II.3), and it is possible to design stimuli
giving known quantum catches in the different
receptor types. For instance, two stimuli can be
chosen to give equal quantum catches in one or even
two spectral types of receptor. If an animal is still
able to discriminate the two colours, this is good
evidence that an additional receptor type is involved.
This approach has provided evidence for trichro-
macy in cats, which are commonly thought to be
cone dichromats (Loop, Millican & Thomas, 1987 ;
Jacobs, 1993). Electrophysiological evidence indi-
cates that in photopic conditions cat ganglion cells
receive input from three spectral types of photo-
receptor, maximally sensitive at 450 nm, 555 nm
(typical mammalian S and L cones), and at 500 nm,
which is typical for rods (Ringo et al., 1977 ; Crocker
et al., 1980). To find out whether the 500 nm
receptor is used for colour vision, Kezeli et al. (1987)
trained cats to discriminate a group of green from a
group of purple stimuli. Both groups of colour
occupied the same area in the cat’s two-dimensional
dichromatic colour space given by S and L cones,
but differed substantially for a putative 500 nm
receptor. To take account of differences between
calculated and actual cone sensitivities, stimulus
colours were varied so that for any reasonable
hypothesis about S and L sensitivities a dichromat
would fail to discriminate at least some of the green
stimuli from the purple. In fact, cats reliably
discriminated purple from green, implicating a third
input. Kezeli et al. (1987) argued for a 500 nm cone
type (photopic) receptor, but rods cannot be
Where spectral sensitivities of receptors are known
and do not overlap too much it is possible to adjust
illumination so that only a subset of receptors are
active in an experiment. Osorio et al. (1999 a) used
this method with domestic chicks, choosing stimuli
and illumination so that only two receptor types
were active in each experiment. They found that
chicks probably use all four single cone types for
colour vision, and that the receptors drive at least
three chromatic mechanisms.
(c)Receptor-based models of colour choices
Given receptor sensitivities it is possible to establish
the receptor inputs to visual responses and the
underlying achromatic and\or chromatic mechan-
isms. Specifically, the strength of a behavioural
response can be related to receptor signals by general
linear models.
One such model has been used to study mate
choice in toads (Bufo viridis). Relative preferences for
a series of pairs of coloured toad-like objects were
measured in dual-choice tests (Orlov & Maximov,
1982). Colour preferences were fitted by a model
(Losev & Maximov, 1982), which assumed that
preference (X) depends on a weighted sum of
receptor quantum catches. It was found that
excitation of the ‘green ’ rods (see Table 1) increases
attractiveness, while excitation of long (L) and
medium (M) cones decreases it. A linear model
nicely explained the preferences:
Xl0n1qSRk0n22 qMk0n1qL, (5)
where qSR,qMand qLare quantum catches of the
toad’s green rod, M and L cones, respectively.
Backhaus (1991) trained bees to coloured stimuli
and tested them with several similar colours sim-
ultaneously. A multidimensional scaling procedure
was used, and choice proportions assumed to depend
on the distance in colour space, S, between the
stimuli, which in turn was dependent on the linear
combinations of receptor signals. Two scales, Aand
B, were needed to describe the data. The distance is
given by:
SlQAQjQBQ, (6)
Alk9n86 ESj7n70 EMj2n16 EL, (7)
Blk5n17 ESj20n25 EMk15n08 EL, (8)
and Eilqi\(1jqi) denotes the receptor excitations,
which are related by non-linear transformations to
receptor quantum catches qi. The scales Aand B
describe chromatic mechanisms, because receptor
signals are combined with opposite signs.
Finally, Kelber (1999, 2001) studied oviposition
in a butterfly (Papilio aegeus), and found that
preferences amongst a number of colours are
described by a model assuming that choice propor-
tions depend on only one linear mechanism (η)
receiving signals from three receptor types such that :
ηlk1n24 qSjqMk0n77 qL. (9)
Section V discussed the existence of colour vision and
studies based on comparing relative preferences for
different colours. Models have been found to be
104 Almut Kelber, Misha Vorobyev and Daniel Osorio
helpful in describing colour vision mechanisms in
various behavioural contexts. If models fit the
behavioural data well, we can then look for a
physiological correlate of the postulated neural
mechanisms. At the same time, quantitative models
can be used to test hypotheses about the evolution
and the ecological value of specific colour vision
An advantage of studying thresholds for colour
discrimination is that it is generally easier to estab-
lish whether or not an animal can discriminate
two colours than to ask how different they look.
Also, non-linearities are usually less important near
threshold. This makes it easier to fit quantitative
models to behavioural data, which may reveal the
neural mechanisms underlying colour vision and
how they limit behavioural judgements.
(1) Measuring thresholds
Generally, it is more difficult to measure accurate
thresholds for animals than for humans, thus
behavioural thresholds have been measured only in
a small number of species (see Table 2), including
several mammals (Jacobs, 1981, 1993), honeybees
(von Helversen, 1972) and goldfish (Neumeyer,
1984, 1985, 1986, 1992). The measurements require
precise stimulus intensities and spectra, such as mono-
chromatic lights. Thresholds are usually measured
in one of two ways, either as spectral sensitivity or
as wavelength discrimination. Spectral sensitivity
is given by the minimal intensity of monochromatic
light that can be detected, on either a dark or an
achromatic background, sensitivity being the inverse
of threshold intensity. In physiological measure-
ments, absolute sensitivity is often measured ; in
behavioural tests, an achromatic background is more
appropriate since many animals would not respond
in complete darkness. In effect the task is to detect
very unsaturated colours. Wavelength discrimi-
nation (λ\λfunction) 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).
On the whole, spectral sensitivity is better suited
to quantitative analysis than wavelength discrimi-
nation. Firstly, spectral sensitivity gives thresholds
about one point in colour space (normally the
achromatic point), while wavelength discrimination
gives thresholds about many points. This means that
modellingspectralsensitivity does not require assump-
tions about changes of threshold values across colour
space (Appendix A; Section VI.3). Secondly, the
highly saturated colours used for wavelength dis-
crimination may saturate opponency mechanisms,
as they do in humans (Mollon & Este
!vez, 1988).
Saturation introduces non-linearities, which com-
plicates modelling.
(2) Interpretations of the shapes of
threshold sensitivity curves
Data on discrimination can give information about
the mechanisms of colour vision. Early analysis of
behavioural spectral sensitivity and wavelength
discrimination asked questions about receptor mech-
anisms, rather than subsequent neural processing
(von Helversen, 1972; Maier, 1992). These interpre-
tations assumed that: (i) local maxima of be-
havioural spectral sensitivity correspond to maxima
of receptor sensitivities; and (ii ) wavelength dis-
crimination is best where the sensitivities of receptors
overlap, i.e. midway between receptor sensitivity
peaks. The number of receptors, and their spectral
tuning can then be inferred from spectral sensitivity
and wavelength discrimination functions. In honey-
bee, goldfish and turtle this method has allowed
determination of the number of receptors involved in
colour vision, before the corresponding photorecep-
tors were directly recorded (Daumer, 1956; Neu-
meyer, 1984, 1985; Neumeyer & Ja
$ger, 1985). Bees
have three maxima in their spectral sensitivity curve
and two minima in the wavelength discrimination
curve indicating that they use three receptor types.
Goldfish and turtle have four maxima in their
spectral sensitivty curve and three minima in their
wavelength discrimination functions, which indi-
cated that they had a fourth VS receptor, which was
then unknown (Neumeyer, 1985, 1986, 1992; Neu-
meyer & Ja
$ger, 1985). The UV maximum in spectral
sensitivity had previously been attributed to the
β-peak of the other (S, M and L) visual pigments
(Beauchamp & Rowe, 1977).
As well as identifying receptor types, behavioural
spectral sensitivities (without quantitative model-
ling) 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 pre-
dicts that peaks of the behavioural spectral sensitivity
curves should be at least as broad as the receptor
105Animal colour vision
Fig. 3. Diagrams of contours of equal colour discri-
minability in trichromatic receptor space. Different
contours are predicted by three models that have been
used to fit experimental data (Fig. 5; Brandt & Vorobyev,
1997). The axes of the space correspond to quantum
catches of short (S), medium (M) and long (L)
wavelength-sensitive receptors. (A) One achromatic
mechanism is used for colour discrimination, where the
distance in colour space Sis given by S#l
(kSqSjkMqMjkLqL)#. The three positive coefficients
(i.e. kS,kM,kL) denote the weights of the inputs of
receptors to a mechanism, that might 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#lgSS q#
SjgMM q#
MjgLL 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 photorecep-
tors, and deduced that there are inhibitory inter-
actions between receptor signals (Fig. 1A, stage 2).
(3) Metric spaces and quantitative analysis
of threshold data
Helmholtz (1896) introduced quantitative mod-
elling 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, Pcorr
(Fig. 1, stage 4), depends on Salone. Where Sis
below a threshold value, colours are assumed to be
indistinguishable. In two-alternative forced-choice
tests Pcorr can vary from 0n5 (random choice) to
1 (100% reliable choice), and threshold is usually
assumed to correspond to Pcorr l0n75. It is im-
portant to note that distances (S) refer to dis-
criminability of stimuli, and say nothing about
perceptual similarity of stimuli that are 100 %
discriminable. In a given space, the rule for calcu-
lating distance between points is called the ‘ metric
of the space. Different metrics make different assump-
tions 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
A given metric model is fitted to colour dis-
crimination data by describing a contour of equal
discriminability, corresponding to a given value of
Pcorr, about each location in a colour space. That is,
all points on the contour are equally well discrimi-
nated from the central colour. Different metric
models predict different contours (Figs 3, 4). The
positive coefficients (i.e. gSS,gMM,gLL) denote the
components of metric tensor fitted to experimental data.
A contour of equal discriminability is ellipsoidal with axes
parallel to the receptor axes. (C) Discrimination is limited
by the most sensitive receptor mechanism. This is an
upper envelope model without interactions between
receptor mechanisms. Distance in this colour space is
given by SlMax(QkiqiQ), where the three positive
coefficients, ki(i lS, M, L), denote the sensitivities of
receptor mechanisms. Contours of equal discriminability
are described by a parallelepiped with sides parallel to the
receptor axes.
106 Almut Kelber, Misha Vorobyev and Daniel Osorio
Fig. 4. Contours of equal discriminability in the chromaticity diagram of a trichromatic receptor space. (A) Colour
(Maxwell) triangle (see Fig. 2B) specified by the surface in receptor space of a plane crossing receptor axes (rep-
resenting quantum catches of receptors, qS,qMand qL), at coordinates (1,0,0), (0,1,0) and (0,0,1). The chromaticity
locus, qc, of a colour is the intersection of a line connecting the location of the colour in the receptor space, Q, with
the origin and the triangle. (B) Spectral loci (in nm) for the honeybee in a colour triangle. See Fig. 2B. Axes X"and
X#of the chromaticity diagram are given in Appendix A, equations (A3) and (A4). (C) Contours of equal dis-
criminability plotted in the colour triangle shown in B. The ellipse is predicted by a line element model (Fig. 3B),
where the distance in the colour space is: S#lg"" X#
"j2g"# X"X#jg## X#
#.Xi(with i l1, 2) denotes the
difference in the chromaticity co-ordinates, and gik (with i, k l1, 2) the components of a metric tensor that can be
fitted to experimental data (see Fig. 5). The parallelogram describes the contours of equal discriminability predicted
by dominance and city-block metrics. The dominance metric predicts a parallelogram with its sides (and axes, dashed
lines) parallel to the axes of the mechanisms mediating discrimination (e.g. receptor or colour opponent signals).
Alternatively, the city block metric postulates that diagonals of the parallelogram correspond to these axes (dotted
lines). A parallelogram can be defined by four parameters describing the length and orientation of its sides. Con-
sequently, dominance and city-block metrics for trichromatic colour space have four parameters, while an elliptic
model has three. (D) A chromaticity diagram corresponding to a receptor-noise-limited colour opponent model (see
Section VI.3b; Appendix B). The axis X"is collinear to the base of colour triangle (in B), while the orientation of X#
in the triangle plane depends on the noise in receptor mechanisms. For thresholds plotted in this chromaticity diagram
(see eqns A3 and A4), the model predicts circular contours of equal discriminability.
most parsimonious approach to calculating distance,
known as a line element, uses a Riemann metric,
which is a generalized Euclidean metric (Wyszecki
& Stiles, 1982). Line element models predict
ellipsoidal contours (Figs 3B, 4C). On the other
hand, two types of Minkowski metric predict
polygonal contours (Figs 3C, 4C), these are domi-
nance (Sperling & Harwerth, 1971; Nuboer &
Moed, 1983) and city block metrics (Backhaus,
(a)Inferring neural mechanisms from threshold data
An important reason for fitting metric models to
behavioural threshold data is that, in principle, they
can give information about neural mechanisms at
107Animal colour vision
Fig. 5. (A) Predictions of models of colour discrimination (solid lines) fitted to honeybee spectral sensitivity data (filled
circles; von Helversen, 1972). Geometrical interpretations of the models are illustrated in Figs 3 and 4. In each case,
curves are least-squared best-fits for the model in question. (i) Discrimination by an achromatic mechanism (Fig.
3A). (ii) Discrimination limited by receptor noise without interactions between receptors (Fig. 3B). (iii ) Discrimi-
nation limited by the most sensitive receptor mechanism, without interactions between receptors (Fig. 3C). (iv) Dis-
crimination by two chromatic mechanisms (ellipse in Fig. 4C), and also dominance and city block models (paral-
lelogram in Fig. 4C), which are indistinguishable for these data (see Section VI.3). Modified from Brandt & Vorobyev
1997. Only curve iv accurately describes the honeybee’s colour thresholds. (B) Spectral sensitivities of three vertebrates
as predicted by the receptor-noise-limited colour opponent model (as curve iv above; see Appendix B): a dichromat,
the tree shrew (Tupaia belangeri; Jacobs & Neitz, 1986) ; a trichromat, human (Sperling & Harwerth, 1971) ; and a
tetrachromat, Pekin robin, (Leiothrix lutea; Maier, 1992). Each study had two subjects, indicated by separate symbols
(o, j). Curves are displaced on the vertical axis for clarity. Modified from Vorobyev & Osorio (1998).
the stage in the visual pathway that limits per-
formance. In practice, however, different models –
that might implicate quite different physiological
mechanisms – often make similar predictions, so that
very accurate behavioural measurements are needed
to distinguish between them (Fig. 5). Sufficiently
accurate measurements are hard to obtain from most
A 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 dis-
crimination thresholds are described by polygonal
contours (dominance metric and city block metric
models; Figs 3, 4), the receptor inputs to neural
mechanisms can be derived from the orientation of
the sides of polygons in the colour space (Brandt &
Vorobyev, 1997). However, for models where the
discrimination thresholds are described by ellipsoidal
contours (Riemann metric; Fig. 3B), the receptor
inputs to neural mechanisms cannot be derived from
the orientation of the main axes of the ellipse. This is
because an appropriate transformation of the colour
108 Almut Kelber, Misha Vorobyev and Daniel Osorio
space maps the ellipsoid onto a sphere, whose main
axes are not defined (Fig. 4D ; Brandt & Vorobyev,
Ellipsoid models (Riemann metric) make very
general assumptions about neural mechanisms of
colour discrimination. They are valid if : (i) post-
receptoral 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 ) behav-
ioural thresholds are set by noise in neural mech-
anisms (Vorobyev & Osorio, 1998, Appendix A).
Of 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 pro-
poses 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 interactions
between the receptors is the simplest case of a
probability summation model whereby the prob-
ability of detection (discrimination) is given by the
sum of probabilities of detection by independent
mechanisms. In the city block metric model, the
absolute values of the differences in the neural
signals are summed and this sum is taken as a
measure for the discriminability of two stimuli.
Polygonal models have been used to find stage 2
mechanisms. Sperling & Harwerth (1971) fitted a
dominance metric model to monkey and human
spectral sensitivities. Later Nuboer & Moed (1983)
used a similar approach to make inferences about
post-receptoral mechanisms from spectral sensitivity
in the rabbit (Oryctolagus cuniculus). Backhaus
(1991) fitted a city block metric model to honeybee
colour discrimination (Section V.2c; Fig. 5).
Polygonal models of colour thresholds have more
parameters than ellipsoid models. Therefore, before
invoking a polygonal model, it is desirable to show
that thresholds are significantly less well fitted by an
ellipsoid (Figs 3B, 4C). In reality, given the scatter of
experimental data, it is difficult to distinguish
between ellipsoidal and polygonal models (Fig. 5).
For example, ellipsoidal 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.c –
do 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 be-
tween receptor signals.
(b)Receptor noise and colour thresholds
The best vision can do is to meet a limit set by the
noise originating in the photoreceptors. Actual
performance is worse than this limit because receptor
signals are corrupted by noise originating more
proximally in the visual pathway. One may expect
receptor noise to set thresholds because phototrans-
duction is metabolically costly (Laughlin, de Ruyter
van Steveninck & Anderson, 1998), so that if it were
not limiting selection would simply reduce expen-
diture on phototransduction. In this context, it is
perhaps surprising that the predictions of classical
line element models (Helmholtz, 1896) that invoke
receptor limits to colour discrimination do not in fact
fit experimental data (Figs 3B, 5A).
A new model of colour discrimination thresholds
(Fig. 5A) suggesting a minor modification of the
noise-limited models discussed so far (Vorobyev &
Osorio, 1998; Appendix B) fits experimental data
well. It takes account of the ‘ecological’ consider-
ation that chromatic signals are more reliable than
achromatic. We have mentioned that both bees and
birds use chromatic signals for colour discrimination
(Section IV). Accordingly, the model assumes that
performance is limited by receptor noise, but also
that colour is coded exclusively by opponent (chro-
matic) mechanisms that are insensitive to intensity
differences. Noise in the opponent signals is set by (or
equals) receptor noise. The only model parameters
are the noise levels in the receptor signals, which can
either be measured physiologically or estimated from
the relative number of photoreceptor cells. Conse-
quently, the model has no free parameters, and its
predictions can be compared directly with behav-
ioural data. It does indeed fit behavioural spectral
sensitivities of birds, mammals and insects (Fig. 5 ;
Vorobyev & Osorio, 1998). For the honeybee, the
model predicts the absolute value of thresholds from
noise measured by electrophysiology (Vorobyev et
al., 2001).
109Animal colour vision
The applicability of this receptor-noise-limited
colour opponent model indicates that its assumptions
hold for a variety of animals. However, for verte-
brates the model often fails to predict thresholds in
dim light (above cone threshold), almost certainly
because the achromatic signal is used (Vorobyev &
Osorio, 1998).
(4) Threshold models as a tool to study the
biological relevance of colour vision
The traditional use of threshold models is to test
hypotheses about physiological mechanisms, al-
though as we have seen (Fig. 5) different mechanisms
can give quite similar predictions. A second use is to
investigate the ecology, evolution and design of
colour vision. For example, it is now easy to measure
spectra of natural objects such as food plants or bird
plumage. Given an accurate model of performance,
one can compare the suitability of different types of
eye for tasks such as discriminating among a set of
spectra, or detecting them against the background.
This is especially worthwhile if performance is
limited by photoreceptor noise, because photorecep-
tor spectral sensitivities are known for many different
animals (Table 1), and one can often make a
reasonable estimate of their relative noise levels
(Vorobyev & Osorio, 1998).
For example, recent studies have asked how well
dichromatic and trichromatic eyes would serve a
primate looking for fruit against a background of
leaves (Osorio & Vorobyev, 1996; Sumner &
Mollon, 2000). Pursuing this idea one can also
model the performance of hypothetical eyes, where
for example visual pigment spectral sensitivities are
shifted, e.g. in birds without oil droplets (Vorobyev
et al., 1998). Finally, we can also ask how a specific
light habitat could influence the evolution of
receptor sensitivities (Chiao et al., 2000).
(1) Animals of all major phyla have multiple
visual pigments and photoreceptor types.
(2) Most animals with multiple receptors use
colour vision.
(3) Achromatic signals and chromatic signals
probably yield different types of information in
natural conditions, and may generally be repre-
sented by separate neural mechanisms. Chromatic
signals and colour vision are important for recover-
ing object surface properties under variable illumi-
(4) A variety of methods can demonstrate colour
vision without knowledge of underlying receptors or
neural mechanisms.
(5) Knowledge of photoreceptor sensitivities per-
mits the use of simple experimental methods to
demonstrate colour vision, to determine the number
of receptors involved and to investigate subsequent
neural processing.
(6) Knowledge of photoreceptor sensitivities, be-
haviourally measured spectral sensitivities and
models together build a powerful tool for studies of
the ecology and evolution of colour vision.
We gratefully acknowledge Simon Laughlin’s construc-
tive comments on an earlier version of the manuscript,
they helped to make the paper readable! Thanks to Tom
Cronin, to Justin Marshall and to everybody in the Lund
Vision Group for inspiring and helpful discussions! This
work was supported by a grant from the Swedish Research
Council to A.K. and by N. S. F. grant no. IBN 9724028 to
T. W. Cronin and NIH grant no. ROI EY0669 to J. Troy.
Graphical representation of colour is useful for
describing experimental data and for modelling
colour thresholds. (Such representations do not
predict thresholds.) Since colour can be defined by
the set of nreceptor quantum catches it can be
represented as a point in the n-dimensional colour
space (Fig. 2). For trichromatic vision, colour can be
presented as a point (Q) in the three-dimensional
receptor space, where quantum catches of the long-
wavelength (QL), middle-wavelength (QM) and
short-wavelength (QS) are placed along the co-
ordinate axes. Where receptor sensitivities are known
quantum catches can be easily calculated for any
light stimulus (equation 1). Generally, it is con-
venient to use a co-ordinate system (qi), where
quantum catches for stimuli are divided by those for
a reference stimulus or the background, Q!
i, to give a
receptor contrast space (Cole, Hine & McIlhagga,
110 Almut Kelber, Misha Vorobyev and Daniel Osorio
If the reference corresponds to a background of a
colour stimulus, equation A1 is a model of chromatic
adaptation. It is the simplest algorithm of correction
for changes of illumination (colour constancy),
allowing independent rescaling of receptor signals,
(von Kries, 1905), and is used widely to model
colour constancy (Hurlbert, 1998; Do
$rr & Neu-
meyer, 2000). This is because for an eye viewing a
reflecting surface, quantum catches change with
changes of illumination but the rescaled receptor
signal (equation A1) changes substantially less.
Instead of the receptor space, ‘chromaticity
diagrams are often useful (Fig. 2; Wyszecki & Stiles,
1982). In these diagrams, the intensity or achromatic
dimension is removed so that the location of a light
stimulus does not depend on its intensity, conse-
quently they have one dimension less than the
corresponding colour space. Chromaticity diagrams
were introduced because humans perceive chromatic
aspects of colour (hue and saturation) to be
substantially independent of intensity. Nonetheless,
chromaticity diagrams reduce the information about
colour, and are useful only for animals with separate
chromatic and achromatic signals. For trichromatic
eyes a common two-dimensional representation is to
plot the unit plane, QSjQMjQLl1, of the
receptor space (Figs 2B, 4A). A line connecting the
origin with the point Qor its extension must intersect
the unit plane at a point qc, whose receptor co-
ordinates are given by:
where i lS, M, L. This intersection gives a stereo-
graphic projection of the point Qonto the unit
plane. The location of that point determines the
chromaticity of the colour, whereas the length of the
vector characterizes its luminosity or brightness.
This chromaticity diagram is an equilateral triangle,
and is called the Maxwell triangle after its inventor.
To plot a point in the plane of a Maxwell triangle it
is convenient to use Cartesian axes:
M), (A3)
Note that these axes are not related to opponent
mechanisms. The vertices of the triangle have the
following co-ordinates:
0, N2
Maxwell’s triangle is the most commonly used
diagram used in studies of trichromatic animals.
However, in physiologically oriented studies it may
be convenient to use axes corresponding to op-
ponency mechanisms. For humans and trichromatic
primates the luminance mechanism is driven by the
summed M and L cone signals; the ‘ yellow–blue
opponency mechanism compares signals of S cones
with signals of both L and M cones, and the
red–green ’ mechanism compares L and M signals.
The existence of separate pathways corresponding to
these three mechanisms is established by psycho-
physical and physiological studies of trichromatic
primates (Jameson & Hurvich, 1955 ; Krauskopf et
al., 1982; Dacey, 2000). Unfortunately, for other
species the directions of opponency mechanisms are
unknown. MacLeod & Boynton (1979) proposed a
two-dimensional diagram, with axes corresponding
to ‘red–green ’ and ‘ yellow–blue ’ mechanisms:
(LkM)\(LjM) l(QLkQM)\(QMjQL), (A6)
S\(LjM) lQS\(QMjQL). (A7)
Note that the position of a point on this diagram is
normalized similarly to that of the Maxwell triangle,
and is thus independent of light intensity. A modi-
fication of this diagram uses log-transformed axes
(Regan et al., 1998).
For tetrachromatic vision (Fig. 2C) colour spaces
are four-dimensional, and corresponding chroma-
ticity diagrams three-dimensional. Generalisation
of the Maxwell triangle gives a tetrahedron (e.g.
Goldsmith, 1991). A three-dimensional stereo-
graphic projection onto unit three-dimensional
space, QVSjQSjQMjQLl1 is given by:
where i lVS, S, M, L. To plot points in the three-
dimensional space, it is convenient to use the
following co-ordinates:
M), (A9)
111Animal colour vision
, (A10)
. (A11)
The Xiand qc
ico-ordinates are related by trans-
formation of rotation. The vertices of this colour
tetrahedron are located at:
0, 0, N3
0, N2
. (A12)
Commercial software can plot three-dimensional co-
ordinates (Fig. 2C).
The model (Vorobyev & Osorio, 1998) is based on
three assumptions: (i) For a visual system with n
receptor channels colour is coded by nk1 unspecified
opponent mechanisms, the achromatic signal is
disregarded. (ii) Opponent mechanisms give zero
signal for stimuli that differ from background only in
intensity. (iii) Thresholds are set by receptor noise,
and not by opponent mechanisms.
The model has the following mathematical for-
mulation. Let fibe the signal of receptor mechanism
i, fithe difference in receptor signals between two
stimuli, and xαthe difference in colour opponent
mechanism, α. Generally, xαis given by a linear
combination of the differences of receptor signals, i.e.
where the coefficient Fαidescribes the input of
receptor ito opponent mechanism α. If opponent
signals only are used for discrimination, then the
distance between stimuli, S, is given by a function
of the noise and differences in opponent signals, xα.
Assuming that receptor noise is dominant, stimulus
discriminability does not depend on how receptor
signals combine to form opponent signals. Conse-
quently, the expression for the distance between
stimuli depends only on fiand the standard
deviation of the noise in the receptor mechanism, ei,
and need not contain Fαi. For stimuli close to an
achromatic background, if assumptions iiii hold,
colour distance is given by the following equations
(Vorobyev & Osorio, 1998):
(eS)#j(eL)#, (B2)
\((eSeMeL)#j(eVS eMeL)#
j(eVS eSeL)#j(eVS eSeM)#), (B4)
for di-, tri- and tetra-chromatic vision, respectively.
Receptor signals are functions of the receptor
quantum catches, and two simple models relating
the receptor signals to quantum catches can be
considered: (i) a linear relationship (Vorobyev &
Osorio, 1998); (ii ) a log-linear relationship (Voro-
byev et al., 1998, 2001). Because results of the model
calculations do not depend on the units in which
receptor signals are measured, receptor signals can
be re-scaled so that they are related to quantum
catches, qi(equation A1) by filqior filln(qi) for
the linear or log-linear models respectively. Note
that for stimuli which are close to a reference, both
models make the same predictions. For the log-linear
model, noise in the receptor mechanism, ei, equals
the Weber fraction of the corresponding mechanism,
ωi(Vorobyev et al., 2001).
If receptor signals are linearly related to quantum
catches, modeled chromatic signals remain insen-
sitive to stimulus intensity only in the vicinity of the
achromatic point. A logarithmic transformation
makes chromatic processing insensitive to changes of
stimulus intensity throughout colour space. Conse-
quently, this logarithmic version of the model gives
a chromaticity diagram, where colour loci are
independent of the stimulus intensity, and Euc-
lidean distance corresponds to the distance given
by equations B2–B4. For trichromatic vision the
112 Almut Kelber, Misha Vorobyev and Daniel Osorio
following axes can be used to plot colour loci (Hempel
de Ibarra, Giurfa & Vorobyev, 2001):
M)), (B5)
(ωM)#j(ωL)#, (B6)
filln(qi), and ωiis the Weber fraction of mech-
anism i. Then the distance in the colour space given
by equation B3 can be expressed as
#, (B7)
where X"and X#are given by equation B5.
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