Biological Journal
of
the Linnean SocieQ (1990), 41: 315-352. With 13 figures
On the measurement and classification of
colour in studies of animal colour patterns
JOHN A. ENDLER
Department of Biological Sciences, Universit3, of Calzfornia, Santa Barbara, California
93106, U.S.A.
Received 6 February 1989, accepted f o r publication 31 J u l y 1989
In studies of animal colouration i t is no longer necessary to rely on subjective assessments of colour
and conspicuousness, nor on methods which rely upon human vision. This is important because
animals vary greatly in colour vision and colour is context-dependent. New methods make i t
practical to measure the colour spectrum of pattern elements (patches) of animals and their visual
backgrounds for the conditions under which patch spectra reach the conspecific’s, predator’s or
prey’s eyes. These methods can be used in both terrestrial and aquatic habitats. A patch’s colour is
dependent not only upon its reflectance spectrum, but also upon the ambient light spectrum, the
transmission properties of air or water, and the veiling light sprctrum. These factors change with
time of day, weather, season and microhabitat, so colours must be measured under the conditions
prevalent when colour patterns are normally used. Methods of measuring, classifying and
comparing colours are presented, as well as techniques for assessing the conspicuousness of colour
patterns as a whole. Some implications of the effect of environmental light and vision are also
discussed.
KEY WORDS: -Adaptive colouration - anti-predator tactics aposematic colouration colour
protective colouration
measurement - colour classification - crypsis mimicry - perception
sexual selection visual communication - visual predation.
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CONTENTS
Introduction .
. . . . . . . . . . .
Measuring colour spectra .
. . . . . . . .
Units of light measurement
. . . . . . .
Derivation of the colour and brightness of a colour pattern
Measurement of ambient light spectra
. . . .
Measurement of reflectance spectra
. . . . .
Measurement of transmittance and veiling light spectra
Appraising colour .
. . . . . . . . . .
Standard methods
. . . . . . . . .
Segment classification . . . . . . . . .
Comparing colours
. . . . . . . . .
Assessing the conspicuousness of colour patterns
. .
Conclusions . . . . . . . . . . . .
Acknowledgements
. . . . . . . . . .
References
. . . . . . . . . . . .
Appendix: summary of symbols used . . . . . .
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35 1
INTRODUCTION
Animal colour patterns are used in thermoregulation, intraspecific communication, and predation avoidance. For efficient communication in courtship or
0024-4066/90/120315
+ 38 $03.00
315
0 1990 T h e Linnean
Society of London
316
J. A. ENDLER
territoriality, or in aposematic or mimetic colouration, colour patterns should be
as conspicuous as possible against the visual background; the signal/noise ratio
should be maximized. To mimimize detection by predators, colour patterns
should be inconspicuous or cryptic; the signal/noise ratio should be mimimized.
The colour patterns of animals and their visual backgrounds may be regarded
as mosaics of patches which vary in size, shape, brightness and colour. A cryptic
animal has a colour pattern which appears to be a random sample of the
background at the time and place when crypsis is necessary. The degree of
crypsis can be estimated by measuring the similarity between animal and
background with respect to the size, shape, brightness and colour distributions
(Endler, 1978, 1984, 1986). For examples see Endler (1984) and Sweet (1985).
Until recently, the least objectively measurable aspect of colour patterns was
colour. Often colour and ‘brightness’ is subjectively ranked by ‘naive’ human
observers (e.g. Baker & Parker, 1979; Hamilton & Zuk, 1982; Read, 1987). This
is dangerous because, for example, parrots are usually so ranked as ‘bright’ but
are among the most difficult birds to see in the equally ‘bright’ canopy of tropical
forests. Since the time of Ridgway (1912), subjectivity has been reduced by
comparing animal and background colours to a set of specially manufactured
colour standards (examples are Munsell, 1976; Kornerup et al., 1978; Smithe,
1974a, b). Unfortunately, ranking and matching methods have five major
weaknesses.
(1) Subjectivity is a problem, especially under difficult or tiring field
conditions.
(2) The colour of adjacent patches can effect the perceived colour of a patch
(Hurvich, 1981; Wyszecki & Stiles, 1982). This can be minimized by using
neutral grey masks to hide all but the colour pattern element and colour
standards being compared (Munsell, 1976; Smithe, 1974a, b).
(3) The colour match depends upon the lighting conditions. The same viewer
may not match a given sample with the same colour standard under different
natural or artificial lights. This may occur because different ambient light
spectra can affect both the actual and perceived colour of objects. In addition,
the human visual system is based upon only three colour sampling elements
(cone types), and, as a result, one neural signal can be caused by several different
light spectra, as long as the three cone systems are stimulated in the same way.
These perceptually equivalent spectra are called ‘metamers’. Two colours can be
‘metameric’ under some lighting conditions but not under others (Wyszecki &
Stiles, 1982; Hurvich, 1981). Repeatability can be increased by making the
comparisons under full sunlight or standard artificial lights (Munsell, 1976), but
this may not be practical in field studies, especially when cloud cover is partial
and moving.
(4) There is variation among people in normal (Neitz &Jacobs, 1986) as well
as abnormal (Hurvich, 1981; Wyszecki & Stiles, 1982) colour vision. Two people
may not match the same colour pattern element with the same standard, even
under identical lighting conditions, and even if both have ‘normal’ vision. This
can be minimized by always using the same person and conditions to make the
matches. However, even the same person cannot be used indefinitely because the
lens yellows with age, altering perceived colours (Wyszecki & Stiles, 1982).
Subjectivity and variation can be eliminated by using a full colour image
analyser and computer to assign sample colours to a pre-existing classification
MEASURING COLOUR PATTERN SPECTRA
317
(Joyce-Loebl, 1985). This classification can be based upon, for example, a
discriminant function analysis of colour images of each of the colour standards in
a colour atlas such as Munsell (1976).
(5) There may be differences in vision between humans and the animals to
which the colour patterns are normally directed. Colour vision is quite variable
among species, and not necessarily the same as humans. Some animals can see
fewer colours than humans, others (birds) can probably see many more than we
can, and still others may be able to see the same number, but in a different
region of the electromagnetic spectrum (Jacobs, 1981; Levine & MacNichol,
1979; Lythgoe, 1979; Mazokhin-Porshnyakov, 1969; Goldsmith & Bernard,
1974; Laughlin, 1981; Land, 1981; Kevan, 1983; Ali, 1984; Menzel & Backhaus,
1989; Backhaus et al., 1987). Differences between human and animal vision will
not be solved using a full colour image analyser, because the colour sensitivities
of the colour camera channels (or black/white camera and colour separation
filters) are generally matched to human rather than animal vision. T o some
extent this problem can be reduced by matching the filters to the visual pigments
of the animals concerned, but this does not account for differences in ‘wiring’
among humans and other animals. Thus, although we may have correctly
matched the colours in an animal and its background to standards in a colour
atlas, this classification may bear little or no relationship to how the predators or
conspecifics distinguish colours. The problem will be particularly difficult if the
patterns of ‘metamerism’ are different among the animal and human viewers.
Because colour is a very important aspect of colour patterns, it is important to
find methods of quantification which are independent of human vision. This is
necessary before attempting to understand conspicuousness and natural selection
arising from differences in perception. The purpose of this paper is to suggest
some methods based upon physical properties of colours. These methods have
only recently become practical with the commercial manufacture of field portable spectroradiometers, and can be used in almost any terrestrial or aquatic
habitat for almost any problem in animal colour patterns. The first part of this
paper deals with the measurement of colours and the second part presents some
methods which help to organize the variations of colours of animals and their
backgrounds. The first section contains well established methods, but the second
section represents only a preliminary attempt at devising methods, and should be
regarded more as a guide for future research than a final word on the subject.
MEASURING COLOUR SPECTRA
Units of light measurement
Light exists as a flow of photons or quanta of energy. Photons behave as both
waves and as particles, and each has a characteristic wavelength, frequency and
energy. Wavelength (A, nanometres = lo-’ m) is related to frequency ( v ) by
A = C V , where c is the velocity of light (2.99792 x lo8 m s-I). A spectrum Q(A) can
be defined as the distribution of numbers of photons at each wavelength A
striking a given area per second. The total light intensity (total photonflux) QTis
obtained by integrating Q(A)over the visible spectrum, Q,.= Q(A)dA. For most
vertebrates the visible spectrum ranges from about 400 nm (blue) through about
318
J. A. ENDLER
700 nm (red) (Lythgoe, 1979; Jacobs, 1981; for exceptions, see Chen &
Goldsmith, 1986; Downing et al., 1986; and Alberts, 1989), while most arthropods range between about 300 (ultraviolet) and 650 nm (Ali, 1984;
Mazokhin-Porshnyakov, 1969; Goldsmith & Bernard, 1974; Kevan, 1983; for
exceptions see Kevan, 1983). The examples and some of the methods in this
paper will use the typical vertebrate spectrum, but in principle all of the methods
can apply to any spectral range. I n fact there is no reason why these methods
could not be applied to crypsis in the infrared with respect to the pit organs of
vipers and boid snakes (Newman & Hartline, 1982).
Vertebrate and invertebrate photoreceptors (as well as chloroplasts in plants)
respond directly to the number of photons striking the photoreceptors rather
than the photons' energy (Lythgoe, 1979; Hurvich, 1981; Wyszecki & Stiles,
1982; Goldsmith & Bernard, 1974; Laughlin, 1981; Kirk, 1983). Therefore the
appropriate unit of light intensity at wavelength A is photon flux per unit area
Q(A), measured in moles m-2 s-l ( 1 mole = 6.02257 x loz3 photons =
1 Einstein). Micromoles ( p ~or
) microEinsteins (pE; 6.02257 x 10" photons) are
often more convenient. For example, full sunlight at noon can have a total
intensity ( QT)as high as 2000 p~ m-' s-' while noon shade in a forest can be as
low as 5 p~ m-'s-'. Oddly enough, there does not appear to be a single unit of
photon flux which includes the scaling factors of metres squared per second. I
propose the unit 1 f i n d a l l = 1 p~ m-'s-'. However, to avoid confusion, I will
use only the existing units in this paper. The instrument used to obtain total light
intensity is called a quantum radiometer, whilst an instrument which also
records the light intensity at each wavelength (or each wavelength interval) is
called a quantum spectroradiometer (Li-Cor, 1982; Kirk, 1983; Wyszecki &
Stiles, 1982).
Confusingly enough, light intensity can also be measured as energy flux per
unit area E(A), in W mP2. This is convenient in the design of instruments
because it is the form of the output of photoelectric devices. But the energy
measure of light intensity is inappropriate and can even be misleading in studies
of animal colour patterns because animal photoreceptors respond to photons
independent of energy. A photon's energy ( is related to its wavelength by
((A) = hv = hc/A = (l/A) 1.9863 x
Joules ( h is Planck's constant; Kirk,
1983); short wavelength photons have more energy than long wavelength
photons (Fig. 1A). Given that 1 W = 1 J s-', for any single wavelength ;Z we can
convert the energy flux E(A) in W m-' to the photon flux Q(A)in PM m-'s-' by
Q(A)= 0.0083519AE(A)
(1)
(after Kirk, 1983; see Fig. IB). For example, 1 W of light a t 400 nm has only
57% the photon flux as 1 W at 700 nm. Because the relationship between Q(A)
and E(A) is wavelength dependent, it is invalid to use a single mult$lier to convert total
light energy E, = E(A)dAto total quantumjux QTunless it is known that all spectra
to be converted have the same shape (colour). For example, if full sunlight is
being measured, the ambient light spectrum has the same shape regardless of
intensity, and the relationship is approximately QT z 4.5935 ET (after Kirk,
1983, using 550 nm in equation ( 1 ) ) . But this relationship will not hold in the
shade of plants or buildings, which can have very different spectra from direct
sunlight (Hailman, 1977; Chazdon & Fetcher, 1984a, b; Lee, 1987; Endler,
1990). Watt meters are called radiometers or spectroradiometers, though some
319
2-
0
I
I
I
I
I
I
I
I
I
I
I
I
I
I
2-
-
u
Figure I . Physical relationships of light. A, Energy per photon
x lo-'!') as a function of
wavelength (nmj. B, Quantum flux ( p =~ pEj for 1 W of energy as a function of wavelength. Short
wavelength photons are more energetic and animal photoreceptors respond to the number of
photons rather than their energy, therefore, using energy ( W ) to estimate light intensity will
underestimate the neural response and perceived brightness at short wavelengths.
(e.g. the Li-Cor model LI-1800) may be set to make the conversion to quantum
intensity at each wavelength automatically. T h e conversion is done by using
equation ( 1 ) at each wavelength interval (A). It is always better to choose a
machine and sensor which is designed for quanta rather than energy; sensors
which are designed to give only total energy ( E , or quantum flux Q,) differ in
their spectral sensitivities (for a particularly clear discussion, see Li-Cor, 1982).
In photography and commercial lighting applications there is yet a third
system of measuring light intensity: this is the photometric system and the
machines are called photometers (see Tenquist et al., 1970; Li-Cor, 1982;
Wyszecki & Stiles, 1982). Photometric devices are entirely inappropriate for
studies of animal colour patterns because they are designed to measure human
perceived brightness and therefore have the same spectral sensitivity as the
human luminous efficiency curve, and are relatively insensitive at short and long
wavelengths (Li-Cor, 1982; Wyszecki & Stiles, 1982). As for energy (W m-')
meters, there is no single conversion factor between the photometric system and
quantum intensity, unless it is known that all spectra to be converted have the
320
J. A. ENDLER
same shape. For example between 400 and 700nm, a halogen lamp gives off
per 1000 lux while a fluorescent lamp gives out only
20 PM m-'s-'
13 PM m-'s-' per 1000 lux; the former has a spectrum which is richer in long
wavelength light (Li-Cor, 1982). Clearly quantum sensors should always be used
instead of energy or photometric sensors.
Optical oceanographers and biologists interested in light in aquatic environments have adopted a set of international standard symbols and units for use in
studies of light (Morel & Smith, 1982). However, the standardization has an
unfortunate ambiguity. The same letter applies to a particular quantity
measured either in energy or in photon flux (Kirby, 1983). For example, the
symbol E in this system stands for irradiance in either W m-' or PM m-'s-'.
However, the SI units associated with each standard symbol were defined in
terms of energy (W or J, Morel & Smith, 1982). For this reason, to avoid
ambiguity of letters with respect to energy and photon flux, and to emphasize
the need to use photon flux in studies of colour patterns and vision, the standard
symbols of Optical Oceanography will not be used in this paper. The symbols
used in this paper will be defined whenever they are first introduced. The
appendix lists the definitions and oceanographic equivalents.
In summary, all studies of animal colour patterns must use light-measuring
equipment capable of giving intensity measures in quantum units
(Q(A),PM m-'s-') throughout the visible spectrum. Other units are inappropriate because they d o not predict the response of animal (or plant) photoreceptors. Quantum measures will be assumed for the remainder of this paper,
and 'intensity' or 'brightness' will always imply quantum flux rather than
energy, hence the symbols Q((n)or QT.
Derivation of the colour and brightness of a colour pattern element
The perceived colour and brightness of an element of a colour pattern depends
upon three processes: (i) the physics of light reflectance and transmission to the
surface of the eye; (ii) the physics of light transmission, refraction and photoreception within the eye; and (iii) the neural processes in the retina and brain
which ultimately lead to perception of colour and brightness. The first depends
only upon the external environment. The second two are species specific, and are
known to vary among species living in different habitats (McFarland & Munz,
1975; Levene & MacNichol, 1979; Lythgoe, 1979; Jacobs, 1981;
Mazokhin-Porshnyakov, 1969; Goldsmith & Bernard, 1974; Laughlin, 1981;
Land, 1981; Kevan, 1983; Chen & Goldsmith, 1986; papers in Ali, 1984).
Differences in vision among species can have strong effects on both the appearance of colour pattern elements (McFarland & Munz, 1975; Lythgoe, 1979;
Kevan, 1983; Endler, 1986; Backhaus et al., 1987) and their evolutionary
dynamics (Endler, 1988). For brevity, this paper will consider only the effects of
varying light conditions on the light spectra which reaches the eye. This has the
advantage of being general to all species, but it must be remembered that the
effects of specific physiological differences in colour vision may in some instances
modify these effects.
The light spectrum which reaches the surface of an eye from a particular
colour pattern element (patch) is a function of the ambient light spectrum
striking the patch, the patch's reflectance spectrum, and the transmission
MEASURING COLOUR PATTERN SPECTRA
s
s
s
s
32 1
S
Figure 2. Example of light paths reaching the viewer’s eye; the principles arc the same in water. S
Sunlight (direct, or diffused through clouds). A : Ambient light striking a colour pattern element
(patch) of the antelope, integrated over 180” solid angle. Ambient light A may come from light
reflected from other objects (tree), through objects (leaves), directly from the sky, and rcflccted from
dust particles (p). R: Fraction of photon flux reflected from the patch. T. Fraction of photons
transmitted from patch to lion’s eyes, some may be absorbed or scattered by dust particles p).
Q: Light beam striking the lion’s eyes. Q,.: Light striking the lion’s eyes after being scattered by dust
particles ( p ) .
spectrum of the medium (air or water; Hailman, 1977; Lythgoe, 1979; Wyszecki
& Stiles, 1982; Kirk, 1983). Figure 2 shows an example from land, but the same
principles hold in water. Direct sunlight (S), or sunlight diffused through clouds,
is the source of light and has a characteristic spectrum which may be modified on
the way to a colour pattern element or patch (on the antelope in Figure 2). A
patch is illuminated from various directions by light reflected from other objects
(the tree), light transmitted through other objects (leaves), directly from
sunlight, and indirectly from particles in the medium (p, in this case dust on a
windy day). The light integrated over 180” solid angle normal to the patch
defines the ambient light spectrum striking the patch ( A ) . The fraction of this
light reflected towards the viewer’s (lion’s) eyes defines the reflectance spectrum
( R ) . The reflected light spectrum can be modified further by absorption,
reflection and scatter by particles (p) in the medium between the patch and the
viewers (more dust in this case); the fraction transmitted over this distance
defines the transmission spectrum T. The narrow beam of light arriving at the
viewer’s eyes from the patch has been affected by all of these factors and is called
Q. If there are enough particles in the medium, they may scatter a significant
amount of light directly into the viewer’s eyes, producing some ‘veiling light’,
here indicated by Q,. This is particularly noticeable during dust storms, fog and
in turbid or stained water.
We can quantify these effects as follows. At any single wavelength, the intensity
322
J. A. ENDLER
of light (number of photons) reaching the eye is simply the product of ambient
light, reflectance and transmittance, or
Q = ART(x)
(2),
where Q is the quantum intensity of light reaching the eye, A is the quantum
intensity of ambient light incident on the colour pattern element or patch, and R
is the fraction of incident light (quanta) which is reflected towards the eye from
the colour pattern element. The function T(x) describes the fraction of the
reflected light which is transmitted through the air (or water) to the eye as a
function of the object-to-eye distance x. Its form is determined by the degree to
which the medium absorbs and scatters light. For most terrestrial species, T(x)is
effectively independent of x in air, except in foggy or dusty weather. The gentle
decline of T(x)with x in air may be important, however, to birds of prey with
very large prey-sighting distances (Duntley, 1946). The situation is quite
different in marine and fresh waters, where T(x)can vary from nearly constant
through a rapidly decreasing function of x, as in blackwater and turbid conditions (examples of Lythgoe, 1979; Kirk, 1983, and Endler, 1986). For many
conditions transmittance has the form T(x)= e-", where M is the beam attenuation coefficient (Kirk, 1983).
In general, A, R and T(x)are not constant, but depend on wavelength A. For
this reason they will now be replaced with the functions A(A),R(A),and T(A,x),
which describe the spectral pattern of ambient light, reflectance, and transmittance as a function of wavelength. Therefore, equation (2) is rewritten as:
Q(A, x) = A(A)R(A)T(2,x)
(3).
Q(A,x) now describes the distribution of light at all wavelengths reaching the eye
at distance x from the patch. For brevity, Q(A, x ) , A(A), R(A), T(A,x) will be
called the colour, ambient light, reflectance and transmittance spectra,
respectively. All must be measured in terms of quantum flux rather than energy.
An example is shown in Fig. 3.
The brightness of a patch may be defined as the total intensity of light (QT)
reaching the eye from the patch at distance x, or
J Q(2, x)dA = J A ( I ) R ( A T(A,
)
x)d2
(4),
where the integration is made over the spectrum visible to the predator or
conspecific. In actual practice, spectra are measured at discrete wavelength
intervals rather than infinitely small intervals, so the practical version of
equation (4) is:
QT(x) E
C
C
w Q(4x) = w A(A)R(A)T(A,
x)
(5),
where the summation is done over the visible spectrum, and w is a constant
which is dependent upon the width of the wavelength interval (Wyszecki &
Stiles, 1982; Kirk, 1983). Clearly, brightness depends upon viewing conditions,
For example, in Fig. 3 the ambient light is rich in middle (yellow and green)
wavelengths, so patches which reflect most strongly in the middle wavelengths
will be brighter than other patches. But if the ambient light contained primarily
only long wavelengths (orange and red) the brightest patches would be those
reflected in longer wavelengths, and the shorter and middle wavelength patclirs
would be relatively less bright.
QT(x) E
ME ASURING C O L O U R PA TTERN SPECTRA
0.10
323
A
0.05
.-.
.;.. ...
C
...
..
...
RG
0
0
0
0
00
a
0
0
a
0.:
. ..
0
.
0
0
0
0
.
.
o
.
.
o
o
o
(
QB
QR
0
0
0
O.O!
(
400
500
600
700
Wavelength (nm)
Figure 3. Example of the results of calculations of colour spectra from ambient light and reflectance
with 151 points sampled between 400 and 700 nm. A: Ambient light spertrum ( A ( l ) ) ,with total
intensity A., = A ( l ) d l = 10 PM m-'s-'. R,,. &,, RR:Reflectance spectra ( R ( R ) )for blue, greenishyellow, and red patches, respectively. These are hypothetical patches with equal total reflectanees
(their brightnesses are each 2.43 PM m-'s-' if illuminated by perfectly white light with A, =
10.0 PM m-' s - I ) . &, &,, Q: Colour spectra Q(d, A ) , calculated using equation ( 3 ) for all I ,
assuming perfect transmission ( T ( d ,x ) = 1.0 for all I and 7 ) . Using equation (5), the brightnesses
( Q , )of the three patches are 2.01, 2.87 and 2.35 PM m-'s- I , respectively, yielding a brightness ratio
of0.70 : 1.0 : 0.82. T h e patches are respectively 83",, I18", and 97",, as bright as they would be in
white light (constant A ( 1 ) for all l ) at 10.0 PM m-'s-'. Note how the more abundant middle
of colour G greater than the other two
wavelength ambient light makes the total brightness
colours. A differently shaped ambient light spectrum would afI'ect the relative brightnesses of the
three colours differently.
(a,)
J. A. ENDLER
324
The colour of a patch is determined (in physical terms) by the shape of the
colour spectrum Q(A,x), examples are shown in Figs 3 and 4. I t is convenient to
make the distinction between apparent and inherent properties (Kirk, 1983). R
is the inherent colour of a patch since it is dependent of environmental
conditions. Qis the apparent colour, since it is the spectrum which reaches the
eye under the current conditions.
When humans perceive and classify colour we use two properties in addition
to brightness: hue and chroma. These are associated with physical properties of
light (see Table 1 and Fig. 4). Hue is the everyday meaning of ‘colour’, e.g.
violet, blue, green, yellow, orange, red, etc. I n general, the hue of a spectrum Q
is a function of its shape. Hue is correlated with the wavelength of the maximum
slope (most rapid change in Q with A), as well as the sign of the slope. For
example, a Qwith a positive slope located at a longer A is an orange or red, while
a Qwith a negative slope located a t a shorter A is a blue or blue-green (Fig. 4).
Some colours are not monotonic and will have two maximum slopes; examples
are yellow-green and green (Fig. 4, curves 6-8) and purple (Fig. 4, curve 10).
Complimentary colours contain complementary parts of the spectrum, and
hence will tend to have maximum slopes of opposite signs a t the same wavelengths (Fig. 4, curves 4 and 9). In general, hues are given names, and are not
generally assigned specific numerical values. Numerical assignment is possible if
we simplify the spectrum; this will be discussed in the section on colour
classification.
Chroma is a measure of the ‘purity’ or ‘saturation’ of a colour, and is a
function of how rapidly intensity changes with wavelength (Table 1, Fig. 4).
Spectra which exhibit steeper maximum slopes and greater differences among
parts of the spectra will appear to have more chroma than spectra with more
gradual and smaller changes (Fig. 4, curves 1-3). This is also true of colours
which occupy narrow bands in the visible spectrum. This is not surprising in that
vertebrate and invertebrate visual neural systems take the differences between
different parts of the spectra to obtain colour sensations; this is known as
‘opponency’ or ‘lateral inhibition’ (Hurvich, 1981; Laughlin, 1981 ) . The evolutionary convergence in visual systems is extensive (Laughlin, 1981) and even
extends to human technology-the same method is also used to classify objects
by colour in image analysis and remote sensing (Castleman, 1979) and for
coding colour in television systems (Limb et al., 1977). The effects of differences
among segments of the spectrum can most easily be seen by considering the total
intensities of two segments ( a and b ) of the spectrum Q(A,x ) at a particular
viewing distance x:
Q, =
I’
Q(4x ) d l
Qb
=
s:
Q(4x)dJ-
(6),
where s, t and u, u are the wavelength limits for the two segments, respectively.
The practical counterpart of equation ( 6 ) is the sum of discrete Qmeasurements
within each segment, as in equation (5).The chroma, or colour signal intensity,
will be proportional to
(71,
C = (Qa- Qb) I(QL,+ Qb)
where the denominator ( Qa Qb)normalizes for total brightness. C is a measure
+
MEASURING COLOUR PATTERN SPECTRA
325
of chroma because it increases with the difference between the intensities of the
two spectral segments independent of brightness. For example, in Fig. 4 the
differences between the total brightnesses of the spectrum from 400-550 nm and
550-700 nm decreases from curve 1 to 3, in parallel with their perceived
reduction in chroma.
The colour spectrum of a patch can also be affected by what occurs between
the patch and the viewer’s eye (Fig. 2). I n foggy or turbid conditions a patch’s
colour will be affected by ambient light which is scattered directly into the eye
by the particles in the medium; this has appropriately been called ‘veiling light’
by Lythgoe (1979, see also Kirk, 1983, and Duntley, 1946). This light will have
its own characteristic colour spectrum Q,,(A,x ) similar to equation (3), or
where P ( 1 ) is the spectrum of light scattered and reflected from the veiling
particles into the viewer’s eye (for a detailed discussion, see Kirk, 1983, and
Duntley, 1946). The light reaching the eye will be the sum of photons from the
colour patch and from the veiling light, or Q* = Q+Q,. Because veiling light
will, in general, add light at more wavelengths than are present in the average
colour patch, the general effect of veiling light will be to reduce the chroma of
colour patches. This can most easily be seen by considering how veiling light
affects C in equation (7). Let the veiling light be white, or Qv(A,x ) = wv for all 1
at a given x . If segments a and b are of equal length then veiling light will
contribute an equal amount u to both segments. So C with added veiling light
(C*) will be
It is clear that as u increases C* decreases. Since u increases with distance (more
particles in front of the eye), C* will decrease with distance. This reduction of
saturation by veiling light will be true as long as the veiling light spectrum (Qv)
has less chroma (is less saturated) than the patch spectrum (Q).This is generally
true in fog or dusty weather on land, and in many aquatic habitats. I n some
aquatic habitats, especially in deep water, the veiling light is often coloured, and
so may affect the hue as well as the chroma of a patch.
In summary, both colour and brightness depend upon the viewing conditions
{ A ( 1 ) , T(1,x ) , and Q,(1x,) } as well as the reflectance spectra R(1) of the patch.
can differ from the
This is equivalent to saying that the apparent colour (Q(1))
inherent colour ( R ( 1 ) ) .Since the viewing conditions during intraspecific
communication may not be the same as during predation, the colour spectrum
(Q(1,x ) (or Q*(A, x ) ) of an animal can vary with function, even if it cannot
change its chromatophores (constant R ( 1 ) )as can a chameleon or cichlid.
Measurement of ambient light spectra
The spectrum of ambient light A ( 1 ) can be measured in various ways (Li-Cor,
1982; Kirk, 1983; Wyszecki & Stiles, 1982; Lythgoe, 1979). The two main
measures are irradiance and radiance (Fig. 5), and differ in the acceptance angle
of the sensor (6). Irradiance is the quantum flux per unit area coming from many
J. A. ENDLER
326
0.!
R
(
0.:
J
00
I
I
500
600
I
00
500
600
700
Wavelength (nm)
Figure 4. Example reflectance spectra R(1) showing variation in colour (hue), chroma (saturation)
and brightness (value): reflectance (R)as a function of wavelength (nm). These spectra were
recorded from samples in the 1976 Munsell Book oJColor (Munsell, 1976). Each Munsell notation has
the format hue (number and letter), value/chroma (Munsell, 1976; Endler, 1984). The rough rolour
names and corresponding Munsell notations are 1: red, 10 R 5/16; 2: red, 10 R 5/10; 3: red,
10 R 5/2; 4: yellow, 2.5 Y 8/16; 5: yellow, 10 Y 7/12; 6: green-yellow, 10 GY 6/12; 7: green-yellow,
10 GY 6/6; 8: green, 7.5 G 6/10; 9: blue, 10 B 5/12; 10: blue-purple, 10 PB 4/12; 11: purple,
2.5 P 4/12. Note how the position of the maximum slope of the spectra changes with hue (compare
curves I & 4 or 5 & 6 or 8 & 9) and how the steepness of the slope, as well as the areas under
different portions of the spectra, change with saturation (compare 1-3 or 6 & 7). The mean height
of, or area under, the curve is proportional to brightness (value).
or all directions (26 = 180" in Fig. 5A). Radiance is the quantum flux per unit
area coming from one direction at a small acceptance angle (26 = 10" in
Fig. 5B). The units are J.LM m-'s-' for irradiance and J.LM m-'s-' for radiance
(sr = 1 steradian, a solid angle of one radian, or the solid angle subtended at the
centre of a sphere of radius r by a n area on the surface of the sphere of r').
Irradiance measures should be used for A ( 1 ) because the light striking an animal
or background usually comes from many different directions; radiance measures
will underestimate A(A). The irradiance sensor must have the Lambert cosine
response, which corrects for the fact that light at low angles to the sensor would
otherwise yield a weaker signal than light at higher angles (Li-Cor, 1982; Kirk,
1983). It is necessary to choose one's instrument and sensor carefully because
manufacturers differ in their characteristics and options. For example, Li-Cor's
machines (LI-ISOSB, LI-1800) come with irradiance sensors with the Lambert
response as standard, and a radiance telescope (LI-1800-6,10) as an option,
while Spectron's machines (CE 395, CE 390) come as radiance sensors, with a
MEASURING COLOUR PATTERN SPECTRA
327
Lambert Cosine adaptor as an option. (Additional care must be taken because
most machines use energy as the 'default' output rather than quantum flux.) For
greatest accuracy and precision, small bandwidths (wavelength intervals) should
be used in all measures. For most natural light a bandwidth of 2-5 nm will
detect most of the changes in intensity (photon flux) with wavelength.
In terrestrial and benthic aquatic habitats, irradiance is usually measured over
a 180" (26) solid angle, preferably aligned with the surface of the background
(Fig. 5 A ) . If the surface of the animal's colour patch is not parallel to that of the
background by an angle 8 (Fig. 5C), then a correction needs to be made to allow
for the fact that the orientations are different. If A ( A ) is the background
irradiance, then the irradiance striking the animal A,(A) at angle 8 is
A,(A) = A ( A ) cos 8
(10).
This correction should be made even though the irradiance meter has the
Lambert cosine response (equation 10 applied to the receptor surface itself),
because the 180" solid angle of acceptance of the receptor measures the light
striking the receptor with respect to the receptors orientation rather than that of
the animal. If it is impractical to align the sensor with the background, it can be
aligned vertically (as in Fig. 5), and equation (10) applied to both animal and
background, with separate 8 for each. In what follows it will always be assumed
that this correction has been made.
In arboreal or non-benthic aquatic habitats, and for very small animals, light
will arrive at the animal's surface from more than a 180" solid angle. I n this case
specially designed sensors will have to be used which integrate light over the
solid angle equal to that of the range of orientation of the animal's exposed
surface. In some cases a spherical sensor may be necessary; in that case it should
be corrected to the patch's acceptance angle co by a factor ofco/4n (4n is the solid
angle of a sphere in sr). For species with a reasonably flat surface (such as larger
fishes), a standard 180" sensor may be sufficient. For a detailed discussion of
measuring ambient light in aquatic habitats see Kirk (1983), Li-Cor (1982) and
Lythgoe ( 1979); these principles also apply to arboreal terrestrial habitats.
If a sensor is designed for air it cannot be used in water (and vice versa)
without recalibration or change in design. Since water has a higher refractive
index than air, the difference in refractive indices between the sensor and the
medium will be less in water. Therefore, proportionally more light will be
scattered rather than absorbed by the air sensor underwater, causing it to
underestimate irradiance (Li-Cor, 1982). The reverse will be true for underwater
sensors used in air. The better machines and sensors come in terrestrial and
aquatic versions, or allow corrections to be made to the output.
It is not valid to measure A ( 1 ) at a random or arbitrary time because its shape
and total intensity ( A , = A(A)d3,)varies with time of day (sun's angle), season,
and weather. In a forest or arborescent coral habitat with sun flecks, the
temporal and spatial variation is even more extreme (examples in Endler, 1978,
1989; Chazdon & Fetcher, 1984a, b; Lee, 1987). Therefore i t is essential that A ( A )
be measured at the time and place at which it is relevant to the function of the
colour pattern. For example, if predation and courtship take place under
different light intensities (as in Endler, 1987), a separate set of measurements of
A ( 1 ) must be taken for each condition. If the animals of interest are also sensitive
to polarization of light (as in insects, Waterman, 1981), then the degree and
328
J. A. ENDLER
direction of polarization will have to be measured, and this also changes with
environmental conditions.
Measurement of rejectance spectra
The reflectance spectra R ( I ) of background and animal colour pattern
elements (patches) describes the fraction of photons at each wavelength A
incident on the patch (A(1)) which are reflected towards the viewer. R ( I ) is a
measure of the 'inherent' colour of the patch.
Since we want the quantum flux reaching the eye, R ( I ) should be measured
using sensors designed to measure photon flux rather than energy. If a watt
meter were used, then the perceived reflectance at short wavelengths would be
underestimated and that at longer wavelengths overestimated. For example, the
quantum reflectance spectrum R ( I ) of a photographic neutral grey card has the
same shape as Fig. 1B because these cards are designed to reflect the same energy
at every wavelength interval. Neutral grey cards are appropriate for predicting
the response of photographic films, but not eyes.
Except in pelagic and aerial habitats, natural colour patterns and backgrounds are rarely uniform, and consist of patches which subtend a small visual
angle. Consequently, radiance rather than irradiance measures (Fig. 5) are
needed to estimate R ( I ) ; we must measure the reflectance of the animal or
background patch over a small angle (6), and this angle should always be
specified.
There are two common methods of measuring radiant reflectance: the beam
and integrating sphere methods (Fig. 6A, B). They differ primarily in the range
of angles at which incident light strikes the patch being measured. This angle is
called the sample acceptance angle (4, Fig. 6C). It should be as similar to
natural conditions as possible.
Both methods involve a light source with a carefully regulated power supply
(or battery) to prevent changes in source brightness within and among scans.
Figure 5. Measuring incident light. S (Black rectangles), light scnsors resting on the visual
background (hatched). T h e vertical line above each sensor is its orientation axis. A, Ivadiance
measurement; the sensor has a 180" acceptance angle 26 = 180").B, Radiance measurement; the field
angle of the sensor (6) is small (here 26 = 10"). When a patch o n the animal's body surface (P) is not
parallel to the visual background by an angle 6 , it receives less (cos 6 ) light per unit area than the
background.
MEASURING COLOUR PATTERN SPECTRA
329
For studies involving ultraviolet reflectance it is necessary to use quartz optics
and it may be necessary to add a special lamp to enrich the ultraviolet
component of the light source (for a discussion of light sources see Spikes, 1983).
A polarizer and analyser will also be required if polarization is an important
component of colour patterns, as in insects (Waterman, 1981).
The beam method (Fig. 6A) simulates a single non-diffuse light source, as is
commonly found in terrestrial habitats (though not necessarily in forests, Endler,
unpublished), and shallow aquatic habitats with clear water. It consists of a light
source striking a single colour patch element of the animal or background at a
similar. angle to that found in nature, and the reflected light sensed by a radiance
sensor, with a known small acceptance angle (6), perpendicular to the surface of
the sample (Fig. 6A). Since natural light sources are not point sources, the source
should have a reasonably large diameter, yielding a sample acceptance angle (4,
Fig. 6C) of 15-30'. The angle chosen should be as close to the natural light
distribution as possible. For measuring very small patches, a microscope can be
placed in front of the sensor, as in Lythgoe & Shand (1982). Microscope optics
are particularly absorbant at short wavelengths, so special optics are needed for
UV reflectance measures. If the beam method is used for animals and backgrounds in habitats with diffuse light, then the radiant reflectance may be
underestimated. Increasing the sample acceptance angle and making the light
source more diffuse will reduce the underestimate, but if the natural sample
acceptance angle is very large, or natural light is very diffuse, then the
integrating sphere method should be used instead. The beam method is most
appropriate when normal light is not diffuse.
The integrating sphere method (Fig. 6B) simulates an evenly diffuse light
source, as is commonly found in deeper, coloured and/or turbid waters, in cloud
forests (during fog), and sometimes in dense terrestrial vegetation. The light
source enters the side of the sphere through a small hole parallel with the sample,
reflects in all directions from the interior of the sphere and strikes the sample
evenly from all directions (4 > 80"). The radiance sensor is placed over a second
hole directly above the sample (Fig. 6B) and must have a small enough
acceptance angle (6) so that it receives only the radiance of the colour patch.
The sphere method will overestimate the reflectance if natural ambient light is
not diffuse, because proportionally more light from the source will strike the
sample.
Plant physiologists and others often use an integrating sphere with a different
arrangement (Fig. 6D) in which the sensor is not aimed towards the sample, but
rather aimed towards part of the interior wall of the sphere (Wyszecki & Stiles,
1982: 156). This has the effect of measuring the total reflectance of the sample
because this arrangement gathers light reflected from the sample at all angles.
This is appropriate in studies of photosynthesis and thermoregulation where the
total fraction absorbed and reflected is important. But it is inappropriate in
studies of animal colour patterns relative to vision, where the narrow angle
reflectance is more important than the entire (wide angle) reflectance. Even if a
patch is seen from several angles, it is seen at only one angle at any one time, so a
radiance measure (Fig. 6A, B) is always the only correct one.
Animal colour patterns can consist of structural colours and pigments. Most
pigment-based colours and some structural colours reflect roughly evenly in all
directions, and their reflectance colour R (2) does not change with the angle of
330
J. A. ENDLER
the reflected light. However, structural colours characteristically change the
form of &(A) with the viewing and lighting angles (Simon, 1971; Parkhurst &
Lythgoe, 1982; Lythgoe & Shand, 1982). Some structural colours and smooth
surfaces will also glare at certain angles. Glare is caused by nearly complete
reflectance of the light source at certain angles, consequently, at the glare angle
R(1) will more closely resemble the ambient light spectrum than the reflectance
spectrum.
T o account for the changing R ( 2 ) with angle, R(A) must be measured at
various angles (not just at the 90" angle shown in Fig. 6); particularly at the
angles most commonly seen by conspecifics and predators. If there are structural
colours or glare in a n animal or background, it is not advisable to use the
integrating sphere method (Fig. 6B) because: (1) it is difficult, if not impossible,
to vary the angle of the sample relative to the sensor, and (2) the integration of
the sphere confounds the various reflectance spectra at different incidence
angles. T h e beam method (Fig. 6A) allows enough freedom to vary both the
angle of the light source and the sensor relative to that of the sample. The beam
method will only underestimate the reflectance for habitats with very diffuse
light, and with proper calibration this could be allowed for in the calculation of
R(4.
The procedure for obtaining R(A) from the sensor output is the same for both
the beam and integrating sphere methods. One scan is made of the object,
yielding Q(A,x ) for the sample under the machine conditions. Immediately
thereafter a second scan is made of a reflectance standard, to yield &,(A, x ) . As
with measuring A(,l), the wavelength intervals or bandwith should be as narrow
as possible. The standard has a known reflectance spectrum, Rs(A),so dividing
Q(A,x) by &,(A, x) at each wavelength interval A yields the ratio of reflectances
R(A)/Rs(A)( A and T i n equation 3 cancel out). When this ratio is multiplied by
R,(A) at each A, it yields the reflectance spectrum R(A).
Barium sulphate is an excellent reflectance standard, it reflects 99% of
incident light ( R x 0.99) between 400 and 700 nm, and is nearly as good down
to 300 nm (Wyszecki & Stiles, 1982: 58). Polished aluminium is also useful
( R x 0.92 between 300 and 700 nm, Wyszecki & Stiles, 1982: 56), especially for
field work, because it is durable. Other useful standards include MgO and
MgCO, (Benford et al., 1948). Any standard can be used so long as its reflectance
spectrum is known, reasonably flat, and it reflects a significant amount of light at
all wavelengths of interest; see Kevan (1983) for a discussion of problems arising
from insufficient reflection from reflectance standards at short wavelengths. The
reflectance figures for these standards (e.g. 0.92 for aluminum) are obtained
using an integrating sphere in a configuration which obtains the total reflectance
from the standard in all directions (Fig. 6D). But in studies of animal and
background colours we need the reflectance spectrum of the standard from only
one direction. This can be obtained in two different ways. (i) If the light source
has been standardized so that it illuminates the sample position in the reflectance
spectroradiometer (Fig. 6A, B) with a known Q(A),the reflectance spectrum of
the standard can be obtained directly by &,(A) = Q,(A)/Qc(A)for each A, where
&,(A) is the measured spectrum at the sensor and Q,(2) is the calibrated
spectrum at the sample position. (ii) If the standard has a known reflectance
spectrum &(A) and is known to reflect this evenly throughout 180" (27~sterawhere 6 is the sensor
dians), then R,(A) can be obtained by R,(A) = (8/n)RC(A),
MEASURING COLOUR PATTERN SPECTRA
33 1
acceptance angle (Fig. 6C). For both methods R,(I) will only be valid for the
specific geometry of the reflectance spectroradiometer. T h e geometry of the
reflectance spectroradiometer must be designed to match as closely as possible
the geometry of viewing conditions in nature (Fig. 6A-C).
Measurement of transmittance and veiling light spectra
After being reflected from a colour pattern element (patch) the light must get
to the eye of the viewer (Fig. 2). A colour pattern element or patch usually
subtends a small visual angle so the radiance rather than the irradiance from the
patch is required for Q(A,x ) . Over the distance x from colour pattern to eye,
some of the light beam will be absorbed, scattered and reflected by material in
the air or water, and this is often wavelength-dependent. Even in a vacuum the
light intensity per unit intersecting surface area decreases with 1/x2. As a result,
the light reaching the eye will be attenuated to an amount T ( I ,x ) which
depends upon both wavelength I and distance x. In clear air or water this can be
ignored, especially over short distances. But in a variety of other terrestrial and
aquatic conditions, light intensity declines approximately as
Q ( I ,x )
=
Q o ( I )c"")
(11)
where Qo(L)is the radiance of the patch at distance x = 0 and a ( I ) is the
wavelength specific beam attenuation coefficient (discussion and examples in
Duntley, 1946; Lythgoe, 1979; Kirk, 1983). If we normalize by setting Q o ( I )=
1.0 p~ m-'sP1 we obtain the transmittance function
T ( I ,x )
(12),
the fraction of light at a given wavelength I reaching a given distance x .
Examples for a(550 nm) = 0.108 (pure water) and 0.60 (coloured water) are
shown in Fig. 7A. Taking natural logs of both sides of equation (12), we obtain
= e-""'"'
In T ( I ,x ) = - x a ( I )
(13).
Therefore, for a given wavelength I , a plot of the natural log of the fraction of
light transmitted to distance x us. x will be linear, with a slope equal to the beam
attenuation coefficient for that wavelength (Fig. 7B).
In practice, instead of calculating transmittance and using equation (13), it is
simpler to measure the radiance of a known source at various distances, and
obtain equation (1 1). Taking natural logs of both sides of equation ( 1 I ) , we
obtain
)
In Q ( I ,x ) = In Q o ( I -xa(I)
Thus a ( I )can be estimated from the slope of the regression of ln(radiance) on x ;
in this case they-intercept ( x = 0) corresponds with the radiance at the patch
Qo(A).Because a ( I ) usually changes with wavelength, this regression must be
done at each measured I in the spectrum. Putting the resulting set (vector) of
beam attenuation coefficients a(L) into equation (12) yields a n estimate of the
transmittance spectrum T(1,x ) .
The relationship is not always linear, indicating that a(A) may sometimes
depend on x (Kirk, 1983). This happens, for example, if the scattering particle
density changed with depth. If a ( I ) depends upon distance, then a careful
J. A. ENDLER
332
S
S
Figure 6. Configurations for measuring the reflectance spectra. A, Beam method. B, Integrating
sphere method. C , Explanation of sensor field (6) and sample (4)acceptance angles. D, Diffuse
integrating sphere method. The beam method (A) simulates a single light source (as in direct
sunlight) while the sphere method (B) simulates diffuse light conditions. The hatched rectangle
represents a single colour pattern element (patch) of the animal or background, and the black
rectangle (S) represents a radiance sensor with a known small field angle (as in Fig. 5B). Arrows
represent the main light paths from the light source. L. In B and C, b is a baffle to maximize the
or sensor (6). The diffuse sphere method (D)
evenness of the diffuse light incident on the sample (4)
measures the total reflectance from all angles, and is not appropriate for studies of animal colours;
eyes receive only a small fraction of the total reflected light a t a narrow acceptance angle.
estimation of T(A,x ) will have to be made over the distances normally seen by
predators and conspecifics.
There are two ways to estimate T(A,x ) in the field, the telescope and tube
methods (Fig. 8 ) . The first is for air or water and the second is useful for
particularly dark or turbid water. Both use radiance sensors (Fig. 5B) rather
than irradiance sensors (Fig. 5A) because we wish to know how much light can
reach the eye from a colour pattern element rather than from the entire visual
field. Both use a battery-operated or regulated light source to provide a constant
radiant source, and the light is colminated by means of lenses and baffles to yield
a narrow parallel-sided beam of known radiance. I n both methods the radiance
of the light source is measured at various distances from the sensor and focussing
lenses. If the beam is properly colminated, the radiance of the light beam will
not decrease over the normal working distances between the source and sensor
unless the medium absorbs or scatters it. If the beam is not well colminated, then
a correction factor must be applied to the sensor output at each distance. The
factor may be obtained either from the inverse square law and the diverging
angle of the source, or empirically in clear air or water.
333
MEASURING COLOUR PATTERN SPECTRA
“.B,
asO.6
I
Distance ( m )
Figure 7. Transmittance for a fixed wavelength ( T ( x ) )as a function of distance ( x ) through water
(or air). A, Fraction oflight transmitted as a function of distance. B, Natural log of transmittance as
a function of distance. Examples are given for beam attenuation coefficients ( a ) of 0.108 (pure
water) and 0.60 (coloured water), for I = 550 nm. If transmittance follows T(x)= e-”
(equation (12)), then a plot of In T(x)us. Y will be linear, with a slope equal to -a, as in panel B.
In the telescope method (Fig. 8A) the light source (L) and sensor (S) are free
in the undisturbed medium (air or water). The sensor is fitted with a telescope so
that it can be carefully aimed at the light source, and so that only the source
beam is within the acceptance angle of the sensor. Fine scale alignment can be
obtained by moving the sensor in a plane perpendicular to the beam axis until
the sensor output is maximized. At each distance between source and sensor x ,
two measurements are made (at each wavelength), one with the light on ( Q L )
and one with the light off (Q,). This can be done by hand, by means of an
automatically operated shutter, or by electronically switching the light on and
off. The latter two methods allow one to obtain average values of Q, and Q L ,
minimizing the effects of random variations resulting from currents and other
factors.
When the source light is of the light reaching the sensor is the environmental
light (Q,). When the source is on the light reaching the sensor is the sum of Q,
and the attenuated spectrum of the source (Q,); Q L = Q,+ Q,. The difference
between the sensor readings with the light on and off yields the radiance of the
source at that distance and wavelength, Q, = QL- Q,. Plotting Q, as a function
of distance, or by means of equation (14) we can estimate a(A)and T (A,x ) .
334
J. A. ENDLER
Q, at various x and 1 can be a good estimate of the veiling light Qv(l,x ) . This
is only possible with a combination sensor-telescope with a small acceptance
angle which can be precisely aimed (such as the Li-Cor 1800-06). If this is not
possible, then Q, will be a mixture of veiling light, ambient light and, in
non-pelagic environments, background colours. I n the latter case Q, estimates
will be reasonable, as long as the sensor aim is precise and constant. T(1,x ) comes
from the difference between the sensor output with the light on and OR only
light from the source can contribute to this difference.
The tube method (Fig.8B) is useful in restricted aquatic habitats (such as
small streams) where the telescope method is impractical, or where water is
highly coloured or turbid. Readings are taken from water in a light-tight vertical
tube painted black on the inside. T h e sensor (S) is mounted a t the bottom and
the light source (L) is mounted in a sliding light-tight seal resting on the water
surface. Water is filled to various depths (each with the light source at the
surface) and a reading taken at each. Water can be quickly drained to a set of
standard depths by means of strategically placed holes in the side of the tube
(sealed by light-tight valves or plugs).
Sediment can settle out on the sensor during or between the readings, causing
an underestimation of transmittance. This may be minimized by means of a
battery-operated air pump of the sort manufactured for fishermen's live bait,
with a tube connected at the bottom of the tube adjacent to the sensor (i,
Fig. 8B). The air connection must not transmit light into the tube. A light-tight
tube is also provided to allow the air to exit ( 0 , Fig. 8B). The air flow must not
be so strong that it causes tiny bubbles to be suspended in the water. The pump
is turned off for the duration of the scan, then turned on again whilst the water
level is being changed.
Another kind of attenuation coefficient is more frequently measured in aquatic
systems, and this is the downward attenuation coefficient xd(1) (for detailed
discussion, see Kirk, 1983). It is measured in a similar way as the beam
attenuation coefficient a ( 1 ) , but the light source is the sun, cannot be turned off,
and the sensor has an irradiance rather than a radiance design (Fig. 5A). Thus
Kd(A)summarizes the attenuation of the ambient light ( A ( 1 ) ) with water depth
rather than the attenuation of a beam of light (radiance) with distance. a ( A ) and
Kd(l)are obviously related to each other in that both depend upon the
scattering, reflectance and absorbance properties of water and particulate
matter, but the relationship is not necessarily linear or simple. Therefore, except
perhaps in the clearest water in full sunlight, &(A) and irradiance sensors should
not be used to estimate T(A,x ) . However, &(A) is useful in predicting the
ambient light ( A ( A ) )at depths at which an animal is actually found, if it is
impractical or expensive to measure A ( A ) directly at those depths.
APPRAISING COLOUR
It is useful to be able to refer to, distinguish and compare different colours in
an unambiguous way, especially when investigating the effects of different
habitats and ambient lighting conditions on colour patterns. This requires a
colour classification. A colour classification is also required to obtain the colour
frequency distribution, which is needed to measure the degree of crypsis or
MEASURING COLOUR PATTERN SPECTRA
335
0
c- L
S
a(L,
Figure 8. Methods of estimating transmittance T(1,x ) and veiling light
x ) in the field.
A, lelescope method (air or water). B, Tube method (water). L: Standardized and regulated
radiant light source with lenses and baffles to yield a collimated-beam of light. In B, the light source
(L) floats on the water surface. T: Telescope/aiming device. S: Radiance light sensor with lenses to
accept the collimated beam from the source L. P: Air pump. I: Light-tight air inlet to minimize
settling of sediment between scans. 0:Light-tight air outlet.
conspicuousness of an animal by comparing its colour pattern parameters with
those of the background (Endler, 1984; Sweet, 1985).
Standard methods
Spectra can be converted to Munsell colour codes of hue, chroma and value
(Munsell, 1976; Li-Cor, 1982; Wyszecki & Stiles, 1982). The Munsell system
classifies spectra into groups with approximately equal steps in degree of
perceived hue, chroma and value (Munsell, 1976; Wyszecki & Stiles, 1982). But
this classification is based upon human perception, so these equal steps may bear
no relationship to how animals perceive differences among the same spectra. A
classification based directly upon the spectra rather than human perception will
therefore be a better starting point in studies of animal colour patterns.
One way to use all the information in spectra is to enter the data of each
spectrum into a principal component analysis (Karson, 1982) or multidimensional scaling (Indow & Uchizono, 1960; Indow & Kanazawa, 1960;
Iis a variable and each spectrum
Backhaus et al., 1987) in which each measured ,
is an observation. T h e eigenvectors can then be used to give scores to each
spectrum which maximize the variance among spectra (Karson, 1982). In order
to eliminate brightness and just examine differences in colour (spectral shape),
336
J. A. ENDLER
one of two methods can be used: (i) multiply each Q(A,x) by a constant for that
spectra which gives all spectra in the analysis the same brightness QTm,where
QTmis the mean QT of the individual spectra; (ii) remove brightness from the
principal components, by means of shear coefficients or other methods. Shear
coefficients are derived from a regression of each spectrum’s QTon the principal
components (Humphries et al., 1981), (i) is simpler, but in either case, a plot of
one principal component us. another will reveal clusters of spectra with similar
shapes; the greater the distance between the spectra in principal component
space, the more different the spectra. Because spectra are relatively simple in
shape, for a wide variety of spectra the first four principal components usually
explain 95% or more of the variance (Endler, unpublished). For example, in an
analysis of 163 equally spaced colours of similar value ( QT)in the Munsell Book
of Color (Munsell, 1976), the first four components explained 55.7, 25.4, 13.8
and 2.8% of the variance, respectively. I n another analysis of 20 miscellaneous
colours of animals and plants, the percentages were 59.0, 24.5, 11.0 and 2.9%.
Very similar results were obtained with other data sets (Endler, unpublished).
Although the principal component method is excellent for using all of the data
in spectra, the results are not comparable among habitats. Although there are
usually only 3 or 4 eigenvectors, they do not correspond to hue, chroma or
brightness, but rather to various aspects of the average geometrical shape of the
spectra, and this depends strongly upon the shapes of spectra actually present in
the habitat. Adding or subtracting only a few spectra to the data can radically
change the eigenvectors (Karson, 1982; Indow & Uchizono, 1960; Indow &
Kanazawa, 1960; Endler, unpublished), so studies of different habitats, or even
different places within habitats, will not be comparable (Endler, unpublished).
In order to provide a standardized classification of colours, it would be better to
devise a system which captures average geometric properties of the shapes of
spectra, but does not depend upon the particular set of spectra being analysed.
There are two approaches to making classifications which are independent of the
spectra analysed: the species-specific or ‘chromaticity’ method, and the segment
classification method.
If a species’ behaviour or neurobiology is well known, then a classification can
be derived from the physical and neurobiological properties of photoreceptor
and associated cells in the retina and brain, or on the basis of inferred response of
these circuits from detailed behavioural experiments. The classification is based
upon a map of colour space which is based upon the relative outputs of the
circuits; the maps are called chromaticity diagrams. Any spectrum will fall on a
particular point in the colour space, and the difference between any two points
(spectra) is correlated with perceived differences in colours. So far this has only
been done for humans (summarized in Wyzsecki & Stiles, 1982) and bees
(Backhaus & Menzel, 1987; Backhaus etal., 1987; Menzel & Backhaus, 1989).
The chromaticity method is not perfect. For example, the Munsell system does
not map onto human chromaticity diagrams without some distortion, and even
the revised CIE human chromaticity diagram does not have the desirable
property of equal perceived differences in colour (hue and chroma) mapping
onto equal distances throughout the entire chromaticity diagram (Wyzsecki &
Stiles, 1982). The chromaticity method also has the major disadvantage of
requiring extensive physiological and behavioural data for every species in which
it is used; this is impractical for the majority of species, hence impractical for
MEASURING COLOUR PATTERN SPECTRA
331
most evolutionary and ecological studies of colour patterns.
The segment classification method (to be described below) is a very simple
method and depends purely upon physical properties of light. It also attempts to
capture some general properties of visual systems without being specific to any
one of them. T h e segment classification method should not be used if the
chromaticity method can be used instead. At the very least it will be useful in
organizing spectral data, and setting up hypotheses about the diversity and
similarities of colour patterns when specific visual data are not available. The
segment classification method is better than the Munsell system for two reasons.
(1) Because it is not specific to any visual system, it will remind the user that it is
only an approximation to the perceptual differences between the spectra
measured. The use of the Munsell system is seductive since it matches our own
perceptions so well, making us tend to forget that it is an approximation to
animal systems, and often a very bad one if the photoreceptors of the animals are
very different from ours. (2) It is far simpler to use than the Munsell system;
Munsell scores are calculated from spectra using empirically determined mathematical transformations which are specific to the CIE standard (Human)
observer and the Munsell system, whereas the segment classification requires
only simple addition and subtraction of segments of the spectrum.
Segment classiJication
The classification method presented here is independent of the specific properties of any particular visual system, but attempts to capture some properties
common to most vertebrate and invertebrate systems. I t is based upon the
magnitude of differences in relative intensity among four equally spaced
segments of the spectrum of interest. It has two justifications:
First, in many visual systems the strength of colour (as opposed to brightness)
signals is proportional to the differences in photon fluxes between different
segments of the spectrum; this is chroma. I n a variety of vertebrates and
invertebrates there are as many as three photoreceptor types, each sensitive to a
different portion of the spectrum (Levine & MacNichol, 1979; Lythgoe, 1979;
Jacobs, 198 1 ; Goldsmith & Bernard, 1974; Laughlin, 198 1; Kevan, 1983;
Menzel & Backhaus, 1989). For example, in humans the absorbance maxima of
the three cones are 450, 530 and 560 nm (Hurvich, 1981), in goldfish they are
455, 532 and 623 nm (Wheeler, 1982), in a moth (Deilephila elpenor) the peaks of
the three photopigments are 345, 440 and 520 nm (Schwemer & Paulsen, 1973),
in Heliconius butterflies 350, 460 and 550 nm, and in honeybees 350, 440 and
540 nm (Menzel & Blakers, 1976). Call the three receptor types shorl, medium and
long. Where there are two or more of these ‘channels’, it is common in both
vertebrate and invertebrate visual systems for differences to be taken between
pairs of these channels; this is called ‘opponency’ or ‘lateral inhibition’ (Dowling,
1987; Gouras & Zrenner, 1981; Hurvich, 1981; Jacobs, 1981; Wheeler, 1982;
Wyszecki & Stiles, 1982; Yager, 1974; Mazokhin-Porshnyakov, 1969; Ali, 1984;
Laughlin, 1981; Menzel & Backhaus, 1989). The two most common differences
between receptor signals resulting from the ‘wiring’ of visual systems are
LM = (long-medium) and MS = (medium-short); the associated signals can be
referred to as the chromatic response functions (Hurvich, 198 1 : chapter 5).
There are some cells in the retina or brain of many different animals which
J. A. ENDLER
338
I.
C
B
G
0
b
0
U
0.
. '
..
....
* *
,
0.
400
500
600
700
Wavelength ( n m )
Figure 9. The segment classification method. The spectrum is divided into four equally spaced (by
A) segments, labelled B, G, Y and R. For each spectrum, the total brightness of each of the four
segments is calculated using equation (6), and these are divided by the grand total & ( x ) calculated
from equation (4). In this example the fraction of photons in segments B, G, Y and R are 0.0030,
0.0857, 0.41 1 1 and 0.5022, respectively, and this is independent of brightness (spectra a, b and c
yield identical results). Taking differences, LM = R-G = 0.4144 and MS = 2--B = 0.4081. The
chroma is C = ,,/(LiZp+Mg) = 0.5817.
respond to the positive parts of these functions and others which respond to the
negative parts. The net effect in humans (Hurvich, 1981), is four sensations: red
(positive L M ) , green (negative L M ) , yellow (positive M S ) and blue (negative
M S ) , and something similar may occur in teleost fishes (Yager, 1974; Burkhardt
& Hassin, 1983) and honeybees (Menzel & Backhaus, 1989). These four signals
divide the spectrum into segments, though not of equal lengths (Hurvich, 1981).
The segments involved in opponency pairs alternate rather than being adjacent.
This suggests that a classification can be made on the basis of differences between
a few segments of the spectrum. The proposed classification is based upon four
segments, and will clearly be inadequate only for species with more than three
receptor types (birds, some fish and crustaceans: Jacobs, 1981; Chen &
Goldsmith, 1986; Jane & Bowmaker, 1988; Levine & MacNichol, 1979;
Downing etal., 1986; Cronin & Marshall, 1989).
Second, and as mentioned in the previous section, a principal component
as a
analysis can be performed using the intensity at each wavelength (Q(1))
MEASURING COLOUR PATTERN SPECTRA
339
R
t
G
Figure 10. The ‘colour space’ of the segment classification; any spectrum falls within the square. The
horizontal axis is MS = Y-B, and ranges from - 1.0 through 1.0. The vertical axis is L M = R-G
and also ranges from - I .O through 1 .O. The axes have been labelled R, 1; G and B because positive
values of LM or MS indicate a relative excess of R or ?^over G or B, and vice versa. Most cutoff or
monotonically increasing or decreasing spectra are found in the shaded portion ( C T ) ; examples are
curves 1-4 in Fig. 4. Spectra with a peak are found in the unshaded region PK, and spectra with a
trough are found in region T R ; examples are curves 5-9, and 10-1 1 in Fig. 4, respectively; see also
Fig. 11.
variable and each spectrum { Q(1)
for all 1) as an observation. When this is done
on many different natural colour spectra, the analysis usually results in only a
few principal components-three or four explain 95% or more of the variance
among spectra (see previous section). The shapes of the resulting eigenvectors
are similar in shape and in numbers to the chromatic response functions,
although they have a less abrupt transition between the spectrum segments
(Endler, unpublished). T h e segment classification takes differences between
segments; this is mathematically equivalent to using step functions as chromatic
response functions. It is also equivalent to making step functions out of the
eigenvectors of a principal component analysis of all colours. The net effect is
essentially that of generalized chromatic response functions, and also fixed principal components for any combination of spectra. Thus, dividing up the spectrum into four segments is likely to do a good job of distinguishing as many
colours as possible as well as capturing the essence of signal processing in many
different visual systems. This method also has the merit of being extremely
simple.
The method is as follows: T h e spectral range of interest is divided into four
equal wavelength intervals; call them B, G, Y and R (Fig. 9). T h e segments
could just as easily have been called A, B, C and D, but the colour mnemonics
(for Blue, Green, Yellow and Red) make the method more readily understood.
J. A. ENDLER
340
(The mnemonics remind us that, in the human visual spectral range of
400-700 nm, a spectrum having light only in one of the segments B, G, Y and R
will appear approximately in that colour.) T h e example in Fig. 9 uses the
vertebrate spectral range (400-700 nm) but the same method could be used for
the arthropod spectrum, or even a combined spectrum of 300-700 nm (in which
case calling the segments A, B, C and D makes more sense). T h e total brightness
QT,and the brightness in each segment Qb,Qg,Q, and Q,, are calculated using
equations (4) and (6). Next, the relative brightness in each segment is calculated:
B = Q,,/QT, G 3 Q$QT, Y = Q,/QT, and R = Qr/QT; this separates colour
from brightness. For example, the three spectra in Fig. 9 differ only in brightness
and all have the same B , G, Y and R.
Next, two segment differences or 'opponents' are calculated:
L M = R-G
(15a)
and
MS= Y-B
(15b)
We can plot L M us. MS to form the segment colour space shown in Fig. 10. The
position of any spectrum in this space is determined by its colour (shape).
Because B+ G + Y+ R = 1.0, all spectra have to fall within the square outline of
Fig. 10, which is determined by the lines LM = 1 - MS, L M = - 1 MS, LM =
- 1 - MS, and LM = 1 MS. As mentioned earlier, naturally occurring spectra
usually have one of three shapes: (i) cutofs: monotonically increasing or
decreasing, or an increasing or decreasing step (curves 1-4, Fig. 4); (ii) peaks:
having a wavelength with a maximum photon flux (curves 5-9, Fig. 4);
(iii) troughs: having a wavelength with a minimum photon flux (curves 10-1 1,
Fig. 4). Cutoff spectra are found in the shaded portion of Fig. 10 (CT); they are
bounded by the edge of the square and the lines L M = ( - 1 MS)/3, MS = 0,
L M = MS, LM = ( - 1 -MS)/3; L M = - 1 +3MS, L M = 0, L M = MS, and
L M = 1 - 3MS. The lower-left shaded region contains spectra with decreasing
cutoffs (violets, blues and blue-greens) . The upper-right shaded region contains
spectra with increasing cutoffs (yellows, oranges and reds). The unshaded region
marked PK (Fig. 10) contains peaks (some blues, greens and some yellows) while
the other unshaded region ( T R ) contains troughs (purples, some reddish- and
violet-purples) .
Since the monotonic colours roughly fall on a line parallel to L M = MS,
which is 45" to the colour space of Fig. 10, we could rotate the entire space by
45" to make the horizontal axis indicate monotonic spectra and the vertical axis
indicate peaks or troughs. Converting to polar coordinates, rotating by 45",
and converting back to Cartesian coordinates indicates that the two new axes
would be c u t o f = 0.7071(LM+MS) = 0.7071(R+ T)-(G+B), and trough =
0.7071(LM-MS) = 0.7071[(R+B)-(G+ 271. Thus the geometry of the
segment classification is not specific to the particular pattern of opponency
chosen in equations ( 15). This suggests that the segment classification method
may be relatively insensitive to differences in neural 'wiring' among species and
is a n additional justification for its use in the absence of detailed neurobiological
or behavioural data.
Spectrally 'pure' colours (photons within only a narrow ;Z range) or colours
with photons wholly within one of the spectral segments B, G, Y and R (Fig. 9)
+
+
+
34 1
MEASURING COLOUR PATTERN SPECTRA
Figure 11. Sample spectra in the colour space of Fig. 9. Large dots and numbers are for the colour
spectra in Fig. 3. Small dots at centre: reflectance spectra including glare from the colours in Fig. 12
(see text).
will fall on either of the LM or MS axes. Spectra with photons within only two of
the spectral segments will fall on the edge of the square. Achromatic spectra
(black, neutral greys or white) will fall at the origin (centre of Fig. 10). Spectra
differing only in intensity (‘brightness’) will fall on the same point. The more
broadly photons are distributed in the spectrum the smaller the values of LA4
and MS. Therefore, two properties of colour can be measured for a spectrum
colour space or equations (15). Chroma (‘saturation’) is estimated by
C
=
J
m
.
(16)
This is the Euclidean distance (Sneath & Sokal, 1973) from the origin of colour
space to the spectrum. A single number for hue can be obtained from
H
= arc Sin
( M S / C )= arc Cos (LMIC)
(171,
measuring the angle H clockwise from R. This is similar but not identical to the
Munsell system (Munsell, 1976) and a suggested colour space of Hurvich (1981:
chapter 7). I t differs from them in the calculation of C and H and in that it is not
dependent upon human colour vision. One could also use a plot of C us. H as a
different kind of colour space, but this method will not be explored in this paper.
Figure 11 (large dots) shows the position of the reflectance spectra of Fig. 4
plotted in the colour space of Fig. 10. Note the change in position ( H ) in colour
space (Fig. 11) with Munsell hue and spectral shape (Fig. 4),and the change in
distance C from the centre of colour space (Fig. 1 1 ) with Munsell chroma
(Fig. 4).Figure 12 shows the positions in colour space of the reflectance spectra
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J. A. ENDLER
Figure 12. 164 colours from the Munsell Book of Color plotted in the colour space of Fig. 10. Letters
(R, YR, etc.) are the Munsell hue letter codes. Radiating lines connect spectra of constant Munsell
hue; hue numbers are 2.5, 5.0, 7.5 and 10.0, going clockwise within each hue letter code. Circular
lines connect spectra ofconstant Munsell chroma; from the centre outward, chromas are 2,6, 10, 12,
14, 16. (Paint pigment chemistry restricts chromas above 12 to the red end of the spectrum.)
of 164 Munsell colour standards (Munsell, 1976), determined using the beam
method (Fig. 6A). The radiating lines connect colours of equal Munsell hue and
the circular lines connect colours of equal Munsell chroma. The pattern is not as
even as it is in human chromaticity coordinates (Wyszecki & Stiles, 1982), a
colour space based upon human perception. This distortion results from three
factors: (i) our differential sensitivity to some colours (where hue lines are
denser), (ii) because the spectrum is divided evenly by the segment system
(Fig. 9), but unequally by the human eye (our cones are not equally spaced and
do not have mutually exclusive spectral absorbances; Hurvich, 1981), and
(iii) because in this case the reflectance spectra were not multiplied by one of the
CIE standard illuminants (Wyszecki & Stiles, 1982). Note that the Munsell
blues (B, Fig. 12) do not fall on the blue line; they are not monotonic (curve 9,
Fig. 4).Some animal blues are close to monotonic, and fall on or near the blue
line, for instance the blues of guppies (Endler, in press). It might therefore be
better to call the left half of the MS axis the violet rather than the blue line, but,
unfortunately, to some, ‘violet’ means ‘purple’, a completely different spectrum.
A similar area of segment colour space is occupied by the colours in the
Naturalist’s Colour Guide (Smithe, 1974a), but the colours are more clustered
since they are meant only to match typical bird colours.
In measuring any natural or artificial colour it is necessary to avoid glare or
surface reflections. Glare acts just like veiling light and reduces chroma
(desaturates colours). T h e effect can be demonstrated by adjusting the angle of
MEASURING COLOUR PATTERN SPECTRA
343
0.75
C
..-. .
.S
90
..
1
..
0.25.
Figure 13. Munsell colours (see Fig. 12) with respect to brightness (Q,) and chroma (C) measured
by equations (4) and (17). 0:Munsell chroma 2. 0:
6. 0 : 10. A:12.
14. .
:
16.
+:
the Munsell (1976) colours so that their glossy surface reflects directly into the
sensor during reflectance measurement. This was done with the colours shown in
Fig. 12, and the result is shown in Fig. 11. The hue relationships are the same,
but the entire pattern is reduced to a cloud of points within a small region of low
chroma. There was also a small blue-green shift, suggesting that the glossy
surface was not spectrally neutral.
Additional information on the similarities and differences among colour
spectra can be obtained by a plot of the total brightness QT us. chroma C; this
adds another dimension to the colour space. Figure 13 shows this for the Munsell
colours of Fig. 12. There is not much spread in brightness QT because the colours
scanned were restricted to Munsell values 5-7. I n general, chroma C
(equation (16)) is correlated with Munsell chroma, and brightness Qr is correlated with Munsell value, but spectra with greater brightness tend also to have
less chroma (Fig. 13). This is probably a result of the properties of paint
pigments.
In summary, the segment classification method has the merit of being independent of human vision while having some general properties of all visual
systems. It assigns colour spectra to positions in a colour space with dimensions
H (hue, equation ( 1 7 ) ) , C (chroma, equation (16)), and QT (brightness,
equation (4)).Similar colours will cluster together whilst dissimilar colours will
be further apart to a degree related to their differences. This classification
scheme is meant only to be used for species in which little or nothing is known
about the colour vision of the species concerned, because the geometric relationships between colours in the segment classification space may not be linearly
related to the perceptual distances between the same colours for animals. If
344
J. A. ENDLER
enough is known about the species's colour vision, then species-specific colour
spaces can be constructed. A superb example is that of Backhaus & Menzel
(1987) for honeybees.
Comparing colours
In studies of the visibility or crypsis of animal colour patterns we do not
merely wish to assign the colours to positions in the colour space, we also wish to
compare them. The positions of all of the colours of an animal and its
backgrounds can be plotted on the same graph, and the mean positions
compared. The closer the mean positions of animal and background, the more
cryptic the animal on that background. We may also wish to compare the
colours of two or more species (as in studies of mimicry), individuals (as in
ecological genetics), or the same individual under different lighting conditions.
In this case, the closer the mean positions of the patterns, the more similar are
the animals' colours.
The difference between any two colours (spectra) can be measured as the
Euclidean distance (Sneath & Sokal, 1973) between their H , C and QT by
where the subscripts a and b refer to animal and background (or two different
individuals), respectively. This measure of colour dissimilarity is not necessarily
linearly related to perceptual dissimilarity in humans (Indow & Kanazawa,
1960; Indow & Uchizono, 1960; Wyszecki & Stiles, 1983) or honeybees
(Backhaus & Menzel, 1987). But it is better than nothing when we are ignorant
of the visual abilities of the species concerned.
In order to compare entire animal and background colour patterns rather
than pairs of patches, D can be calculated between all possible pairs of animal
and background patches. This distribution is then used to obtain a mean b,
standard deviations sD, and standard error seD of D. b estimates the average
difference between all of the animal and all of the background patch spectra,
hence is a measure of overall conspicuousness. For example, a colour pattern
with green patches of only one spectral shape but varying chroma seen against
a background with green patches with spectra of differing shapes (varying H and
C) will have a larger b than another pattern including both shades of green. sDis
a measure of the range of differences among the patches. Two patterns may have
the same D but the first may have only slight variation in D (for example
variations on green) while the second has larger variations (e.g. yellows as well as
greens). Because the range of colours of animals and backgrounds varies
differently in different habitats, it would be useful to have a measure of the
average difference between animal and background corrected for the range of
differences. One measure is
This measure of conspicuousness will be larger for greater b and smaller se,. It
has one unfortunate property, and that is, if colours are equally different within
the two colour patterns, T is greater for more colours. So it is only a reasonable
MEASURING COLOUR PATTERN SPECTRA
345
measure when comparing colour patterns which do not differ greatly in the
number of colours. D is not necessarily normally distributed, so i t is invalid to
compare T to the t distribution as a statistical test of minimum conspicuousness.
Instead, this test should be made by means of a canonical correlation analysis of
all the patches in the animal and background. Canonical correlation analysis
finds groups of X variables (Hb,C, and QTb)which together are correlated with
groups of Y variables (Ha:C,, and Q ). If all or most of these pairs of groups are
T’!
highly correlated, the animal is cryptic, if not, then the animal is conspicuous to
a degree related to the lack of a positive canonical correlation (i.e. zero or
negative) of the entire data set (Karson, 1982; Seal, 1964).
A disadvantage of equations ( 18) and (19), and canonical correlation of H , C
and QT, is that they do not account for the skewed frequency distribution of
colours in natural colour patterns. I n natural habitats colours are not normally
or evenly distributed; greens, yellows, reds, browns, and greys predominate
(Endler, 1984). There are three ways to allow for this: (i) Do the calculations for
equations ( 1 7) and (19), but weigh each colour by the area of that colour within
the animal and background. This will not be practical if some colours are not
found in both animal and background (as in Endler, 1984). (ii) Calculate
weighted mean Ha, Hn, C,, q,QTaand QTbseparately for animal and background
and use these means in equation (18) as an overall measure of conspicuousness.
The disadvantage of (ii) is that it cannot account for the variation of H , C and
(& among patches within the animal and background. (iii) Perform a canonical
correlation analysis as described above, but include duplicate spectra in proportion to their frequencies in the animal and background; this is the best method.
This general problem needs more research.
Although the segment classification is excellent as a standard method of
comparing colours, it may lose information about spectra which change rapidly
within the four segments of Fig. 9; ‘metamerism’ is possible. The result is that
some spectra which have the same position in colour space will in fact have
different spectra. This is most likely when the overall range of animal and
background colours only occupies a small region of colour space. I n this case,
calculate the difference between each wavelength interval of the spectrum of
animal and background rather than differences among the four segments. The
simplest method is to calculate a Euclidean distance between any two spectra as
where the subscripts a and b refer to animal and background, and the summation is done for each of all wavelengths A in the spectrum visible to conspecifics or
predators, at a particular viewing distance x . D,will be larger for spectra with
more divergent shapes (colours). D,will also be greater for two spectra with the
same shape but more different brightnesses ( Q T ) , as in Fig. 9. In order to make
D, independent of differences in QT, multiply Q ( A , x ) by a constant for that
spectra which gives both !&(A, x ) and &,(A, x ) the same brightness Q,,,,,, where
is the mean of QTa and QTb. This rescaling makes D, proportional to
differences in colour rather than to both brightness and colour. I n order to test
for statistical differences between spectra, either a polynomial regression, or a
polynomial regression with orthogonal polynomials (Snedecor & Cochran, 1967)
should be done. The polynomial coefficients of a given spectrum describe its
shape. The more different two spectra are, the more different their polynomial
a.,,,
346
J. A. ENDLER
coefficients will be. An analysis of covariance will test whether the coefficients
differ significantly between animal and background, but this will only work for
pairwise comparisons of colours. To compare the spectra of the entire background and the entire animal, the canonical correlation analysis can be used.
The method is similar to that outlined earlier, but instead of using only the
variables H , C and QT, the entire spectrum of each patch is used. T h e disadvantage of using the entire spectrum is that a large sample size is required for
the analysis to be reliable; the sample size must be at least as large as the number
of points in the spectrum (Karson, 1982).
The results of statistical tests for differences between spectra must be used with
caution because there is no necessary reason to assume that a statistically
significant difference between animal and background is necessarily distinguishable by an animal and vice versa. I n addition, humans, at least, can distinguish
slight differences among spectra (Wyszecki & Stiles, 1982) which may not be
statistically significant. However, D, T or D,which are barely significant can
serve as arbitrary thresholds to separate cryptic from conspicuous colour
patterns, and their magnitudes used to estimate the degree of conspicuousness.
More work needs to be done on this problem.
Assessing the conspicuousness of colour patterns
A subjective ranking of conspicuousness is often used in the literature (Baker &
Parker, 1979; Hamilton & Zuk, 1982; Read, 1987). The word often used in this
context is ‘brightness’, but the meaning intended is clearly conspicuousness rather
than brightness in the sense of Q,. An examination of the published ‘brightness’
methods suggests that, although meanings and methods vary, all are proportional to a combination of H , C and QTrather than just QT.I n addition, most of
them are also dependent upon the degree of differences in colour and QT
brightness between patches within an animal’s colour pattern (e.g. Baker & Parker,
1979: 79). None of these methods take the appropriate visual background into
account, though some methods (Chai, 1986) have been tested using predators
and natural backgrounds. For brevity I will refer to these within-pattern
differences as contrast. O n a given visual background, increasing colour and
brightness contrast will increase the conspicuousness of colour patterns
(Wyszecki & Stiles, 1982).
The segment classification allows us to quantify conspicuousness in the sense of
colour and brightness contrast. First, calculate the parameters H , C and QTfor
each patch within the animal’s colour pattern. Then calculate their means,
standard deviations and coefficients of variation (CV = s.d./mean, Snedecor &
Cochran, 1967), weighted by the total areas of the patches on the animal. The
means give an estimate of the hue, chroma and brightness of the entire animal,
and these may be important if the viewing distance is sufficiently far away that a
predator or conspecific’s visual acuity angle is larger than the patch sizes
(Endler, 1978). The coefficients of variation of the three parameters are the
estimates of hue, chroma and brightness contrast. The greater the variation
among patches relative to the mean, the more within-pattern contrast there will
be. Provided the within-background contrast is not greater than the withinanimal contrast, the greater the within-animal contrast, the more conspicuous it
will be, but if both have high contrast (as in parrots), the animal will be cryptic.
MEASURING COLOUR PATTERN SPECTRA
347
In order to take the background contrast into consideration, both the means and
CVs of H , C and QT should be used in a n analysis similar to the analysis of patch
size and colour class frequency (Ender, 1984). I n fact the best measures of crypsis
and conspicuousness will incorporate all aspects of colour pattern, rather than
just colour, brightness or patch size distributions alone. Measures of crypsis or
conspicuousness should be tested directly by behavioural measures and estimates
of fitness consequences of colour pattern variation. An example would be a
multiple regression of (say) mating success on the means and variances of H , C,
QT, and patch size relative to those of the background.
I n summary, these methods provide the first step in addressing the conspicuousness or crypticity of colour patterns as perceived by animals. If these
methods suggest that a colour pattern is conspicuous to a predator or conspecific,
then the colour pattern probably is conspicuous. However, if a colour pattern is
predicted to be cryptic, in some cases specific properties of the visual systems of
some animals may make the colour pattern conspicuous. For example if the
animal has more than three receptor types, or if its ‘opponencies’ involve very
different combinations ofspectral segments from those in equations ( 15) and Fig. 9,
the animal may be able to detect differences which do not show in the colour
space of Figs 10 and 13. If it is practical to experimentally investigate animal
colour vision, then detailed models of colour perception and discrimination can
be made (as in humans: Hurvich, 1981; Wyszecki & Stiles, 1983; fish: Yager,
1974; and honeybees: Backhaus & Menzel, 1987; Backhaus et al., 1987; Menzel
& Backhaus, 1989), and these models used to calculate indices of crypsis or
conspicuousness in the same way they were calculated for the colour space
described in this paper. For species in which it is impractical to do neurophysiology and psychophysical experiments, or for species for which such experiments
have not yet been done, the methods described in this paper will serve as a first
approximation to the degree of crypsis.
CONCLUSIONS
With the recent development of field portable and relatively inexpensive
spectroradiometers it is now possible to quantify colour and colour patterns more
precisely, and these methods can be used in both terrestrial and aquatic habitats.
I t is no longer necessary to rely on subjective assessments of colour and
conspicuousness, nor on assessments which rely upon human vision. This is
important because the vision of many animals is different from that of ours, to
say nothing of within-population variation in human colour vision. It is now
practical to measure the colour spectrum of pattern elements (patches) of
animals and their visual backgrounds for the conditions under which patch
spectra reach the conspecific’s, predator’s or prey’s eyes, and the resulting
parameters of colour and colour patterns precisely specified.
A patch’s colour spectrum is dependent not only upon its reflectance spectrum, but also upon the ambient light spectrum, the transmission properties of
air or water and the veiling light spectrum. These factors change with time of
day, weather, seasons and microhabitat. If the conditions during intraspecific
communication are not the same as during predation, then the colour spectrum
of an animal can vary with function, even if it does not have adjustable
chromatophores like a chameleon or cichlid. T h e colours of animals and visual
348
J. A. ENDLER
backgrounds are extremely context-dependent, and so must be measured at the
times and places at which the colour patterns are used in crypsis or signalling to
conspecifics or predators.
‘Metamerism’ is a phenomenon in which several different colour spectra are
perceived as the same colour, and is a result of the spectral sensitivity of the
viewer’s eye, as well as the ‘wiring’ in the eye and brain. Because different
animals differ not only in spectral sensitivity, but also in visual system ‘wiring’, it
is likely that spectra which are metameric to some species are not metameric to
others, and vice versa. This is so well known in humans that different patterns of
metamerism are used to distinguish different kinds of ‘abnormal’ human colour
vision. Metamerism may actually be used in crypsis if lighting conditions and
vision are different during intraspecific communication and predation. For
example, guppies (Poecilia reticdata) do most of their visual display mode of
courtship under different lighting and times than maximum predation (Endler,
1987, in press). The different lighting conditions make it possible that some pairs
of colour pattern elements are metameric during predation conditions, but
perceptibly different during courtship. The major predator of guppies, Crenicichla
alta (a cichlid, Endler, 1978, 1983), has a different set of cone pigments from
guppies (Levine & MacNichol, 1979; Endler, 1986), making differential metamerism even more likely.
At first consideration, the fact that the colours of animals and backgrounds
shift with environmental conditions is a nuisance because it makes proper data
collection as well as interpretation more complex. But actually it makes the study
of animal colour patterns more interesting. Because the different functions of
colouration may act at different times of day, seasons and microhabitats, hence
under different environmental conditions, this opens up the essentially unexplored possibility that colour combinations evolve which can perform multiple
functions without the expense of innervated chromatophores. I t may also now be
possible to determine the conditions under which ‘plastic’ us. fixed chromatophores should evolve. Studies of the coevolution with colour patterns of courtship, predation timing and microhabitat choice will also be more practical with
precise measurements of animal colour patterns and backgrounds under varying
natural conditions.
ACKNOWLEDGEMENTS
I thank Rich King, John Kirk, Cathy Langtimm, Kevin Long, John Lythgoe,
Margaret McFall-Ngai, Jane Rienks, Victor Rush, Ray Smith, and an anonymous reviewer for valuable conversations, help, and valuable comments on the
manuscript. I gratefully acknowledge the financial support of the John Simon
Guggenheim Memorial Foundation, The Hasselblad Foundation, and the
National Science Foundation (BSR 86-14776).
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APPENDIX: SUMMARY OF SYMBOLS USED
The use of symbolism in the literature is variable. T h e symbols of optics
(Tenquist et al., 1970) and optical oceanography (Morel & Smith, 1982) were
modified to emphasize quantum units, and to avoid ambiguities such as c being
used for the speed of light (physics convention), the beam attenuation coefficient
(Morel & Smith, 1982) and chroma (colormetry). The equivalent optical
oceanography symbols are given in parenthesis (M&S).
Beam attenuation coefficient (c in M&S).
Wavelength-specific beam attenuation coefficient (equations 1 1,
12).
Energy of a photon.
Wavelength of light, nm (1 nm = lo-' m).
MicroEinstein = 1.0 p~ = 6.02257 x l O I 7 photons.
MicroMole = 1.0 pE = 6.02257 x I O l 7 photons.
Frequency of light = L/c.
Ambient light spectrum, measured in quantum flux ( p m-'s-')
~
(E
or Ed in M&S, but ambiguous for quantum flux or energy units).
Ambient light spectrum striking a surface which is not parallel to
the measurement axis (equation 10).
Fraction of QT in the shortest wavelength segment in the segment
classification (equation 15, Fig. 9).
Chroma, standardized difference in brightness among spectral
segments (equation 7 ) , or geometric distance between a colour and
the neutral point in the segment classification space (equation 16).
Chroma of a patch including the effects of veiling light.
Velocity of light 2.99792 x lo8m s-'.
Geometric difference between any two colours in terms of H , C, QT
(equation 18).
Geometric difference between any two colours in terms of Q(L,x)
(equation 20).
Energy spectrum (W m-' or W m-'sr-'), not appropriate for
studies of animal colours ( E or I; in M&S).
Total energy in a spectrum, integrated over a given spectral range,
ET = J E(L)dL.
Fraction of QT in the second shortest wavelength segment in the
segment classification (equation 15, Fig. 9).
Planck's constant 6.62554 x
Hue measure in the segment classification (equation 1 7 ) .
Long-medium wavelength 'opponent' in segment classification
(equation 15a).
Medium-short wavelength 'opponent' in segment classification
(equation 15b).
352
Q
Q(4
QT
Y
J. A. ENDLER
Refers to quantum flux, PM m-'s-' or pE m-'s-I ( L or E in M&S,
but ambiguous about energy or photons).
Quantum spectrum, distribution of quantum flux at each wavelength 1.
Total quantum flux in a spectrum, integrated over the spectral
range of the viewing animal, QT= Q(1)dA. A measure of brightness (equations 4 or 5 ) .
(also Qb, (&, Qy,Q,) Brightness (total quantum flux) of a segment
of a spectrum smaller than the animal's spectral range
(equation 6);
d QT, Q,, < QT.
Quantum radiance spectrum from a patch at distance 0.0
(equation 11).
Quantum spectrum of veiling light (equation 8 ) .
Quantum spectrum of a patch at distance x from the patch
(equation 3 ) .
Quantum spectrum of a patch, including the effects of veiling light.
Total quantum flux at distance x from colour pattern element
(patch).
Fraction of QTin longest wavelength segment in segment classification (equation 15, Fig. 9 ) .
Reflectance spectrum, measured as the fraction of incident
quantum flux reflected at each wavelength 1in a particular direction at a small solid angle ( p for a given 1 in M&S, but ambiguous
for energy or photons).
Standardized difference between two colours (equation 19).
Transmission spectrum of a beam of light at wavelength 1 to
distance x ( T in M&S, but ambiguous for energy or photons).
fraction of Q T in the second longest wavelength segment in the
segment classification (equation 15, Fig. 9 ) .