1
Spider mimicry in prey and predator visual systems
Marc Théry & Jérôme Casas
Manuscript reference number TX7018A
Details of modelling calculations
Determination of colour loci in the hexagon of Hymenoptera colour vision
We proceeded as Chittka et al.1. To determine photoreceptor excitations for
each measured spectra, we used spectral sensitivity functions of standard
photoreceptors for trichromatic Hymenoptera2.
The sensitivity factor R for each photoreceptor is determined by the
equation
R 1

I B λ S λ Dλ dλ
700
300
(1)
Where I B λ  is the spectral reflection function of a large sample of green
foliage background to which the receptors are adapted; S λ  is the spectral
sensitivity function of the receptor in question and Dλ  is the illuminating
daylight spectrum (CIE D65).
The effective quantum flux P for a given spectra in the respective
photoreceptor is computed as
P  R  I Sλ S λ Dλ dλ
300
700
(2)
Where I S λ  is the spectral reflection function of spiders or flowers.
2
It is assumed that the photoreceptors display half their maximum
response when stimulated by the light reflected from the adaptation
background. When the maximum excitation E max of the photoreceptor is
normalised to unity, the physiological receptor voltage signals E UV , E B and E G
are computed for each photoreceptor as
E  P /( P  1)
(3)
The two dimensions of the colour hexagon are calculated using receptor
excitations as
x = sin 60°( E G - E UV )
(4)
y = E B - 0.5( E UV + E G )
(5)
Euclidean distances St between stimuli are calculated as
St 
 x    y 
2
2
(6)
Determination of colour loci in the tetrahedron of bird colour vision
To compute colour loci of spiders and flowers seen by a tetrachromat, we use
spectral sensitivities of single cones determined in the passeriform bird Leiothrix
lutea3, and optical models derived from microspectrophotometry of cone
pigments with oil droplets4.
The sensitivity factor R, the effective quantum flux P and the
physiological receptor voltage signals E UV , E B , E G and E R were determined
respectively from equations (1), (2) and (3).
3
The three dimensions of the tetrahedron5 are calculated using receptor
excitations as
x = 2 2 cos30° ( E G - E R )
3
(7)
y = E UV - 1 ( E B + E G + E R )
3
(8)
z = 2 2 [sin30°( E G + E R ) - E B ]
3
(9)
Euclidean distances between stimuli are calculated as
St 
 x    y    z 
2
2
2
(10)
Quantification and test of colour contrast for Hymenoptera and birds
The null hypothesis is verified if Euclidean distances are randomly distributed
above and below a threshold of colour contrast discrimination for both predators
and preys. For a honeybee, colour discrimination is a function of wavelength
with an optimal resolution of 5 nm around 500 nm 6. We shifted 81 twin
reflectance spectra from 300 to 700 nm in 5 nm steps to compute the mean
Euclidean distance of colour contrast discrimination, which was measured as
0.05. A colour contrast of 0.1 is considered as equivalent to about 70%
discriminability7,8. For each pair of spider and flower, colour contrasts were
compared to the 0.05 discrimination value providing a measure of individual
colour mimicry. We tested the frequencies of colour contrasts below the
discrimination threshold against the null hypothesis using chi-square tests.
We proceeded similarly for birds by computing the minimal colour
distance allowing to discriminate two object spectra differing by 4 nm 9. In the
colour tetrahedron, two spider or flower reflectance spectra shifted between 300
4
and 700 nm in 4 nm steps were separated by a mean Euclidean distance of
0.06. As for Hymenoptera, frequencies of colour distances below the
discrimination value were contrasted against the null hypothesis of random
distribution using chi-square tests.
Quantification and test of achromatic contrast for Hymenoptera and birds
Instead of colour contrast, honeybees are known to use the signal of green
receptors for detection of small targets10. Green receptor signals were
computed for each spider and flower spectra, and compared using repeatedmeasures ANOVAs after controlling data normality.
Birds are known to use double cones to detect achromatic contrast 11,12.
The spectral sensitivity of double-cones was computed by combining
absorbance spectra of the medium- and long-wavelengths sensitive
photoreceptors13. Double cone signals produced by each spider and flower
spectra were compared using repeated-measures ANOVAs after controlling
data normality.
1.
Chittka, L., Schimda, A., Troje, N. & Menzel, R. Ultraviolet as a
component of flower reflections, and the colour perception of
Hymenoptera. Vis. Res. 34, 1489-1508 (1994).
2.
Peitsch, D., Fietz, A., Hertel H., de Souza, J., Ventura, D. F. & Menzel,
R. The spectral input systems of hymenopteran insects and their
receptor-based colour vision. J. Comp. Physiol. A 170, 23-40 (1992).
5
3.
Bowmaker, J. K., Heath, L. A., Wilkie, S. E. & Hunt, D. M. Visual
pigments and oil droplets from six classes of photoreceptor in the retina
of birds. Vis. Res. 37, 2183-2194 (1997).
4.
Vorobyev, M., Osorio, D., Bennett, A. T. D., Marshall, N. J. & Cuthill, I. C.
Tetracromacy, oil droplets and bird plumage colours. J. Comp. Physiol. A
183, 621-633 (1998).
5.
Goldsmith, T. H. Optimization, constraint, and history in the evolution of
eyes. Quart. Rev. Biol. 65, 281-322 (1990).
6.
von Helversen, O. Zur spectrale unterschiedsempfindlichkeit der
honigbiene. J. Comp. Physiol. 80, 439-472 (1972).
7.
Chittka, L. Optimal sets of colour receptors and opponent processes for
coding of natural objects in insect vision. J. Theor. Biol. 181, 179-196
(1996).
8.
Chittka, L. Camouflage of predatory crab spiders on flowers and the
colour perception of bees (Aranida: Thomisidae / Hymenoptera: Apidae).
Entomol. Gener. 25, 181-187 (2001).
9.
Neumeyer, C. Evolution of color vision. In Vision and Visual Dysfunction
(eds. Cronley-Dillon, J. R. & Gregory, R. L.) 284-305 (Macmillan,
London, 1991).
6
10.
Spaethe, J., Tautz, J. & Chittka, L. Visual constraints in foraging
bumblebees: flower size and color affect search time and flight behavior.
Proc. Natl Acad. Sci. USA 98, 3898-3903 (2001).
11.
Osorio, D., Miklósi, A. & Gonda, Zs. Visual ecology and perception of
coloration patterns by domestic chicks. Evol. Ecol. 13, 673-689 (1999).
12.
Osorio, D., Vorobyev, M. & Jones, C. D. Colour vision of domestic
chicks. J. Exp. Biol. 202, 2951-2959 (1999).
13.
Hart, N. S., Partridge, J. C., Cuthill, I. C. & Bennett, A. T. D. Visual
pigments, oil droplets, ocular media and cone photoreceptor distribution
in two species of passerine bird: the blue tit (Parus caeruleus L.) and the
blackbird (Turdus merula L.). J. Comp. Physiol. A 186, 375-387 (2000).