Vision Research 49 (2009) 1939–1947
Contents lists available at ScienceDirect
Vision Research journal homepage: www.elsevier.com/locate/visres
Avian colour vision: Effects of variation in receptor sensitivity and noise data on model predictions as compared to behavioural results Olle Lind *, Almut Kelber Department of Cell and Organism Biology, Lund Vision Group, Lund University, Helgonavägen 3, 223 62 Lund, Sweden
a r t i c l e
i n f o
Article history: Received 13 February 2009 Received in revised form 7 May 2009
Keywords: Bird Colour vision Modelling Spectral sensitivity Colour match Colour discrimination
a b s t r a c t Colour vision models require measurement of receptor noise and the absorbance of visual pigments, oil droplets, and ocular media. We have studied how variation in these parameters influences colour matching, spectral sensitivity, and colour discrimination predictions in four bird species. While colour match predictions are sensitive to variation in visual pigment and oil droplet absorbance data, discrimination predictions are mostly sensitive to variation in receptor noise. Ocular media transmittance influences only modelled spectral sensitivities at short wavelengths. A comparison between predicted and measured spectral sensitivities in domestic fowl and duck revealed large discrepancies, likely because of influences from achromatic mechanisms. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Birds use colours in various tasks such as foraging and mate choice (see e.g. Bennett & Cuthill, 1993; Cuthill, Bennett, Partridge, & Maier, 1999; and references therein). To understand bird behaviour it is therefore important to gain knowledge about avian visual processing, the link between the spectral composition of stimuli and the perception of colours. There may be many stages of signal processing between the response of the photoreceptors and the behavioural outcome. Still, the most commonly used models suggest that certain behavioural responses can be predicted from the calculations of colour representation at the photoreceptor and early post-receptor (colour opponency) level (as reviewed in Kelber, Vorobyev, & Osorio, 2003). Diurnal birds, with few exceptions, sample visual information by a retinal array consisting of four types of single cones, one type of double cone, and one type of rod (Hart, 2001b). However, it is generally assumed that only single cones are involved in colour vision (Maier & Bowmaker, 1993; reviewed in Martin & Osorio, 2008). The visual pigments of the single cones are grouped into four classes designated SWS1, SWS2, RH2, and M/LWS (Ebrey & Koutalos, 2001; Yokoyama, 2000). These are found in the ultraviolet or violet-sensitive (UVS/VS), the short-wavelength-sensitive
* Corresponding author. E-mail addresses:
[email protected] (O. Lind),
[email protected] (A. Kelber). 0042-6989/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.visres.2009.05.003
(SWS), medium-wavelength-sensitive (MWS), and the long-wavelength-sensitive (LWS) cone, respectively (Hart, 2001b). The spectral sensitivities of bird cones also depend on pigmented oil droplets in the cone inner segments by which incident light is filtered. The oil droplets act as long-pass cut-off filters that narrow the spectral sensitivity of the photoreceptors and shift their spectral position of peak absorbance towards longer wavelengths (Goldsmith, Collins, & Licht, 1984; Hart & Vorobyev, 2005; Partridge, 1989). This is true for all oil droplets but those of the UVS/VS cones that absorb insignificant amounts of light from 300 to 800 nm. Even before reaching the cones, light is filtered through the ocular media that absorb light of short wavelengths (e.g. Hart, 2004; Hart, Partridge, Bennett, & Cuthill, 2000; Hart, Partridge, Cuthill, & Bennett, 2000; Jane & Bowmaker, 1988; Wright & Bowmaker, 2001). The spectral sensitivity of a cone is thus a function of the ocular transmittance together with the absorbance of the cone’s oil droplet and visual pigment. The absorbance of the visual pigments and the oil droplets are commonly described by models of which the most frequently used are those suggested by Govardovskii, Fyhrquist, Reuter, Kuzmin, and Donner (2000; for the visual pigments), and by Hart and Vorobyev (2005; for the oil droplets). These models are convenient since they can be used to reconstruct the sensitivity of a cone from only a few known parameters; the spectral position of the visual pigment’s peak absorbance (kmax) and the oil droplet’s cut-off wavelength (kcut). The cut-off wavelength is the shortest wavelength at which there still is a significant transmittance of light (Hart & Vorobyev, 2005; Lipetz, 1984). In addition to this, also the wavelength of 50% transmittance (kmid) of the oil droplet is
1940
O. Lind, A. Kelber / Vision Research 49 (2009) 1939–1947
needed for the model calculations. However, there is a correlation between kcut and kmid that makes it possible to approximate kmid when only kcut is known (Hart & Vorobyev, 2005). The parameters (kmax, kcut, kmid) required in the models are estimated by microspectrophotometry (MSP; Hart, 2001b; Liebman, 1972). Due to the small dimensions of the oil droplets and the photoreceptors, MSP measurements are noisy (Bowmaker, Heath, Wilkie, & Hunt, 1997; Hart & Vorobyev, 2005; Lipetz, 1984; MacNichol, 1986), which leads to a considerably amount of variation in the parametric values. Hence, there is a certain level of uncertainty in the model predictions. Cone spectral sensitivities can also be explored in colour matching experiments. These tests are based on the theory that any spectral stimulus coded by n receptors can be matched by a specific mixture of n other spectral stimuli (Goldsmith & Butler, 2005; Kelber et al., 2003). When a match is established, the single stimulus and the mixture excite the receptor array equally and are thus inseparable. Colour matching results are thus directly related to the absorbance properties of the cones. This allows for a direct comparison between receptor responses that are measured through the behavioural experiments and those that are estimated through model predictions based on MSP measurements (Goldsmith & Butler, 2005). A colour matching test provides information on the number of active, colour coding receptor types and their spectral sensitivities. Another behavioural experiment, the spectral sensitivity threshold test can also be used to explore these properties and this test might also serve to reveal mechanisms in colour vision such as the post-receptor processing of receptor outputs (Kelber et al., 2003). The spectral sensitivity experiment tests a subject for its performance in distinguishing large chromatic stimuli presented on an adapting background (Goldsmith & Butler, 2003; Kelber et al., 2003; Maier, 1992). In 1998, Vorobyev and Osorio proposed a model in which they assumed that spectral sensitivity thresholds are set by receptor noise as it is propagated into higher-order neural mechanisms. The model is most carefully tested for honeybees (Vorobyev, Brandt, Peitsch, Laughlin, & Menzel, 2001) but has also been used for several other di-, tri-, and tetrachromats (Vorobyev & Osorio, 1998). The receptor noise-limited model allows for an estimation of discrimination thresholds. It is today widely used in various studies to answer the questions whether, and how well, birds (or other animals) can detect and discriminate objects such as fruit, other birds, or other stimuli (e.g. Håstad, Victorsson, & Ödeen, 2005; Herrera et al., 2008; Schaefer, Schaefer, & Vorobyev, 2007; Vorobyev, Osorio, Bennet, Marshall, & Cuthill, 1998; Vorobyev, 2003). Considering the frequent use of colour vision models it is of importance to determine how sensitive they are to parametric variation. With such information it is possible to appreciate how precise the model predictions are and to what extent it is possible to rely on model predictions instead of performing time-consuming behavioural tests on a large number of species. In this study we examine how sensitive the models describing colour matching, spectral sensitivity, and wavelength discrimination thresholds are to variation in receptor noise, visual pigment absorbance, oil droplet absorbance, and ocular media absorbance. This is done by comparing model predictions to behavioural data describing the same properties. Four species of bird are included in the study; the budgerigar (Melopsittacus undulatus), the pigeon (Columba livia), the domestic chicken (Gallus gallus), and the domestic duck (Anas platyrhynchos). For this purpose, we also measured the ocular media transmittance in the budgerigar, the pigeon, and the chicken, for which data are either missing (budgerigar) or ambiguous (chicken and pigeon; Emmerton, Schwemer, Muth, & Schlecht, 1980; Govardovskii & Zueva, 1977).
2. Methods and theory 2.1. Experimental data Experimental data from earlier studies presented in graphic form were digitized using WinDig 2.5 (Lovy, 1996) and Plot Digitizer 2.4.1 (Huwaldt, 2005). The stimuli spectral distributions used in the budgerigar colour matches were provided by the authors directly (Goldsmith, personal communication). The monochromatic stimuli used in the colour matches of the pigeon were assumed to be Gaussian functions with full bandwidths at half maximum as specified in the articles (Palacios, Martinoya, Bloch, & Varela, 1990; Palacios & Varela, 1992). 2.2. Measurements of pre-retinal tissue transmittance Three budgerigars were anaesthetized with carbon dioxide and decapitated. The eyes were excised and a small portion (approximately 3 3 mm) of the sclera and retina at the posterior pole of the eye was removed. The eye was placed with the pupil facing downwards in a plastic container (12 mm path length), through which a 4 mm hole had been drilled in the bottom and covered by a fused silica window (UQG optics). Metallic ring inserts were used to stabilize the position of the eye. Eyes were bathed and measured in 340 mosmol kg1 PBS. Reference scans were made with the same container including the inserts and PBS. The light source was a xenon lamp (Cermax Xenon Fiberoptic Light Source, ILC Technologies). The transmittance of the ocular media of each eye was measured with five repeats at 1 nm steps from 220 to 1050 nm with a spectroradiometer (International light, RPS 900-R) attached to a 3 mm hole in the top cover of the container. One eye was damaged by the preparations and data from this eye were therefore excluded from further analysis. The data from each eye were smoothed with an 11-step running average to reduce noise. The transmittance was normalized to the value at 700 nm, where we assume that only insignificant amounts of light are absorbed by the ocular media. As a final step the mean transmittance of the 25 measurements of all five eyes was calculated. The experiments were approved and followed the ethical guidelines of the Swedish board of agriculture (M206-07). This procedure was repeated for the domestic fowl and the pigeon with few modifications. The excised portions of the sclera at the posterior pole of the eye were approximately 4 4 mm and the eyes were placed in a plastic container similar to that used in the budgerigar measurements but larger (26 mm path length). Four eyes from two domestic fowls and seven eyes from four pigeons (one pigeon eye was damaged and could not be used) were measured and each eye was sampled three times. 2.3. Colour match model A colour match is established when an array of n photoreceptors is stimulated equally by a single spectral stimulus and the mixture of n other stimuli (Kelber et al., 2003). For the budgerigar and the pigeon we can limit the number of photoreceptors to n = 2 because these species have cones with narrow spectral sensitivities so that their eyes are functionally dichromatic in each spectral region for which colour match tests have been performed. The double cones are assumed to transfer achromatic information only and are ignored in this study. For a dichromatic colour match two photoreceptors, Ps and Pl, respond to a single stimulus, S0, and the mixture of two stimuli, Ss + Sl (the subscripts refer to the relative wavelength position of peak absorbance or quantum flux, s = shorter, l = longer). The expected ratio, r, of the stimuli intensities, I, in the mixture at match is then related to the quantum catches of the photoreceptors, q, through,
1941
O. Lind, A. Kelber / Vision Research 49 (2009) 1939–1947
r¼
IðSl Þ qSs ;Ps qS0 ;Pl qS0 ;Ps qSs ;Pl ¼ IðSs Þ qS0 ;Ps qSl ;Pl qSl ;Ps qS0 ;Pl
ð1Þ
(Goldsmith & Butler, 2005) and the quantum catch of photoreceptor P for stimulus S is given by:
qS;P ¼
Z
700
where i ¼ 1; 2; . . . ; n; k is wavelength; Ri(k) is the spectral sensitivity of photoreceptor i; It (k) is the threshold intensity of the spectral stimulus; and ki is a scaling factor given by:
K i ¼ R 700 300
Q S ðkÞRP ðkÞdk
ð2Þ
300
where QS(k) is the relative quantum flux of the stimulus S normalized to a maximum of one; RP(k) is the sensitivity of the photoreceptor P; and integration is over the visible spectrum. For truly monochromatic stimuli it would be possible to replace the quantum catches of the receptors (q) with the receptor sensitivities at the corresponding stimulus wavelengths, RP(kS)). However, in the experiments with the pigeon (Palacios & Varela, 1992; Palacios et al., 1990) and the budgerigar (Goldsmith & Butler, 2005) pseudo-monochromatic stimuli with different spectral bandwidths were used, which requires the use of quantum catches in the models. Receptor sensitivity is a function of ocular transmittance, oil droplet transmittance and visual pigment absorbance and was calculated using the theoretical framework presented in previous studies (Govardovskii et al., 2000; Hart & Vorobyev, 2005). The parameters used in the calculations can be found in Table A1 (Appendix A). Self-screening was ignored since it is not an important factor in light-adapted receptors (as presumed in the budgerigar and the pigeon experiments) and preliminary calculations show that it has insignificant or no effect on the model predictions. Finally, the relative contribution of Sl in the stimuli mixture at a match is:
Sl ¼ r=ð1 þ rÞ
ð3Þ
2.4. Spectral sensitivity model Spectral sensitivities were predicted using the same models for cone sensitivities as before, and the receptor noise-limited model of colour discrimination suggested by Vorobyev and Osorio (1998). This model is based on three general principles; (i) For a receptor array of n types of receptors, colour is coded by n-1 unspecified chromatic opponent mechanisms and achromatic signals are ignored; (ii) opponent mechanisms give no signal for stimuli that differ only in intensity; (iii) thresholds are set by receptor noise. Spectral sensitivity is inversely related to the minimum intensity, It(k), of a spectral stimulus needed to make it detectable against an adapting background. For the model calculations, we assume true monochromatic stimuli of single wavelengths, k. The colour contrast between a stimulus and the background in terms of quantum catches of the photoreceptors is:
Dqi ¼ ki Ri ðkÞIt ðkÞ Quantum flux (normalized)
ð4Þ
1
650
500
ðDSt Þ2 ¼ ððe1 e2 Þ2 ðDq4 Dq3 Þ2 þ ðe1 e3 Þ2 ðDq4 Dq2 Þ2 þ ðe1 e4 Þ2 ðDq3 Dq2 Þ2 þ ðe2 e3 Þ2 ðDq4 Dq1 Þ2 þ ðe2 e4 Þ2 ðDq3 Dq1 Þ2 þ ðe3 e4 Þ2 ðDq2 Dq1 Þ2 Þ=ððe1 e2 e3 Þ2 þ ðe1 e2 e4 Þ2 þ ðe1 e3 e4 Þ2 þ ðe2 e3 e4 Þ2 Þ
0.8
450
350
pffiffiffiffiffi ei ¼ 1= gi :
ð7Þ
2.5. Colour discrimination calculations To test the influence of parametric variation on the discrimination values produce by the receptor noise-limited model we constructed four theoretical stimuli by adding Gaussian curves (75 nm half width) to the spectrum of a green leaf. The unchanged green leaf spectrum served as an adapting background. These stimuli were centred at 350, 450, 500, and 650 nm (Fig. 1). One set of such stimuli was constructed for the budgerigar and one set for the pigeon. The amplitudes of the Gaussian curves were adjusted such that the stimuli had chromatic distances of 2 JNDs from the background. These reference distances were calculated using the receptor-noise limit model (Eq. (6)) as described by Schaefer et al. (2007), the photoreceptor parameters defined in Table A1, and an absolute noise level of 0.05 for the UVS/VS cones (cf. Schaefer et al., 2007; Vorobyev et al., 1998). We then manipulated the values for the absorbance of the ocular media, the visual pigments, the oil droplets, and the receptor noise one by one (as defined in Table 2), calculated the new chromatic distances, and studied the change relative to the reference distances in the original model (2 JNDs).
650
500
0.6
0.6
0.4
0.4
0.4
0.2
0.2
0.2
400
500
600
700
0 300
Sesame seed
400
500
600
Dry grass
1 0.8
0.6
0 300
ð6Þ
The units for DSt are JNDs (just noticeable differences) and 1 JND corresponds to the threshold. No noise measurements exist for the cones of any bird species used in this study. Therefore, the noise level, e, in receptor channel i is assumed to be proportional to the relative number of that receptor type, gi, within the retinal integration area (Goldsmith & Butler, 2003; Vorobyev & Osorio, 1998) by:
C
1
450
350
ð5Þ
where Ib is the background spectrum and integration is over the visual spectrum. The threshold distance (DSt) between stimuli in receptor space depends on the quantum catches, Dqi, and the noise, ei, of the receptors. For large stimuli in photopic conditions the following equation gives the relative spectral sensitivity thresholds for tetrachromats (Vorobyev & Osorio, 1998):
B
A 0.8
1 Ri ðkÞIb ðkÞdk
700
0 300
Apple
Flax seed 400
500
600
700
Wavelength (nm) Fig. 1. The stimuli and backgrounds used in the colour discrimination analysis. (A) The spectra of the four theoretical stimuli and the green leaf background used for the budgerigar (Melopsittacus undulatus) and (B) for the pigeon (Columba livia). The stimuli (broken lines) were constructed by adding Gaussian functions centred around 350, 450, 500, and 650 nm (arrows) to the green leaf background (solid line). The amplitudes of the Gaussian functions were adjusted so that the chromatic distances between the stimuli and the background are 2 JNDs when using the receptor noise limited model (see Section 2) and the parameters in Table A1. (C) the spectra of flax seed, sesame seed, an apple, and dry grass as defined by the inserts. All spectra are normalized to a highest value of one.
1942
O. Lind, A. Kelber / Vision Research 49 (2009) 1939–1947
Table 1 Colour match predictions and behavioural results in the budgerigar and the pigeon. Species
Single stimulus (S0)
Stimuli mixture (Ss + Sl)
Contribution of Sl at match (%) Predicted
Measured
–
Estimated kmid-value of oil droplet
Without ocular media absorption
Budgerigar (Melopsittacus undulatus)
590 420
563 + 640 371 + 440
88 94
89 93
88 95
90 85–90
Pigeon (Columba livia)
590 600 450 450
580 + 640 580 + 640 430 + 470 410 + 470
38(35) 75(72) 33 40
41(40) 78(77) 32 39
39(36) 77(72) 35 43
40 40–60 10 10–20
The colour match predictions using the parameters specified in Table A1 are shown in the column denoted by a hyphen. The predictions using estimated kmid-values of the oil droplets were calculated with cone sensitivities as described by Hart and Vorobyev (2005). Stimuli are denoted by their wavelength positions of maximum quantum flux. The behavioural data come from Goldsmiths and Butler (2005; budgerigar); Palacios et al. (1990; pigeon), and Palacios and Varela (1992; pigeon). Predicted colour matches for the pigeon were calculated with the Y-droplet of the ventral retina, and the dorsal retina (within brackets).
3. Results 3.1. Ocular media of the budgerigar, the pigeon, and the domestic fowl The ocular media of the budgerigar have a high transmittance for UV-light and still transmit about 10% of light at 300 nm (Fig. 2). The ocular media of the pigeon and the domestic fowl absorb more of the UV light but the transmittance curves of all three birds are similar at wavelengths longer than approximately 400 nm. The wavelength of half maximum transmittance (kT0.5) is 314 nm for the budgerigar, 337 nm for the pigeon, and 351 nm for the domestic fowl. 3.2. Effect of parametric variation on colour matches of the budgerigar and the pigeon We studied the effect of parametric variation by measuring changes in the predicted contributions of stimulus Sl in colour matches with the stimuli S0 = Ss + Sl. These results were compared to corresponding behavioural measurements. The contribution of Sl in the stimuli mixtures of all the budgerigar colour matches are predicted with less than a 5% deviation from the behaviourally estimated values, (Table 1). The stimuli mixture in the test with the stimuli, S0(590) = Ss(580) + Sl(640), of the pigeon is also predicted with high precision, but the contribution of Sl in the other matches is overestimated by 15% or more (Table 1). Parametric variation was simulated by spectral shifts of the visual pigment absorbance curves and the oil droplet transmission curves 10 nm in both directions. The shifts of the oil droplet transmittance curves produces changes within the range of 0–25% of predicted Sl contributions (Fig. 3A–F) while shifting the visual pigment absorbance curves in the same manner causes slightly smaller changes, within 0–21%, (Fig. 4A–F). Mean changes in Sl contribution for 10 nm shifts of the oil droplet transmittance, and the visual pigments absorbance curves are 10% and 6%, respectively.
Shifting the R-droplet transmittance curve of the pigeon 10 nm towards longer wavelengths moves the predicted match conditions of the test with the, S0(600) = Ss(580) + Sl(640) stimuli to lie within the colour match region established in behavioural test (Fig. 3B). A similar shift of the pigeon C-droplet has a similar effect for the colour matches at shorter wavelengths (Fig. 3C and F). By contrast, shifting the position of the pigeon Y-droplet or any of the budgerigar oil droplets has little, or no effect (Fig. 3A, B and E). Likewise, pigeons have one type of Y-droplets in the dorsal retina (kcut = 539) and a different type in the ventral area (kcut = 513), and this difference has a little effect on predicted colour matches (Table 1). Match mixture predictions are barely changed when the cone sensitivities are modelled using approximated instead of experimentally determined kmid-values for the oil droplet absorbance curves (Table 1). Furthermore, excluding the ocular transmittance from the calculations changes the estimated Sl-contribution by only 3% or less (Table 1). 3.3. Spectral sensitivity and colour discrimination of the budgerigar, the pigeon, the domestic fowl, and the domestic duck Simulations of the parametric variation were also performed on predicted spectral sensitivities and colour discrimination values
1 0.9 0.8
Transmittance
The use of hypothetical stimuli allowed us to analyse model predictions for the full visual spectrum and with controlled chromatic distances. To further test the sensitivity of the model in a more natural scenario, and for a different background, we performed the same analysis on the discrimination values for a set of biologically relevant stimuli (flax seed, sesame seed, and apple) as viewed against a background of dry grass. The radiance of these stimuli and the background was measured with a spectroradiometer (International Light RSP900-R) and converted to quantum flux units.
0.7 0.6 0.5 0.4 0.3
Budgerigar Pigeon Domestic fowl
0.2 0.1 0 300
350
400
450
500
550
600
650
700
Wavelength (nm) Fig. 2. The transmittance of the budgerigar (Melopsittacus undulatus, solid line), the domestic fowl (Gallus gallus, broken line), and the pigeon (Columba livia, dotted line) ocular media. The curves show the mean of five eyes from three individuals (budgerigar), four eyes from two individuals (domestic fowl), and seven eyes from four individuals (pigeon) normalized to the transmittance at 700 nm. The spectral position of half maximum transmittance (kT0.5) is at 314 nm for the budgerigar, 351 nm for the domestic fowl, and 337 nm for the pigeon.
1943
O. Lind, A. Kelber / Vision Research 49 (2009) 1939–1947
(chromatic distances). We observed that the exclusion of the ocular media absorption (Fig. 2) from the calculations changes the predicted spectral sensitivities in the UV part of the visual spectrum substantially (Fig. 5). At longer wavelengths, the effect of the ocular media absorption is negligible (Fig. 5). By contrast, the exclusion of ocular media absorption changed the modelled chromatic distances for hypothetical stimuli viewed against a green background and natural stimuli viewed against a background of dry grass by only 15% or less (Tables 2 and 3). Likewise, the predicted chromatic distances were little or moderately
A
Contribution of Sl at match (%)
100
Budgerigar S0(590) = Ss(563)+Sl(640)
B 90
90
80
80
70
70
60
60
40 -10
100
Pigeon S0(600) = Ss(580)+Sl(640)
-5
50 40 30
+5
30 -10
+10
E
S0(420) = Ss(371)+Sl(440)
90 80 70 60 C-type
40 -10
-5
+5
+5
+10
-10
F
50
50
40
40
30
30
-5
0
+5
+10
20
R-type Y-type
-10
-5
S0(450) = Ss(410)+Sl(470)
60
+10
C-type
10 0
S0(590) = Ss(580)+Sl(640)
10 0
-5
60
20
50
20
R-type Y-type
40 0
Pigeon S0(450) = Ss(430)+Sl(470)
C 60
50 R-type Y-type
50
D
affected by 10 nm shifts of the spectral positions of the visual pigments’ and the oil droplets’ absorbance curves (within the range of 0–20%; Tables 2 and 3). Shifting the relative receptor noise levels of the four cone types by changing the relative cone frequencies see (Eq. (7)) from 1:1:2:2 (UVS:SWS:MWS:LWS; budgerigar) and 1:1:1:2 (VS:SWS:MWS:LWS; pigeon) to a hypothetical cone ratio of 1:4:4:8 changes the predicted chromatic distances within the range of 10–95% (Tables 2 and 3). In addition to the investigation of the effects from parametric variation, we examined the correlation between modelled
C-type
10 0
+5
+10
-10
-5
0
+5
+10
Shift of oil droplet absorbance curve (nm) Fig. 3. Changes in predicted colour match conditions as a function of shifts of the spectral position of the oil droplet absorbance curves. Behaviourally established colour match conditions (Goldsmith & Butler, 2005; Palacios & Varela, 1992; Palacios et al., 1990) are shown by dashed lines or gray zones. Model predictions are represented by squares or stars as designated by the inserts. The colour matches of the budgerigar (Melopsittacus undulatus, A and D) are relatively insensitive to spectral shifts of the oil droplets compared to those of the pigeon (Columba livia, B–F). For the budgerigar, shifting the R-droplet towards shorter wavelengths (A) or the C-droplet towards longer wavelengths (D) changes good predictions to be excellent. In the pigeon, more dramatic effects are seen for shifts of the R-droplet or the C-droplet since erroneous predictions change to be good (F) or even perfect (B and C).
A Contribution of Sl at match (%)
100
Budgerigar S0(590) = Ss(563)+Sl(640)
B 90
90
80
80
70
70
60
60
-10
D 100
-5
+5
+10
S0(420) = Ss(371)+Sl(440)
90 80 70
40 30
E
20
LWS MWS -10
-5
0
+5
+10
S0(590) = Ss(580)+Sl(640)
50 -10
-5
60
50
50
40
40
+5
+10
-5
0
+5
+10
S0(450) = Ss(410)+Sl(470)
30 20
LWS MWS
10 0
-10
F
60
20
SWS2 SWS1
SWS2 SWS1
10
30
60
40
30
Pigeon S0(450) = Ss(430)+Sl(470)
50
40 0
C 60
50 LWS MWS
50 40
Pigeon S0(600) = Ss(580)+Sl(640)
-10
-5
SWS2 SWS1
10 0
+5
+10
-10
-5
0
+5
+10
Shift of visual pigment absorbance curve (nm) Fig. 4. Changes in predicted colour match conditions as a function of shifts of the spectral position of the visual pigment absorbance curves. Model predictions are represented by squares or stars as designated by the inserts. The dashed lines and the gray zones are the colour match conditions established by behavioural experiments (Goldsmith & Butler, 2005; Palacios & Varela, 1992; Palacios et al., 1990). (A) A shift of the LWS or the MWS visual pigment of the budgerigar (Melopsittacus undulatus) 5 nm towards shorter wavelengths changes a good colour match prediction to be perfect. (D) This is also true for a 5 nm shift of the SWS1 pigment towards longer wavelengths. Shifting any of the visual pigments of the pigeon (Columba livia) towards longer wavelengths produces better model predictions (B, C and F) except for the S0(590) = Ss(580) + Sl(640) match (E), for which any shift result in a less good fit.
1944
O. Lind, A. Kelber / Vision Research 49 (2009) 1939–1947
With ocular media absorption Without ocular media absorption -1
A
-1
Budgerigar
Log relative sensitivity
-1.5 -2
-2
-2.5
-2.5
-3
-3
-3.5 300
-3.5 300
-1
B
Pigeon
-1.5
400
500
C
600
700
-1
Domestic Fowl
-1.5
500
D
600
700
Domestic duck
-1.5
-2
-2
-2.5
-2.5
-3 -3.5 300
400
-3 -3.5
400
500
600
700
300
400
500
600
700
Wavelength (nm) Fig. 5. The influence of ocular media transmittance on predicted spectral sensitivities of (A) the budgerigar (Melopsittacus undulatus), (B) the pigeon (Columba livia), (C) the domestic fowl (Gallus gallus), and (D) the domestic duck (Anas platyrhynchos). The lines represent spectral sensitivity calculations including (solid lines) versus excluding (dashed lines) the transmittance of the ocular media. The spectral sensitivities are predicted using a green leaf spectrum as the adapting background (see Fig. 1).
and behaviourally tested spectral sensitivities of the domestic fowl and the domestic duck with a background lightning of incandescent lights (Barber et al., 2006; Prescott & Wathes, 1999). This correlation is weak throughout the visual spectrum although the discrepancy is most profound at short wavelengths (Fig. 6).
4. Discussion 4.1. Ocular media transmittance The ocular media of birds having UVS visual pigments are usually transmitting more UV light (kT0.5 < 350 nm) than in birds that
Table 2 The influence of parameter inaccuracies on predicted chromatic distances between four different stimuli and a green leaf background. Parameter change
Chromatic distance between stimulus and background (JNDs) Budgerigar (Melopsittacus undulatus) Spectral position of stimulus peak (nm)
Reference NOM VP + 10 VP 10 OD + 10 OD 10 CR 1:2:2:4 CR 1:4:4:8
Pigeon (Columba livia) Spectral position of stimulus peak (nm)
350
450
500
650
350
450
500
650
2.0 2.1 1.8 2.3 – – 2.1 2.2
2.0 – 1.8 2.2 – – 2.8 3.9
2.0 – 2.1 1.9 2.1 1.9 2.6 3.7
2.0 – 2.2 1.8 2.3 1.7 2.6 3.6
2.0 2.3 1.6 2.4 – – 2.1 2.2
2.0 1.9 – 2.1 1.8 2.2 2.7 3.6
2.0 – 1.9 – 2.1 1.9 2.8 3.9
2.0 – 2.1 1.9 2.3 1.8 2.7 3.8
The chromatic distances were calculated using the receptor noise-limited model of colour discrimination (Schaefer et al., 2007). The reference distances were calculated using the parameters specified in Table A1 (the oil droplets of the ventral pigeon retina), and cone abundance ratios (UVS/VS:SWS:MWS:LWS) of 1:1:2:2 for the budgerigar (Wilkie et al., 1998) and 1:1:1:2 for the pigeon (Bowmaker et al.,1997). The left column indicates parameter changes; Reference = no change of parameters, NOM = no ocular media absorption, VP + 10 = visual pigment absorbance curves shifted 10 nm towards longer wavelengths, VP 10 = visual pigment absorbance curves shifted 10 nm towards shorter wavelengths, OD + 10 oil droplet absorbance curves shifted 10 nm towards longer wavelengths, OD 10 = oil droplet absorbance curves shifted 10 nm towards shorter wavelengths, CR = cone abundance ratios (UVS/VS:SWS:MWS:LWS). A hyphen indicates no change of the chromatic distance as compared to the reference.
Table 3 The influence of parameter inaccuracies on predicted chromatic distances between three naturally occuring stimuli and a dry grass background. Parameter change
Chromatic distance between stimulus and background (JNDs) Budgerigar (Melopsittacus undulatus) Stimulus
Reference NOM VP + 10 VP 10 OD + 10 OD 10 CR 1:2:2:4 CR 1:4:4:8
Pigeon (Columba livia) Stimulus
Sesame seed
Flax seed
Apple
Sesame seed
Flax seed
Apple
4.8 4.6 4.3 – 4.9 4.6 – 5.6
11.7 11.8 10.2 13.1 11.8 11.6 11.9 13.2
13.9 14.0 13.2 14.4 14.1 13.3 16.2 22.9
2.7 – 2.4 3.1 – – 3.4 4.4
6.5 6.7 5.7 7.5 – – 7.6 9.2
10.5 – – 10.9 – 10.6 14.3 19.7
The left column indicates parameter changes; Reference = no change of parameters, NOM = no ocular media absorption, VP + 10 = visual pigment absorbance curves shifted 10 nm towards longer wavelengths, VP 10 = visual pigment absorbance curves shifted 10 nm towards shorter wavelengths, OD + 10 oil droplet absorbance curves shifted 10 nm towards longer wavelengths, OD 10 = oil droplet absorbance curves shifted 10 nm towards shorter wavelengths, CR = cone abundance ratios (UVS/ VS:SWS:MWS:LWS). A hyphen indicates no change of the chromatic distance as compared to the reference. For more details see Table 2.
O. Lind, A. Kelber / Vision Research 49 (2009) 1939–1947
-1
A
Domestic fowl
-1.5 -2
Log relative sensitivity
-2.5 -3 -3.5 350
-1
400
450
500
550
600
B
650
700
Domestic duck
-1.5 -2 -2.5 -3 -3.5 350
400
450
500
550
600
650
700
1945
MSP measurements (Bowmaker et al., 1997) contain variation that is sufficient to cause the mismatches. Although variation in the spectral positions of the visual pigment and the oil droplet absorbance curves has only a moderate impact on the colour matches of the budgerigar (Figs. 3 and 4A, D), the pigeon colour matches are more sensitive (Figs. 3 and 4B–F). In fact, shifting the pigeon C and R-type droplet absorbance curves 10 nm towards longer wavelengths changes all erroneous predictions to acceptable or even very good predictions. This is a reasonable shift when compared to the variation of the MSP data from this species (Bowmaker et al., 1997). This suggests that shifted oil droplet absorbance curves could be used with advantage for future modelling of pigeon colour vision. Furthermore, we found that the absorption of the ocular media influences the predicted colour matches little (Table 1). Neither did the predictions change much from using approximated instead of measured kmid-values (Hart & Vorobyev, 2005; Table 1). Nevertheless, it is possible that these small changes are of importance and should be considered in colour vision modelling of a higher precision.
Wavelength (nm) Fig. 6. Relative spectral sensitivities of (A) the domestic fowl (Gallus gallus), and (B) the domestic duck (Anas platyrhynchos). Sensitivity is expressed as arbitrary inversed quantum units. The lines and the filled circles represent the model predictions and the behavioural data (Barber et al., 2006; Prescott & Wathes, 1999) respectively. The sensitivity of the domestic fowl was modelled with a cone abundance ratio of 1:1:3:1.5 for the VS, SWS, MWS, and the LWS cone (Bowmaker et al., 1997) and the domestic duck with a cone abundance ratio of 1:2:4:4 (Hart, 2001a). The mismatches between the model predictions and the experimental data from the domestic fowl and the domestic duck are large. The prediction curves have been shifted along the y-axis to produce best fits with the experimental data.
have VS visual pigments (kT0.5 > 350 nm; Hart, 2002; Hart, Partridge, Bennett, et al., 2000; Hart, Partridge, & Cuthill, 1998; Hart, Partridge, & Cuthill, 1999; Hart, Patridge, Cuthill, et al., 2000; Herrera et al., 2008; Jane & Bowmaker, 1988; Wright & Bowmaker, 2001). However, Govardovskii and Zueva (1977) suggest that the ocular media of the pigeon (which has a VS pigment) are transparent down to 340 nm and Emmerton et al. (1980) found that the pre-retinal tissues of the pigeon absorb only very small amounts of UV light down to approximately 310 nm. We have also found that the ocular media of the pigeon transmit an unexpectedly large amount of UV light (kT0.5 = 337 nm) but less than is suggested in earlier studies (Emmerton et al., 1980; Govardovskii & Zueva, 1977). This difference might be the consequence of using different protocols. While we measured the ocular media transmittance in intact eyes, except for the removal of a small piece of the posterior sclera and retina, the results in the earlier studies are based upon separate measurements of the cornea, the lens, the aqueous and the vitreous humour in opened eyes. 4.2. The sensitivity of colour match predictions Predictions of the colour matches of the budgerigar, based upon parameters generally used (Table A1; Bowmaker et al., 1997; Hart & Vorobyev, 2005) are in good agreement with behavioural results (Table 1). Thus, for the budgerigar, our study shows how sensitive these predictions are to small parametric variation due to experimental errors or individual variation (Figs. 3 and 4). By contrast, the predicted colour matches of the pigeon agree with the behavioural data for only one test, when the normally assumed parameters (see Table A1) are used (Table 1). The discrepancies between the predicted and behaviourally measured colour matches of the pigeon are likely the consequence of variation in the experimental data. Indeed, the data from the
4.3. The sensitivity of spectral sensitivity and colour discrimination predictions The spectral sensitivity and discrimination threshold predictions from the receptor noise-limited model depend on many factors; photoreceptor absorbance properties, ocular media transmittance, the background spectrum of the experimental setup, and noise in the receptors. Our results show that the precision (within a 20 nm range) by which the spectral tuning of the visual pigments and the oil droplets are approximated is of little or moderate importance for predictions of discrimination thresholds (Tables 2 and 3). Ocular media transmittance influences the predicted spectral sensitivities at wavelengths below 400 nm (Fig. 5), but it appears to be of minor importance for discrimination threshold predictions except for calculations that aim to reveal minute differences within the range of 0.1–0.3 JNDs (Tables 2 and 3). By contrast, receptor noise is a very important parameter in the calculations. Chromatic distances change markedly (up to 95%) when different estimations of cone abundances (relative receptor noise levels, see Eq. (7)) are used (Tables 2 and 3). This illustrates how important a factor noise is. One should be careful when drawing conclusions on object discrimination based on chromatic distances since the noise levels in avian photoreceptors are unclear. The sensitivity of the colour discrimination modelling to variation in different parameters is similar in two different scenarios; the hypothetical stimuli against a green background and natural stimuli against a background of dry grass. This implies that we have disclosed general principles concerning the sensitivity of colour discrimination modelling to variation in the experimental data. However, the importance of the changes in chromatic distances resulting from parametric variation has still to be investigated and it is uncertain how the discrimination of stimuli above threshold is related to chromatic distance close to threshold. In addition, our analysis does not include the modelling of narrow banded stimuli for which the results might be different. 4.4. The influence of achromatic mechanisms and double cones The receptor noise-limited model has successfully been used in earlier studies to describe the spectral sensitivity results from behavioural experiments with the budgerigar (Goldsmith & Butler, 2003), the pigeon, and the pekin robin (Vorobyev & Osorio, 1998).
1946
O. Lind, A. Kelber / Vision Research 49 (2009) 1939–1947
In contrast to these studies we found large differences between the predicted and the behaviourally determined sensitivity curves of the domestic fowl and the domestic duck, especially at shorter wavelengths (Fig. 6). Intriguingly, the measured spectral sensitivity curves of the domestic fowl and the domestic duck show similarities with spectral sensitivity curves of other animals that are obtained in dim light conditions (Fig. 6; Vorobyev & Osorio, 1998). As already stated by Vorobyev and Osorio (1998), dim light conditions favours additive – achromatic – receptor mechanisms instead of subtractive – chromatic – opponent mechanisms, which means that spectral sensitivity curves for animals adapted to mesopic or scotopic conditions probably reflect both achromatic and chromatic mechanisms. The lights used in the domestic fowl and domestic duck studies (100 and 50 lux, respectively) were assumed to yield photopic conditions (Barber et al., 2006; Prescott & Wathes, 1999). Still, this might not have been the case since the intensity range of mesopic vision has not been determined in any bird to our knowledge. Achromatic mechanisms are thought to be mediated by double cones but double cones could even be involved in chromatic vision although several studies indicate that they do not (reviewed in Martin & Osorio, 2008). Finally, the mismatch between the predicted and the measured spectral sensitivities might also be the result of influences from higher order mechanisms (e.g. neural noise) in the behavioural data. This is plausible but not accounted for in the receptor noise-limited model (Vorobyev et al., 2001). 5. Conclusions We have found that parametric variation or inaccuracies can be of high importance in modelling colour vision. However, different models have different tolerances to this variation. Deviations in photoreceptor absorbance data seem to influence colour match modelling to a large extent while spectral sensitivity and colour discrimination modelling is relatively insensitive to such variation. Furthermore, colour discrimination predictions are highly sensitive to variation in receptor noise. Ocular media transmittance is important for modelling concerning short wavelength regions. However, while the exclusion of ocular media absorption changes spectral sensitivity predictions, colour match and discrimination predictions are little affected. The expected uncertainty, or variation, in the model predictions can thus not be generalized but each kind of test should be preceded by a careful investigation of the parameters upon which the calculations rely. Finally, the uncertainty about the avian mesopic range calls for careful assumptions about the ambient light conditions in which the model predictions and the corresponding behavioural tests are performed. Acknowledgments We like to thank Timothy H. Goldsmith for sharing his experimental data with us, Yakir Gagnon for help with the programming, Arne Johansson for technical assistance, and Lund Vision Group for helpful discussions. We also thank two anonymous reviewers for helpful comments on the manuscript. Financial support from the Swedish Research Council is gratefully acknowledged.
Appendix A The cone sensitivities of the budgerigar, the pigeon, the domestic fowl, and the domestic duck (Table A1).
Table A1 Spectral parameters of the ocular media, the oil droplets, the visual pigments and the predicted cone sensitivities in four species of bird. Budgerigar (Melopsittacus undulatus)
Pigeon (Columba livia)
Domestic fowl (Gallus gallus)
Domestic duck (Anas platyrhynchos)
314
337
351
371
411 429
448 470
443 460
445 456
507 526
513(539) 541(567)
505 523
506 516
566 592
586 613
561 586
561 576
Visual pigments (kmax) SWS1 SWS2 RH2 M/LWS
371 440 499 566
404 452 506 566
418 453 507 571
426 456 501 570
Calculated cone sensitivity (kmax) UVS/VS SWS MWS LWS
374 452 536 604
406 481 547(565) 619
420 475 537 602
426 472 528 594
Ocular media kT0.5 Oil droplets C-droplet kcut kmid Y-droplet kcut kmid R-droplet kcut kmid
The oil droplets are denoted by the cut off wavelength (kcut) and the wavelength of 50% transmittance (kmid). Visual pigments and cone sensitivities are denoted by the wavelength position of maximum absorbance (kmax), and ocular media by the wavelength positions of 50% transmittance (kT0.5). Data come from Bowmaker and colleagues (1997; visual pigments and oil droplets of the budgerigar, the pigeon, and the domestic fowl) and Jane and Bowmaker (1988; ocular media, oil droplets, and visual pigments of the domestic duck). The values within brackets are for the pigeon dorsal retina (Bowmaker et al., 1997).
References Barber, C. L., Prescott, N. B., Jarvis, J. R., Le Sueur, C., Perry, G. C., & Wathes, C. M. (2006). Comparative study of the photopic spectral sensitivity of domestic ducks (Anas platyrhynchos domesticus), turkeys (Meleagris gallopavoo) and humans. British Poultry Science, 47, 365–374. Bennett, A. T. D., & Cuthill, I. C. (1993). Ultraviolet vision in birds: What is its function? Vision Research, 34, 1471–1478. Bowmaker, J. K., Heath, L. A., Wilkie, S. E., & Hunt, D. M. (1997). Visual pigments and oil droplets from six classes of photoreceptor in the retinas of birds. Vision Research, 37, 2183–2194. Cuthill, I. C., Bennett, A. T. D., Partridge, J. C., & Maier, E. J. (1999). Plumage reflectance and the objective assessment of avian sexual dichromatism. American Naturalist, 160, 183–200. Ebrey, T., & Koutalos, Y. (2001). Vertebrate photoreceptors. Progress in Retinal and Eye Research, 20, 49–94. Emmerton, J., Schwemer, J., Muth, I., & Schlecht, P. (1980). Spectral transmission of the ocular media of the pigeon (Columba livia). Investigative Ophthalmology and Visual Science, 19, 1382–1387. Goldsmith, T. H., & Butler, B. K. (2003). The roles of receptor noise and cone oil droplets in the photopic spectral sensitivity of the budgerigar, Melopsittacus undulatus. Journal of Comparative Physiology A, 189, 135–142. Goldsmith, T. H., & Butler, B. K. (2005). Colour vision of the budgerigar (Melopsittacus undulatus): Colour matches, tetrachromacy, and intensity discrimination. Journal of Comparative Physiology A, 191, 933–951. Goldsmith, T. H., Collins, J. S., & Licht, S. (1984). The cone oil droplets of avian retinas. Vision Research, 24, 1661–1671. Govardovskii, V. I., Fyhrquist, N., Reuter, T., Kuzmin, D. G., & Donner, K. (2000). In search of the visual pigment template. Visual Neuroscience, 17, 509–528. Govardovskii, V. I., & Zueva, L. V. (1977). Visual pigments of chicken and pigeon. Vision Research, 17, 537–543. Hart, N. S. (2001a). Variations in cone photoreceptor abundance and the visual ecology of birds. Journal of Comparative Physiology A, 187, 685–698. Hart, N. S. (2001b). The visual ecology of avian photoreceptors. Progress in Retinal and Eye Research, 20, 675–703. Hart, N. S. (2002). Vision in the peafowl (Aves: Pavo cristatus). Journal of Experimental Biology, 205, 3925–3935.
O. Lind, A. Kelber / Vision Research 49 (2009) 1939–1947 Hart, N. S. (2004). Microspectrophotometry of visual pigments and oil droplets in a marine bird, the wedge-tailed shearwater Puffinus pacificus: Topographic variations in photoreceptor spectral characteristics. Journal of Experimental Biology, 207, 1229–1240. Hart, N. S., Partridge, J. C., Bennett, A. T. D., & Cuthill, I. C. (2000). Visual pigments, cone oil droplets and ocular media in four species of estrildid finch. Journal of Comparative Physiology A, 186, 681–694. Hart, N. S., Partridge, J. C., & Cuthill, I. C. (1998). Visual pigments, oil droplets and cone photoreceptor distribution in the European starling (Sturnus vulgaris). Journal of Experimental Biology, 201, 1433–1446. Hart, N. S., Partridge, J. C., & Cuthill, I. C. (1999). Visual pigments, cone oil droplets, ocular media and predicted spectral sensitivity in the domestic turkey (Meleagris gallopavo). Vision Research, 39, 3321–3328. Hart, N. S., Partridge, J. C., Cuthill, I. C., & Bennett, A. T. D. (2000). 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). Journal of Comparative Physiology A, 186, 375–387. Hart, N. S., & Vorobyev, M. (2005). Modelling oil droplet absorption spectra and spectral sensitivities of bird cone photoreceptors. Journal of Comparative Physiology A, 191, 381–392. Håstad, O., Victorsson, J., & Ödeen, A. (2005). Differences in color vision make passerines less conspicuous in the eyes of their predators. Proceedings of the National Academy of Sciences of the United States of America, 102, 6391–6394. Herrera, G., Zagal, J. C., Diaz, M., Fernández, J., Vielma, A., Cure, M., et al. (2008). Spectral sensitivities of photoreceptors and their role in colour discrimination in the green-backed firecrown hummingbird (Sephanoides sephanoides). Journal of Comparative Physiology A, 194, 785–794. Huwaldt, J. A. (2005). Plot Digitizer 2.4.1. Freeware software distributed from (verified June 2008). Jane, S. D., & Bowmaker, J. K. (1988). Tetrachromatic colour-vision in the duck (Anas platyrhynchos L.): Microspectrophotometry of visual pigments and oil droplets. Journal of Comparative Physiology A, 162, 225–235. Kelber, A., Vorobyev, M., & Osorio, D. (2003). Animal colour vision – Behavioural tests and physiological concepts. Biological Reviews, 78, 81–118. Liebman, P. A. (1972). Microspectrophotometry of photoreceptors. In H. J. A. Dartnall (Ed.). Handbook of sensory biology (Vol. VII/1, pp. 481–528). Berlin: Springer. Lipetz, L. E. (1984). A new method for determining peak absorbance of dense pigment samples and its application to the cone oil droplets of Emydoidea blandingii. Vision Research, 24, 597–604. Lovy, D. (1996). WinDig 2.5. Department of Physical Chemistry, University of Geneva, Switzerland. Freeware software distributed from (verified June 2008).
1947
MacNichol, E. F. (1986). A unifying presentation of photopigment spectra. Vision Research, 26, 1543–1556. Maier, E. J. (1992). Spectral sensitivities including the ultraviolet of the passeriform bird Leiothrix lutea. Journal of Comparative Physiology A, 170, 709–714. Maier, E. J., & Bowmaker, J. K. (1993). Colour vision in the passeriform bird, Leiothrix lutea: Correlation of visual pigment absorbance and oil droplet transmission with spectral sensitivity. Journal of Comparative Physiology A, 172, 295–301. Martin, G. R., & Osorio, D. (2008). Vision in birds. In D. Masland & R. M. Albright (Eds.). The senses: A comprehensive reference (Vol. 1, pp. 25–52). San Diego: Academic Press. Palacios, A. G., Martinoya, C., Bloch, S., & Varela, F. J. (1990). Colour mixing in the pigeon – A psychophysical determination in the longwave spectral range. Vision Research, 30, 587–596. Palacios, A. G., & Varela, F. J. (1992). Colour mixing in the pigeon (Columba livia) II: A psychophysical determination in the middle, short and near-UV wavelength range. Vision Research, 32, 1947–1953. Partridge, J. C. (1989). The visual ecology of avian cone oil droplets. Journal of Comparative Physiology A, 165, 415–426. Prescott, N. B., & Wathes, C. M. (1999). Spectral sensitivity of the domestic fowl (Gallus g. domesticus). British Poultry Science, 40, 332–339. Schaefer, H. M., Schaefer, V., & Vorobyev, M. (2007). Are fruit colours adapted to consumer vision and birds equally efficient in detecting colourful signals? American Naturalist, 169, 159–169. Vorobyev, M. (2003). Coloured oil droplets enhance colour discrimination. Proceedings of the Royal Society of London B, 270, 1255–1261. Vorobyev, M., Brandt, R., Peitsch, D., Laughlin, S. B., & Menzel, R. (2001). Colour thresholds and receptor noise: Behaviour and physiology compared. Vision Research, 41, 639–653. Vorobyev, M., & Osorio, D. (1998). Receptor noise as a determinant of colour thresholds. Proceedings of the Royal Society of London B, 265, 351–358. Vorobyev, M., Osorio, D., Bennet, A. T. D., Marshall, N. J., & Cuthill, I. C. (1998). Tetrachromacy, oil droplets and bird plumage colours. Journal of Comparative Physiology A, 183, 621–633. Wilkie, S. E., Vissers, P. M. A. M., Das, D., DeGrip, W. J., Bowmaker, J. K., & Hunt, D. M. (1998). The molecular basis for UV vision in birds: Spectral characteristics, cDNA sequence and retinal localization of the UV-sensitive visual pigment of the budgerigar (Melopsittacus undulatus). Biochemical Journal, 330, 541–547. Wright, M. W., & Bowmaker, J. K. (2001). Retinal photoreceptors of paleognathous birds: The ostrich (Struthio camelus) and rhea (Rhea americana). Vision Research, 41, 1–12. Yokoyama, S. (2000). Molecular evolution of vertebrate visual pigments. Progress in Retinal and Eye Research, 19, 385–419.
