0042~6989/89S3.00 + 0.00 PergamonPnss plc
VisionRes. Vol. 29, No. 12, pp. 1719-1727, 1989 Printedin Great Britain
TETRACHROMATIC COLOR VISION IN THE GOLDFISH BECOMES TRICHROMATIC UNDER WHITE ADAPTATION LIGHT OF MODERATE INTENSITY CHRISTA NEUMEYER and KARIN ARNOLD
Arbeitsgruppe III (Biophysik), Institut fur Zoologie, I. Gutenberg ~niv~rsit~t, Saarstr. 21, 6500 Mainz, F.R.G.
(Received 24 May 1989) Abstract-Spectral sensitivity of the goldfish was measured under white room light of 5 Ix and 1.5 Ix illuminance, using a behavioral training technique. Compared with the result obtained under 251x (Neumeyer, 1984), the functions differed remarkably in the mid- and longwave spectral ranges. Under I.5 lx, the longwave maximum was absent, and wavelength discrimination was impossible in the mid- and iongwave range (between 555 and 663 nm). This indicates that the longwave cone type does not contribute to color vision in these conditions. Since ~~~rnina~on ability was not affected in other spectral ranges, we conclude that color vision is trichromatic then, being subserved by the ultraviolet, the short- and the midwave cone types only. Under 5 lx, the longwave cone type contributes to color vision, but, as shown in color mixture experiments, to a lesser extent. Goldfish Color vision Light adaptation
Spectral sensitivity
Tetrachromasy
INTRODUCTION
Spectral sensitivity functions measured in the goldfish with different behavioral techniques have yielded very different results (for a review see Jacobs, 1981). Even when the same training technique was used in which the fish had to discriminate between an illuminate test field and a dark test field, different functions were obtained: in a measurement performed by Yager (1967), a rather broad function was found with highest sensitivity in the shortwave range. In our own experiment (Neumeyer, 1984), a function with three pronounced maxima was obtained when measured in the spectral range between 400 and 720nm. A fourth maximum was found in the ultraviolet range around 360 nm which was attributed to a fourth, ultraviolet sensitive cone type (Hawryshyn & Beauchamp, 1985; Neumeyer, 1985). A comparison with the spectral sensitivity functions of the cone types indicated that the ~haviorally obtained function can be explained by the envelope of the cone sensitivity functions which are modified by mutual inhibitory interactions between the different, spectrally adjacent, cone mechanisms. This was supported by measurements under chromatic adaptation and by model computations
Wavelength discrimination
(Neumeyer, 1984, 1988). The result obtained by Yager (1967), on the other hand, was explained by a summation model of the cone sensitivities. We assumed: that the different results in the two experiments could be due to the different state of adaptation under which the measurements were performed: in Yager’s experiment a tungsten-white adaptation light was used which was switched off whenever the test field stimulus was presented. This could have driven the fish into an adaptation state “lower” than in our experiment, in which a neon-white room illumination of 25 lx was present during the entire measurement. The inhibitory interactions concluded from the measurements of spectral sensitivity under 25 lx (Neumeyer, 1984) not only shift the maxima and steepen their limbs but also reduce sensitivity in absolute terms. Therefore, they should be of advantage only under a relatively “high” level of light adaptation. Under reduced intensities of overall light, the inhibitor interactions should be weaker or even absent. Then, the behaviorally measured spectral sensitivity functions would show a course which could be explained on the basis of the (unmodified) cone sensitivity functions, or even by their sum, as proposed by Yager (1967).
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CHRISTANEUMEYER and KARIN ARNOLD
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To test this possibility, we performed measurements of spectral sensitivity with the same behavioral method as in the previous experiment (Neumeyer, 1984) but in the presence of a white room light of reduced illuminance of 5 and 1.5 lx. (As in the other experiments, the measurements do not include the ultraviolet range.) We expected that a decrease of overall light intensity to values of 5 and 1.5 Ix should (1) increase absolute sensitivity, and (2) change the shape of the function compared with the function obtained under 25 lx. To get insight into the physiological basis underlying the obtained spectral sensitivity functions, measurements of wavelength discrimination and color mixture experiments were also performed. MATRR~~
(I)
AND METHODS
Animals
Nine goldfish (4-7 cm) were trained; they were not the same individuals as in the previous measurement under 25 lx (Neumeyer, 1984). Different individuals were also used in the measurements of spectral sensitivity, wavelength discrimination and color mixture, respectively. The fish were kept at room temperature (20-24”C), and under natural daylight (with the exception of the experimental sessions). (2) Room illumination One or two neon tubes (Osram-L, 40 W/19, 5000 de luxe) illuminated the tanks indirectly, and gave illuminances of 5 and 25 lx, respectively. To obtain 1.5 lx, one tube was used and masked in part with black cardboard. Light measurement was performed by directing the detector head of the photometer (EG & G, 550-I) towards the ceiling just above the tanks. Due to the reflections at the white side walls and the dark grey food plate at the rear side of the tank, the illuminance inside the tank had values which were, on the average, about 1 log unit below the illuminance measured at the surface of the tank. (3) Experimental setup and procedure la) measurements of spectral se~itivity. Apparatus and procedure were the same as in the measurement under 25 lx white room light (Neumeyer, 1984). Three goldfish were trained to swim to the unilluminated test field, while the comparison test field was illuminated with
monochromatic light of adjustable wavelength and intensity. The relative frequency with which the two test fields were chosen was recorded. Seventy-five per cent relative choice frequency was used as the threshold criterion. The fish were adapted to the white room light (1.5 and 5 lx) for at least 15 min prior to each experiment. It was present during the entire experimental session (l-2 hr) during which 3-6 “measurements” were performed. In each measurement 100 “choices”, each consisting in a “bite” at the test field, were collected. Here, the monochromatic light was shown at one of the two test fields for ca 2 min during which the fish made 25 choices while summing around freely. Then, a small amount of the food paste was given as a reward through the feeding tube directly at the (dark) training test field. After a delay period of 1-2 min, in which both test fields were dark, the monochromatic light was shown at the other test field. Then, another 25 choices of the fish were registered before the reward was given, and so on. As a total of 50 choices was counted at each side, a possible side preference of the fish did not affect the data. (6) measurement of wa~eIength discrimination. Wavelength discrimination was measured for only a few training wavelengths (621, 555, 501 and 404 nm). The same procedure as described in detail by Neumeyer (1986) was used. The measurement was performed under a white room illumination of 5, 1.5 and, for comparison, 25 lx. The two monochromatic lights were presented at equal subjective “‘brightness” (stimulus efficiency). The intensities corresponded to the values obtained in the measurements of spectral sensitivity under 5 and 1.5 lx (i.e. the intensities given in quanta/cm2sec at which, for example in Figs 1 and 2, 80% choice frequency was reached). The values for 25 lx were taken from Neumeyer (1984). The fish were trained on one of the wavelengths given above and tested against adjacent wavelengths. A relative choice frequency of 70% was used as the threshold criterion. (c) Color mixture experiment. This experiment was performed under 5 lx room illumination, and, for comparison, under 25 lx. The goldfish were trained on wavelengths 584, 599 and 608 nm, respectively. An additive mixture of green (523 nm) and red light (641 nm) was shown on the comparison test field and the specific mixture proportion was determined at which a match, i.e. a choice frequency of 50%, was obtained. The intensities of the
Goldfish color vision
intensity range of about 1 log unit. The slope of the curves obtained for the various wavelengths was approximately constant and was the same as that obtained in the previous measurement under 25 lx (Neumeyer, 1984, Fig. 3). The amount of quanta/cm’s at which the threshold criterion of 75% choice frequency was reached is shown as a function of wavelength in Fig. 3 for 5 lx, and in Fig. 4 for 1.5 lx room light. For comparison, the result obtained under the 25 lx room illumination (open circles) is also given. The position of the s~o~r~uve maximum was at 470 nm under 5 lx (Fig. 3), as well as under 1.5 lx (Fig. 4). It was the same as under 25 lx. Absolute sensitivity at 470 nm increased, as expected, with decreasing room illumination, for a total of about 0.7 log units (between 25 and 1.5 lx, Fig. 4.). The position of the midwave maximum shifted from 540 to 555-584nm when room illumination was decreased from 25 lx to 5 lx (Fig. 3). Sensitivity was high in this range, where a minimum had been found under 25 lx. Absolute
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Fig. I. Choice behavior of fish G, under 5 Ix room illumination. Ordinate: relative choice frequency (per cent) at which tbe unill~inat~ (turning) test field was chosen. Abscissa: log amount of quanta x cme2 x see-’ of the monochromatic light presented on the comparison test field. Threshold criterion: 75% choice frequency. Parameter of the curves: wavelength of light incident on the comparison test field. Each data point stands for 100 choices by the fish.
monochromatic lights used in the mixture were first adjusted according to the approp~ate spectral sensitivity function. In the mixture, the primaries (523 and 641 nm) varied between 10 and 90% of the total, and always added up to 100%. The monochromatic light was attenuated by neutral density filters (type NG, Schott & Gen). The actual mixture proportions were determined by measuring the amount of quanta/cm2s of the two components separately with a radiometer (EC & G, 550-l). RESULTS [I)
Spectral sensitivity
Figures 1 and 2 show examples of the choice behavior of one fish. Relative choice frequency increased from 50% to about 90% within an
_I
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Fig. 2. Choice behavior of the same fish under 1.5 lx room illumination. (Details as in Fig. 1.)
CHRISTANEUMEYERand
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Fig. 3. Log spectral sensitivity under 5 Ix room light. Ordinate: log amount of quanta x cm-* x set-’ at which the threshold criterion of 75% choice frequency was obtained. (a) G6, (A) G,, (m) G,, the black line connects the mean values of all results; open symbois: results obtained under 25 lx room illumination,from Neumeyer(1984).
sensitivity was about 0.5 log units higher than the midwave maximum obtained under 25 lx. Measured under 1.5 lx room illumination, location and absolute sensitivity coincided with the maximum under 25 lx (Fig. 4). Thus, on decreasing the intensity level of the adaptation light, absolute sensitivity first increased between 25 and 5 lx, but then unexpectedly decreased between 5 and 1S lx. In the longwave range, absolute sensitivity under 5 lx was the same as under 25 lx, and more than 0.5 log units below the sensitivity in the midwave range (under 5 lx). The maximum was not as pronounced as under 25 lx, and was shifted to 640 nm (Fig. 3). Under 1.5 lx room illumination (Fig. 4), the result was even more surprising: there was no maximum at all in the longwave range. Sensitivity decreased continuously from the midwave maximum at 540 nm towards longer wavelengths. At 650 nm, absolute sensitivity was approximately 1 log unit below the value found under 25 lx.
KARINARNOLD
is also possible that the longwave cone types are still involved albeit to an extent not strong enough to be reflected in the sensitivity function. To decide between these two possibilities, we measured the ability of wavelength discrimination in the long- and midwave spectral range. Discrimination should not be possible if only the midwave cone type is active. Figure 5a shows the choice behavior of fish G,, which was trained on wavelength 621 nm. Training wavelength and comparison wavelengths were adjusted to equal brightness according to the spectral sensitivity functions measured under the corresponding room illuminations. Under 25 lx (black symbols), the fish chose the training wavelength 621 nm with a relative choice frequency of about 80% when wavelength 570 nm was given for comparison. In the same test, performed under 5 Ix room illumination, choice frequency was significantly lower, with a value of less than 70% (blackwhite symbols). Under 1.5 lx, however, choice frequency measured for these wavelengths was 50% which indicates that the fish was not able to discriminate between 621 nm and 570 nm. Only when tested against 540 nm or, more clearly against 523 nm, was the fish able to discriminate. The corresponding result was found for fish G,, (Fig. 5b) which was trained on 555 nm and tested against longer wavelengths. -
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(2) Wavelength discrimination The gradual decrease of 540 nm towards the longwave trum found under 1.5 lx might the sensitivity of the midwave
sensitivity from end of the specbe entirely due to cone type. But it
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hlnml Fig. 4. Log spectral sensitivity under 1.5 Ix room light. Symbols as in Fig. 3.
Goldfish color vision
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Fig. 5. Wavelength discrimination in the mid- and longwave spectral range measured under the three different room illu~nations. Ordinates: relative choice frequency in per cent. (a) Fish G,, trained on wavelength 621 nm, and tested against shorter wavelengths. (b) Fish G,, trained on wavelength 555 nm, and tested against longer wavelengths. Mean values and standard deviations of 3-4 measurements, each with 100 choices per fish.
choice frequency was around 50% between 555 nm and all longer wavelengths, up to 663 nm, tested. Thus, under a room illumination of 1.5 lx, the goldfish were not able to discriminate between wavelengths which appear to a human observer as “red” and “green”. To see whether in other
spectral ranges wavelength discrimination was possibfe, corresponding measurements were performed for training wavelengths 501 nm and 404 nm, which are located in the ranges of best wavelength discrimination ability (Neumeyer, 1986). Figure 6 shows the results for the two fish tested. Here, choice behavior did not differ
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Fig. 6. Wavelength discrimination in the short- and midwave spectral range measured under the different room illuminations. Above: training wavelength 404 nm tested against longer wavelengths; below: training wavelength 501 nm tested against longer and shorter wavelengths. As in Fig. 5.
CHRISTANEUMEYERand KARIN
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significantly under the three room illuminations and indicated an unaltered high discrimination ability. (3) Color mixture experiment Under 5 lx room illuminance, wavelength discrimination in the range of 600 nm was still possible but not so good as under 25 lx. This could be due to a reduced sensitivity of the longwave cone type in relation to the midwave one. A reduced sensitivity should also be
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ARNOLD
reflected in the result of a color mixture experiment: if trained on a wavelength in the range between 540 and 621 nm and tested against additive color mixtures of 523 and 641 nm, matches should be found at mixture proportions which contain relatively less 641 nm light than the corresponding mixtures under 25 lx. Figure 7 shows the choice behavior when the fish was trained on wavelength 608, 599 or 584 nm and tfsted against additive mixtures of 523 and 641 nm light. The mixture proportions were tested in the sequence indicated by the arrows in Fig. 7: the tests started with a mixture containing more 523 nm than 641 nm light, and continued by reducing the amount of 523 nm in favor of 641 nm. The first intersection of the relative choice frequency with the 50% confusion line gave the mixture proportion which, for the fish, was subjectively equal to the training wavelength. The mixture proportions at which the match was obtained are listed in Table 1 and are compared with the corresponding results of measurements performed under 25 lx room illumination (from Neumeyer, in preparation). For fish G,, which was tested under both conditions, we found that, under 5 lx, less red light was necessary to obtain the match than under 25 lx. This indicates that the longwave cone mechanism was less sensitive under 5 lx than under 25 lx. Fish G,* with which the measurement under 25 lx had been performed was not available any longer so that fish G,, was used for the measurement under 5 lx. The results of this fish are similar to those of G,, only for 608 nm, the other values are larger. As the values of G,,, and G,, under 25 lx show remarkable individual differences, a comparison of two different fish under different conditions is not very conclusive. Table 1. Relative proportion of red light (641 nm) in per cent in the additive mixture of red (641 nm) and green (523 nm) light which, for the fish, was subjectively equal to the training wavelength. Measurements were performed under 5 lx, and for comparison, under 25 Ix white room illumination
100 0
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Fig. 7. Choice behavior of fish G,, in the color mixture experiment under 5 lx room light. Ordinates: relative choice frequency in per cent with which the training wavelength was chosen. Abscissa: relative mixture proportion of green (523 nm) and red (641 nm) light. Arrow: sequence in which the mixtures were presented during one experimental session. Vertical lines: mixture proportions at which 50% choice frequency was reached; x,: mean values of the proportion of red light. One point represents 100 choices.
Training wavelength (nm)
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Fish
5 Ix
Fish
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10% 37% 49% 87%
G,, G,, G,, G,,
15% 39% 54%
GUI G,, G,, G,,
570 584 599 608
14% 52% 60% 82%
G,* G,, G,, G,,
26% 39.5% 67% 53%
G,, G,, G,, G,,
Goldfish color vision DisCUsSION
(a) The effect of reduced room light intensity on spectral sensitivity and wavelength discrimination The spectral sensitivity function obtained under a white room illumination of 25 lx was described by the envelope of cone sensitivity functions which are modified by inhibitory interactions (Neumeyer, 1984). Under reduced intensities of ambient light, we had expected that the spectral sensitivity function would be changed in such a manner that it reflected the unmodified cone sensitivity functions either as the envelope or as the sum. This, however, was not the case. In the shortwave range, but only there, a narrow, pronounced maximum was found, located at 470 nm in all adaptation conditions (Figs 3 and 4). This indicates unaltered inhibitory interactions which consist in an inhibition of the shortwave cone mechanism by the ultraviolet as well as by the midwave cone mechanisms (Neumeyer, 1988). Before it was known that there is an ultraviolet receptor in the goldfish (Neumeyer, 1985; Hawryshyn 1985), more complicated, & Beauchamp, nonlinear interactions had to be assumed (Neumeyer, 1984). Absolute sensitivity in the shortwave range changed in the expected manner showing increasing sensitivity as overall illumination decreased. In the mid- and longwave spectral range, shape and location of maximal sensitivity were different under the different states of adaptation, but the changes were not in line with our expectations. Most surprising was the finding that under I.5 lx the longwave maximum was entirely missing (Fig. 4). In this range, absolute sensitivity was about 1 log unit lower than under 5 or 25 lx, and not higher as a “normal” adaptation behavior would suggest. In the midwave range, position and absolute sensitivity of the maximum were about the same under 1.5 lx as under 25 lx room illumination, with the longwave limb being less steep. We assume that the shape of this maximum is due to the midwave cone mechanism being inhibited by the shortwave cone mechanism but not by the longwave one. Under 5 lx, the midwave maximum was slightly shifted towards longer wavelengths, which might be explained by assuming an increased inhibition by the shortwave cone mechanism. The midwave maximum was much broader than under 25 lx. Its longwave limb follows the course of the midwave cone sensitivity function, which indicates that, similar to
1725
the result under 1.5 lx, there is no inhibition by the longwave cone process. The finding that, under 1.5 lx, the fish were not able to discriminate wavelengths in the range between 555 nm and 663 nm (Fig. 5) indicates that the longwave cone type does not contribute to color vision under this state of adaptation. Since, in the spectral regions around 5OOnm and around 400nm, wavelength discrimination was as good as under 25 lx (Fig. 6), we conclude that color vision under 1.5 lx is only trichromatic, subserved by the ultraviolet, the short- and the midwave cone types. It is then similar to the color vision of the honeybee (von Helversen, 1972). Under a room ill~ination of 5 lx, the longwave cone mechanism contributes to color vision, but to a lesser extent than under 25 lx. This can be concluded from the findings that (1) wavelength disc~mination was possible but not as good as under 25 lx, and (2) that in the color mixture experiment (Fig. 7) less red light (by a factor of 0.4-0.8) was necessary to obtain the match. This can be explained by assuming that the longwave cone mechanism was less sensitive than the midwave one by this factor, as is also indicated by a comparison of the relative ~nsitivities at 5 and 25 lx in Fig. 3. Thus, the contribution of the longwave cone mechanism to color vision, which is absent at 1.5 lx gradually increases at higher states of light adaptation. The spectral sensitivity functions obtained in no case resemble the broad sensitivity curve obtained by Yager (1967) in a similar measurement. Therefore, a difference in the state of light adaptation cannot provide an explanation for the different results. Instead, we assume that the difference in the training procedure is decisive: in our experiments, the fish were always trained to swim to the dark test field, while the illuminated one was given for comparison (the advantages of this method are discussed in Neumeyer 1984); in Yager’s measurement, the fish were trained on the illuminated test field. As shown recently, the two methods yield remarkably different results (Neumeyer, in preparation), indicating that the fish uses different criteria for discrimination in the two cases. {b] comparison with morpho~agica~and electrophysiological findings As the photoreceptors themselves increase in sensitivity within certain limits when ambient light intensity is reduced, we must assume that
1726
CHRISTANEUMEYERand KARIN ARNOLD
the observed sensitivity loss of the longwave mechanism is due to changes in the neural circuitry. In the following we discuss first the effects of dark adaptation on color opponency at the level of ganglion and horizontal cells in the retina as known from electrophysiological and neuroanatomical investigations. Secondly, the interactions between rods and cones are taken into account. Retinal ganglion cells in goldfish that were characterized as R/G-double opponent in the light-adapted state lost their opponency after prolonged dark adaptation (Raynauld, Laviolette & Wagner, 1979). This was accompanied by interesting morphological changes at the synaptic terminals of horizontal cells within the cone pedicles. The horizontal cell dendrites located laterally to the synaptic ribbons show finger-like extensions (the so-called “spinules”) in the light-adapted state. During dark adapthese structures disappear almost tation, completely. This was found in cyprinid and other teleost fishes but not in other vertebrates (Raynauld et al., 1979; Wagner, 1980). The reduction in the number of spinules runs parallel with a change in the response behavior of the horizontal cells in the dark-adapted state. Biphasic H,-horizontal cells, which respond with hyperpolarization to light in the short- and midwave range and with depolarization to light in the longwave range, showed this opponency only in the light-adapted state: in the darkadapted state the cells were monophasic and responded with hyperpolarization only (Weiler & Wagner, 1984; Djamgoz, Downing, Prince & Wagner, 1985a; Djamgoz, Downing & Wagner, 1985b; Djamgoz, Downing, Kirsch, Prince & Wagner, 1988; Kohler, Rambold, Wagner & Weiler, 1986). According to a model by Lipetz (1978) which is based on the dynamic properties of horizontal cell responses reported by Spekreijse and Norton (1970) and supported by the anatomical findings of Stell and Lightfoot (1975) and Stell, Lightfoot, Wheeler and Leeper (1973, the depolarizing response of the biphasic H,horizontal cells is due to a sign-inverting feedback activity of monophasic, mainly longwave driven H,-cells within the midwave cone pedicles. It is assumed that in the dark-adapted state, this inhibitory pathway is decoupled by the morphological changes in the synaptic terminals, so that the H, cells receive only the direct input from midwave cones (Djamgoz et al., 1988).
It is possible that the morphological and physiological changes at the horizontal cell level occur at an ambient illumination level of 1.5 lx. The “mesopic” illumination, under which the experiments of Djamgoz et al. (1985b) were performed, corresponded to a luminance about 1 log unit below the lowest level in our experiment. If the plasticity of the synaptic connections of the horizontal cells is indeed the reason for the changes in the contribution of the longwave cones to color vision, this would imply that the horizontal cell pathway is essential for color coding. It would mean that the input of the longwave cones into color vision does not take the direct pathway: longwave cones-bipolars-ganglion cells, but an indirect one: longwave cones-H 1 horizontal cellsmidwave cone pedicles-bipolars-ganglion cells. It seems that there is also a direct pathway for longwave cones which is not affected by the adaptation level. This longwave cone contribution, however, would not play a role in color vision but in other visual functions such as perception of lightness. This view is supported by recent behavioral experiments (Neumeyer, in preparation), and also by a measurement of spectral sensitivity using the method of classical conditioning which revealed longwave cone contribution even in the dark-adapted state (Powers & Easter, 1978). As the lowest adaptation level of 1.5 lx may be regarded as a “mesopic” state in which cones as well as rods are active, it is possible that the missing longwave cone contribution at low light levels can be explained alternatively on the basis of rodcone interactions. In cyprinid fish, there is no evidence that cones are inhibited indirectly by rods as is the case in mammals. Instead, the activities of the two subsystems seem to be separated by retinomotoric movements. Simultaneous activities of rods and cones are to be expected only in an intermediate state in which rods as well as cones are not covered by the pigment epithelium. In recordings from opponent ganglion cells in the isolated retina, the center response showed the same sign for rods in the dark-adapted state as for longwave cones in the light-adapted state (Raynauld, 1972). As rods have essentially the same spectral sensitivity as midwave cones but contribute to opponent ganglion cells with opposite sign, the “longwave” response characteristics in the light-adapted state might be transformed into a “midwave” one in the dark-adapted state. This would be in line with our behavioral results
Goldfish color vision
under 1.5 lx. However, it is unclear which response behavior we may expect at intermediate adaptation levels corresponding to 5 lx. Here, rod and midwave cone contribution should cancel each other out which might lead to a decreased midwave sensitivity. This was not observed in our experiments. To decide whether the plasticity at the horizontal cell level or the activity of rods is responsible for the decreasing longwave cone contribution at low adaptation levels, electrophysiological recordings from retinal ganglion cells under different states of adaptation are being performed at present. The functional significance of decoupling the longwave cone type from the color vision system under conditions of reduced overall light is not clear. Perhaps it improves the signal-to-noise ratio under these conditions. The biological significance might be seen in context with the changes in the spectral distribution of natural daylight: in twilight (before sunrise or after sunset), daylight contains relatively more ultraviolet and shortwave light than mid- and longwave light (McFarland & Munz, 1975). Reduced light intensities in combination with a shift of spectral composition towards shortwave light also occur in water as the depth increases. are very grateful to M. B. A. Djamgoz for critically reading the manuscript, and to N. Beckhaus for improving the English. Part of this work has been reported in the Habilitationsschrift: Ch. Neumeyer, Das Farbensehen des Goldfisches. Thieme Verlag, 1988. The study was financially supported by Deutsche Forschungsgemeinschaft (Ne 215/3-5).
Acknowledgements-We
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