The angular range of achromatic target detection by ... - CiteSeerX

J Comp Physiol A (1998) 183: 101 ± 110

Ó Springer-Verlag 1998

ORIGINAL PAPER

M. Giurfa á M. Vorobyev

The angular range of achromatic target detection by honey bees

Accepted: 23 February 1998

Abstract Honeybees Apis mellifera were trained to enter a Y-maze and choose the arm with a rewarded disc presented against a grey background. The alternative arm displayed the unrewarded grey background alone. Training and testing were performed with the rewarding disc subtending di€erent visual angles. The training disc was either achromatic and provided green contrast, or chromatic and provided the same amount of green contrast as the achromatic one. The bee-achromatic disc could be learned and detected by the bees whenever it subtended 5° or 10°, but not if it subtended 30°. The chromatic disc was learned well and detected at all three visual angles. However, at 5° the maximum level of correct choices was ca. 75% with the achromatic disc whilst it was ca. 90% with the chromatic one. Thus, the presence of chromatic contrast enhances considerably the level of correct choices for the same amount of green contrast. The lower threshold of achromatic target detection lies between 3.7° and 5°; the upper threshold between 15° and 10°. At the upper threshold, detection switches from chromatic-based to achromatic-based. Thus, in the context of target detection, the achromatic green contrast channel specialises in the detection of objects of reduced angular size, whilst the chromatic channels are specialised for objects of large angular size. We suggest that achromatic detectors with a centresurround organisation are involved in the task of detecting achromatic targets. Key words Honeybee á Vision á Detection á Green contrast á Receptive ®elds

M. Giurfa (&) á M. Vorobyev Institut fuÈr Neurobiologie, Freie UniversitaÈt Berlin, KoÈnigin-Luise-Strasse 28/30, D-14195 Berlin, Germany Tel.: +49-30 838-3247; Fax: +49-30 838-5455 e-mail: [email protected]

Introduction For the detection of coloured stimuli, honeybees make use of their colour vision system (Lehrer and Bischof 1995; Giurfa et al. 1996) as well as an achromatic visual system based on the long-wave photoreceptor type (Giurfa et al. 1996, 1997). The minimum visual angle required for detection of a coloured stimulus is ca. 15° if the stimulus presents chromatic contrast but no contrast to the long-wave photoreceptors (henceforth ``green contrast'') (Giurfa et al. 1996), whilst it is ca. 5° if it presents both kinds of contrast (Lehrer and Bischof 1995; Giurfa et al. 1996). A stimulus which does not present chromatic contrast but o€ers green contrast is not learned at a visual angle of 30° (Giurfa et al. 1996). Both the chromatic and achromatic green-contrast systems are alternatively used depending on the visual angle subtended by the targets at the bee's eye (Giurfa et al. 1997). At larger visual angles (>15°) bees use the chromatic properties of the targets; at smaller angles (5°) they use of achromatic green contrast of the targets against the background. Thus, the achromatic cue provided by green contrast enlarges the detection range of a coloured target but is not used at larger visual angles. We suggested two hypotheses to explain why bees are unable to use the green contrast to detect a large stimulus. The ®rst hypothesis, called the ``Facilitation Hypothesis'' (Giurfa et al. 1996), referred to the learning phenomena that may have been involved in the detection context in which bees were trained and tested. It postulates that the weak sensory cue of green contrast would be learned only through the more salient cue of chromatic contrast. At large visual angles, the primary association between chromatic contrast and reward might push the weak green-contrast cue above threshold so that it becomes the guiding cue for the choice behaviour of bees at smaller visual angles in which chromatic cues are no longer available. The second hypothesis, called the ``Angular-Size Tuning Hypothesis'' (Giurfa et al. 1997), referred to the

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sensory level and the spatial properties of the visual elements involved in the detection performance. It postulates that the green-contrast channel and the colourcontrast channel di€er in their angular-size tuning so that the chromatic channel does not convey information about objects of reduced angular size and the greencontrast channel does not convey information about objects of large angular size. This would explain why, at large visual sizes, green contrast is ignored, whilst it is learned and used for discrimination at small visual sizes. In the present work we tested these hypotheses by training bees to a bee-achromatic stimulus having green contrast. If bees were not able to learn the presence of the achromatic stimulus at any visual angle, chromatic contrast is necessary for detecting a coloured target independently of its visual angle. Chromatic contrast would act as a facilitating cue, allowing the learning of green contrast. This would support the ``Faciliation Hypothesis''. However, if bees can learn the presence of the achromatic stimulus within a range of small visual angles, the green-contrast and the chromatic-contrast channels have di€erent angular-size tuning. This would support the ``Angular-size Tuning Hypothesis''. Moreover, if the latter hypothesis is correct, it is also possible to determine precisely the threshold angle at which bees start to use the green contrast of targets, i.e. to detect the presence of the bee-achromatic stimulus Fig. 1 View of the decision chamber of the Y-maze apparatus. Arms had movable back walls. The decision between the arm with the training disc and that with the background alone could only be made by the bee after it has entered the decision chamber, from which the back walls of both arms could be viewed simultaneously. A choice was counted when the bees crossed the imaginary line leading from the decision chamber to one arm. The decision point was de®ned as the point being in the middle of the decision chamber. Visual angles a correspond to the distance D of the target to this point. Since the bees could make their decisions either from the maximal distance D1 or from the minimal distance D2 , each angle a is given with its respective angular range (a1 ; a2 ) calculated on the basis of D1 and D2, respectively (a1 < a < a2 )

providing green contrast. More speci®cally, it is possible to characterise the properties of the receptive ®elds of the achromatic detectors operating in this behavioural context by ®nding their lower and upper angular thresholds.

Materials and methods Experimental setup Individually marked honeybees, Apis mellifera carnica, were trained to enter a Y-shaped, dual-arm apparatus (see Giurfa et al. 1996, 1997) to collect 50% (weight/weight) sucrose solution. The apparatus was placed close to an open window of the laboratory, so that it was illuminated by natural day light. The arms had movable back walls (20 cm ´ 20 cm) covered by a grey, achromatic paper. In one of the arms, termed positive, a training disc (8 cm in diameter) was presented ¯at against the grey background. A bee entering this arm received a reward of sucrose solution at this disc. The reward was provided by an injecting pump mounted behind the back wall. The alternative arm, termed negative, displayed the grey background alone and o€ered no reward. The training disc was presented alternately, in a pseudo-random succession, in the right or the left arm, to ensure that bees did not associate the reward with a particular arm. The decision between the two arms could only be made by the bee after it had entered the decision chamber, from which the back walls of both arms could be viewed simultaneously. Thus, the distance of the bee to the stimulus, and therefore the visual angle subtended by the latter at the bee's eye as viewed from the decision point, could be controlled for. A choice was counted when the bees crossed the imaginary line leading from the decision chamber to one arm (Fig. 1). We de®ned the decision point as the point being in the middle of the decision chamber (Giurfa et al. 1997). Visual angles a correspond to the distance D of the target to this point (Fig 1). Since the bees could make their decisions either from the maximal distance D1 or from the minimal distance D2, representing the limits of the decision chamber, each angle a is given with its respective angular range (a1, a2) calculated on the basis of D1 and D2, respectively. Thus, a1 < a < a2. Stimuli and background The training disc and the background were cut out of HKS-N pigment papers (K + E Stuttgart, Stuttgart-Feuerbach, Germa-

103 ny). The training stimulus was cut either from human-pink HKS21N or human-green HKS-60N paper. The grey background was cut from HKS-92N paper. Spectral re¯ectances of the stimuli and background were measured with a ¯ash photometer (SR01, GroÈbel UV-Elektronik, resolution 1 nm) and calibrated against a BaSO4 white standard. Figure 2 shows the spectral re¯ection curves of stimuli and background and their loci in the colour-opponent-coding diagram of the honeybee (Backhaus 1991, 1993). This diagram allows the perceptual di€erence between pairs of colours to be read as the sum of the absolute di€erences of the corresponding scale values on the two axes (according to a city-block metric). Receptor-speci®c contrasts and chromatic contrast of the training stimuli against the background were calculated (for explanation see Giurfa et al. 1997). Receptor-speci®c contrasts, i.e. the relative number of absorbed quanta q with respect to the background, were calculated as: R1 I…k†R…k†Si …k†dk qi ˆ R01 ; i = uv, blue, green receptor, …1† 0 I…k†B…k†Si …k†dk with I…k† being the spectral intensity distribution of the illuminating light (normlight function D65), R…k† the spectral re¯ectance of the stimulus, B…k† the spectral re¯ectance of the background and Si …k† the spectral sensitivity of the receptor with index i (Menzel and Backhaus 1991). Chromatic contrast between a stimulus, S, and the background (Back.) was calculated as: D…S; Back:† ˆ jAS j ‡ jBS j where AS and BS are the chromatic co-ordinates A and B of stimulus, S, in the colour-opponent-coding diagram of the honeybee (Backhaus 1991, 1993), de®ned as: X X qi qi Aˆ ai bi ; Bˆ ; …2† q ‡ 1 q ‡1 i i iˆu;b;g iˆu;b;g

Fig. 2a, b Stimuli and background used. a Spectral re¯ection curves of the training discs and background. b Loci of the training stimuli and background in the color opponent coding diagram. The diagram represents the cell excitations of two types of colour opponent coding cells, A and B. The origin (Back.) represents the grey background. The closed line gives the loci of spectral colours in 10-nm steps, and the mixtures of 300 nm and 550 nm marked in 10% steps

with ai ˆ fÿ9:86; 7:70; 2:16g and bi ˆ fÿ5:17; ‡20:25; ÿ15:08g; i ˆ uv, blue, green receptor. Chromatic contrast (Lehrer and Bischof 1995; Giurfa et al. 1996) and green contrast (Giurfa et al. 1996, 1997) are the only cues that in¯uence the bees' performance in a detection paradigm like the one employed. Their values are given in Table 1. Both training stimuli di€ered in their chromatic contrast: the human-pink stimulus (HKS-21N) was achromatic to the bees, whilst the humangreen stimulus (HKS-60N) was chromatic to them. Both provided the same receptor speci®c green contrast value (Table 1) which was above detection threshold (Giurfa et al. 1996). Procedure Each experiment began by training a group of individually marked foragers to enter the Y-maze to collect sucrose solution. During training and tests only one experimental bee was present at a time in the apparatus. Recruited bees were excluded by closing the sliding access door. We recorded only the ®rst choice on each visit, because every further choice might be in¯uenced by the outcome of the previous one. The training disc was often replaced by a new one to exclude the use of olfactory cues. Every time the bee chose the arm with the training disc, it was rewarded and the choice counted as correct. If the bee chose the arm with the background alone, the choice was counted as incorrect and the bee was immediately tossed away from the maze. The bee would then enter the maze again, but its second choice was not noted. The visual angle of the training disc was changed by moving the back walls to a new position in the arms of the maze. Changing the distance between the decision point and the targets does not in itself a€ect the bees' performance, because performance depends only on the visual angle subtended by the training disc and not on alternative distance cues (Giurfa et al. 1996, 1997). In experiment 1 we asked whether the presence of a beeachromatic stimulus providing green contrast can be learned and detected by the bees depending on its visual angle. Two experimental schedules in which three visual angles were presented in ®ve successive phases were performed with two groups of bees: 1. The ®rst schedule started with achromatic training disc subtending an angle of 30° (i.e. at 15 cm from the decision point). In the second phase the back walls were moved for the training disc to subtend 10° (i.e. at 45 cm from the decision point). In the third phase the disc subtended 30° again. In the fourth phase the visual angle of the disc was reduced to 5° (i.e. at 85 cm from the decision

104 Table 1 Characteristics of the background and training stimulus used in the present study. Chromatic coordinates in COC space (Backhaus 1991), chromatic contrast, and receptor-speci®c contrasts for the three receptor types, ultraviolet (UV), blue (B) and green (G) Chromatic coordinates A Background Bee-achromatic disc (HKS-21N) Bee-green disc (HKS-60N)

0 )0.06 0.5

Chromatic contrast (COC units) B 0 0.04 )5.2

Receptor speci®c contrast (absorbed quanta relative to the background) UV

B

G

0 0.1

1 2.5

1 2.4

1 2.4

5.7

0.6

0.6

2.4

point), and in the ®fth and last phase, it was increased to 30° again. Thus, the experimental situation with the visual angle of 30° constituted a control for the bees' performance at other visual angles. Six bees were tested with this experimental schedule. 2. The second schedule started with the achromatic, training disc subtending 5° (at 85 cm from the decision point). In the second phase the disc subtended 10° (at 45 cm from the decision point). In the third phase its visual angle was again reduced to 5°. In the fourth phase it was increased to 30° (at 15 cm from the decision point), and in the ®fth and last phase it was reduced to 5° again. Thus, the experimental situation with the visual angle of 5° constituted a control for the bees' performance at other visual angles. Four bees were tested with this experimental schedule. Since it was dicult to make the naive bees ¯y for the ®rst time into the positive arm if the rewarding stimulus was placed at 85 cm from the decision point, the back walls were ®rst placed at 15 cm from it; when the bees landed on the disc and found the reward for the ®rst time, the back walls were slowly moved to their ®nal position. Repeating this procedure two to three times was generally enough to make the bees ¯y towards the distant back walls at the end of the tunnel. The second experimental schedule was repeated with the chromatic green stimulus as training disc (i.e. sequence of: 5°, 10°, 5°, 30°, 5°). Five bees were tested. Since this stimulus had the same green contrast as the achromatic one tested above, the aim of this control experiment was to test if bee's performance changes with the addition of chromatic contrast. In experiment 2 we characterised more precisely the working range of the green-contrast detectors operating in this behavioural context by ®nding their lower and upper angular thresholds for the detection of the bee-achromatic training stimulus. To this end, a group of seven bees were presented with ®ve di€erent visual angles presented in sequence of nine experimental phases. The sequence was: 5° (disc at 85 cm from the decision point), 15° (30 cm distance), 5°, 10° (45 cm distance), 5°, 7° (65 cm distance), 5°, 3.7° (125 distance) and 5°. Again, the experimental situation with the disc subtending a visual angle of 5° constituted a control for the bees' performance at other visual angles. Statistics A binomial test was used to judge whether or not bees chose the arm with the training stimulus with a probability P0 > 0.6 (a ˆ 0.05). Each phase lasted until bees ful®lled this criterion; otherwise a maximum of 30 choices (i.e. 30 visits to the apparatus) was recorded for each phase. Since the same individuals were tested repeatedly over a period of time in both experiments, an analysis of variance (ANOVA) for repeated measurements was employed and comparisons between means were performed with a Newman-Keuls test modi®ed for repeated measurements (Winer 1971).

Results The working range of the achromatic detectors Experiment 1 shows that the bee-achromatic disc providing green contrast could be learned and detected by the bees whenever it subtended 5° or 10°, but not if it subtended 30° (Fig. 3; black bars). These results were independent of the particular sequence with which the di€erent subtended angles were presented, as shown by the comparison between the corresponding curves in Figs. 3b and 3d (black squares). Therefore, the percentage of correct choices signi®cantly varied with the experimental phase, i.e. with the visual angle subtended by the bee-achromatic, training disc (Fig. 3a: one-way ANOVA for repeated measurements: F ˆ 39.4, df ˆ 4, 20, P < 0.0001; Fig. 3c: F ˆ 5.3, df ˆ 4, 12, P ˆ 0.01). These results are consistent with the ®nding that at a visual angle of 30° subtended by the targets, the bees' choice behaviour is governed by the di€erences in chromatic properties, whilst at small visual angles it is governed by di€erences in the amount of achromatic green contrast (Giurfa et al. 1996, 1997). The control experiment performed with the chromatic, green training stimulus tested under the same experimental schedule yielded di€erent results. As expected from a stimulus presenting chromatic and green contrast (See Table 1), the training disc was well detected at any of the visual angles tested (Fig. 3c: empty bars; Fig. 3d: triangles). The percentage of correct choices did not vary with the experimental phase (Fig 3c: F ˆ 1.6, df ˆ 4, 16, NS), i.e. with the visual angle subtended by the green disc. However, comparing results of both the achromatic and the chromatic training stimuli (black versus empty bars in Fig. 3c; squares versus triangles in Fig. 3d, respectively) shows that the maximum level of correct choices was ca. 75% with the achromatic stimulus, whilst it was ca. 90% with the chromatic stimulus (twoway ANOVA for repeated measurements: factor stimulus: F ˆ 468.5, df ˆ 1, 7, P < 0.0001; comparisons between phases 1, 3 and 5 for both groups of bees: P < 0.05). This di€erence in the level of correct responses is noteworthy because at the visual angle of 5°, bees would see the same information both the achromatic and the chromatic stimuli since both had the same

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Fig. 3a-d Results of experiment 1. A bee-achromatic disc providing green contrast is learned and detected by the bees depending on its visual angle (black bars), whilst a chromatic disc presenting the same amount of green contrast is well learned and detected at any visual angle tested (empty bars). Means SE. a and c First and second experimental schedule, respectively. In both schedules the bees' performance (percentage of correct choices) was recorded during ®ve consecutive experimental phases where the visual angle of the training disc was varied. In the ®rst schedule a the visual angles were: 1 30°; 2 10°; 3 30°; 4 5°; 5 30° (n ˆ 6 bees). In the second schedule c both the achromatic (black bars) and the chromatic disc (empty bars) were tested; the visual angles were: 1 5°; 2 10°; 3 5°; 4 30°; 5 5° (achromatic disc: n ˆ 4 bees; chromatic disc: n ˆ 5 bees). The hatched line at 50% indicates a random choice. Values in parentheses indicate the number of bee choices. b and d Percentage of correct choices as a function of the visual angle of the achromatic stimulus, calculated from a and c, respectively. Squares: achromatic disc; triangles: chromatic disc. Horizontal bars represent the angular range (a1 ; a2 ) calculated for each angle tested (see Materials and methods)

amount of green contrast, and this is the cue that they would use. Experiment 2 established the lower and upper angular thresholds for the green-contrast detection system. In this experiment, the percentage of correct choices also varied signi®cantly with the experimental phase, i.e. with the visual angle subtended by the training disc (Fig. 4a: F ˆ 7.2, df ˆ 8, 16, P < 0.0005). Figure 4 shows that training with the disc subtending 5° and 7° yielded the highest level of correct responses

(75%), which is similar to the results of the previous experiment. On the other hand, bees could not detect the disc subtending 3.7°. Thus, the lower threshold lies between 3.7° and 5°. Training with a disc subtending 15° was also unsuccessful, as it was with 30° in the previous experiment. In this case, the bees' performance was close to random. At a visual angle of 10°, however, bees reached a 62% level of correct choices (similar to the results of the previous experiments), a level that was signi®cantly higher than random but lower than that reached at visual angles of 5° and 7°. Thus, the upper angular threshold at which bees ®rst detect the achromatic disc lies between 15° and 10°. Since stimuli providing chromatic contrast but no green contrast are detected down to a minimal visual angle of ca. 15° (Giurfa et al. 1996), the threshold angle we found corresponds to that at which switching from chromatic-based detection to achromatic-based detection takes place. A linear description of the receptive ®elds of the achromatic detectors Considering the particular angular characteristics of the achromatic detectors involved in this behavioural task, it is tempting to suggest that they have a centre-surround organisation as found in the receptive ®elds of mammalian retinal ganglion cells (Ku‚er 1953). Such de-

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Fig. 4a, b Results of experiment 2. The angular range of achromatic, green-contrast based, target detection system. Means ‹ SE (n ˆ 7 bees). a The bees' performance (percentage of correct choices) was recorded during nine consecutive experimental phases where the visual angle of the training disc was varied: 1 5°; 2 15°; 3 5°; 4 10°; 5 5°; 6 7°; 7 5°; 8 3.7° and 9 5°. b Symbols: percentage of correct choices as a function of the visual angle of the achromatic stimulus. Horizontal bars represent the angular range …a1 ; a2 † calculated for each angle tested (see Materials and methods). Line: ®t of the experimental data by a linear model that assumes that detection is mediated by units having centre-surround receptive ®elds described by Gaussian functions of equal size (see Appendix for explanations about the model)

tectors do not respond to large uniform stimuli, because the signal from the centre of the receptive ®eld is inhibited by the surround, but they are sensitive to the small stimuli and to the edges (Fiorentini et al. 1990). To test this hypothesis we compared the predictions of a simple linear model with our experimental results. A mathematical formulation of the model is given in the Appendix. The model is based on the following assumptions: 1. All neurones have equal sizes of receptive ®elds. 2. Centre and surround are described by Gaussian functions (Fig. 5a). 3. In the case of uniform stimulation, the response of the centre is fully inhibited by that of the surround. 4. The response of each neurone is a linear function of the receptor inputs (see Eq. A1 in Appendix). 5. The eciency of the stimulation is given by the average of the squares of the amplitude of responses of individual neurones (See Eq. A2 in Appendix). In the case of a circular stimulus, a simple expression relates the eciency of the stimulus, W, to the ratio of sizes of the centre, rc, and surround, rs, to the radius of

the stimulus, R (see Eqs. A8, A9 in Appendix). For the sake of simplicity we assume that the size of the surround is twice that of the centre, that is rs ˆ 2rc (see Fig. 5a). Thus, the size of the receptive ®eld is given by only one parameter, namely the size of the centre of the receptive ®eld, rc, which can be estimated from experimental results. The best performance, i.e. the maximal percentage of correct choices, corresponds to the maximum eciency of the stimulus. Such an eciency is shown in Fig. 5b as a function of the ratio of the size of the centre of the receptive ®eld to the radius of the stimulus. The optimum corresponds to rc =R ˆ 0:56. Since in our experiments the optimal stimulus had a diameter of 7° (see Fig. 4b), rc ˆ 0:56
7°= 2 2°. Using this value of rc we calculated the dependence of the percentage of correct choices on the angular size of the stimulus. The percentage of correct choices has been assumed to be related to the eciency of the stimulus by a standard function approximating the probability of the detection curve (see Eq. A9 in Appendix). We found a good agreement of the theoretical and experimental data (see Fig. 4b). This suggests that the achromatic visual pathway in the honeybee may be mediated by neurones with Gaussian centre-surround receptive ®elds. It is important to note that size of the receptive ®eld depends on the width of the angular sensitivity function of single photoreceptor within the ommatidia and on the angular distribution of ommatidia connected to the neurones mentioned above. The angular sensitivity of photoreceptor can be approximated by a Gaussian function (GoÈtz 1964):   U2 A…U† ˆ Exp ÿ ; 2rom 2

107

Discussion

Fig. 5 a Response of a neurone with a Gaussian centre-surround receptive ®eld, G (in arbitrary units), as a function of the angular coordinates, Fx, Fy, of the projection of a circular stimulus onto the eye (see Eq. A5). The surround is assumed to be twice the centre, that is rs ˆ 2rc ; rc ˆ 2 . Optimum detection for such a neurone corresponds to stimuli having a diameter of 7°. b Stimulus eciency, W (in arbitrary units), as a function of the ratio of the size of the centre of the receptive ®eld, rc , to the radius of the stimulus R (see Eq. A9). The diameter of the surround is assumed to be twice that of the centre, that is rs ˆ 2rc

Where U is the angle of the visual axis of the photoreceptor and rom characterises the width of the distribution. The angular sensitivity is often characterised p by its half-width, Dq, and rom ˆ Dq =…2 …2Log…2† †. If only one ommatidium contributes to the central part of the receptive ®eld, rc would be close to rom ; otherwise, rc must exceed rom . The half-width of the photoreceptor angular sensitivity, Dq, is equal to 2.6° ‹ 0.7 (Laughlin and Horridge 1971), which corresponds to rom ˆ 1.1° ‹ 0.3; i.e. rc (2°) signi®cantly exceeds rom , thus indicating that the signals of two or more adjacent ommatidia interact in the central part of the receptive ®eld.

The present work shows that bees can detect the presence of an achromatic stimulus providing green contrast only within a range of small visual angles. This supports the notion that, in the behavioural context of target detection, both the chromatic and the green-contrastdependent achromatic channels have di€erent angularsize tuning. The fact that an achromatic stimulus subtending 30° could not be learned by the bees, and that learning was only possible when the visual angle of the stimulus was considerably reduced, is consistent with the ®nding that at larger visual angles the bees' choice behaviour is governed by the di€erences in chromatic properties, whilst at small angles it is governed by differences in the amount of achromatic green contrast (Giurfa et al. 1996, 1997). In a previous paper (Giurfa et al. 1996) it was shown that adding green contrast to chromatic contrast extends the detection range of coloured stimuli, enabling the detection of small targets down to a visual angle 5°. Here we show that the opposite is also possible: adding chromatic contrast to a certain amount of green contrast also enlarges the detection range, allowing larger targets to be detected. It was thus possible to characterise more precisely the working range of both operating systems, the chromatic and the achromatic detection system. Such a system operators between 4° and 15° (Fig. 4b). On the other hand, the chromatic detection system operates from 15° upwards (Giurfa et al. 1996). Thus, considering the angular errors inherent in the experimental situation [i.e. the bees' decision point was ®xed as the middle point of the decision chamber, but the bees' decision may have been taken at any point within (D1± D2)], both systems appear to be tuned to act sequentially in the approach ¯ight of a bee towards a target. Therefore, results obtained with both the achromatic and the chromatic training discs clearly support the ``Angular-Size Tuning Hypothesis'': the green-contrast channel and the colour-contrast channels di€er in their angular-size tuning so that the achromatic channel specialises in the detection of objects of reduced angular size and the chromatic channels in that of objects of large angular size. The comparison between results obtained with achromatic and chromatic discs having the same amount of green contrast, and thus di€ering only in the presence of chromatic contrast (Fig. 3c, d), distinguishes between the ``Facilitation'' and the ``Angular-Size Tuning'' hypotheses. Our results may be explained by the ``Angular-Size Tuning'' hypothesis. Nonetheless, this hypothesis alone does not explain why, at a visual angle of 5°, the chromatic stimulus yields a higher level of correct choices than for the achromatic stimulus. At this visual angle, bees would see only the green contrast of the stimuli and this information was the same for both the achromatic and the chromatic stimuli. This indicates that the presence of chromatic contrast enhances considerably the level of

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correct choices for the same amount of green contrast. In other words, although the ``Angular-Size Tuning Hypothesis'' accounts for our results, an interaction between chromatic contrast and green contrast, leading to an improvement of the bees' performance, cannot be discarded. Chromatic and green contrast have di€erent saliences in terms of learning performances. Whilst chromatic contrast is easily and quickly learned by the bees (three rewards on a colour target are enough to establish a stable memory that lasts for the whole life of a forager; Menzel 1968), green contrast requires many more learning trials and yields a lower level of correct choices. It is thus tempting to suggest that when the less salient cue of green contrast is combined with the salient cue of chromatic contrast a facilitation e€ect takes place that increases the level of correct choices when green contrast alone guides the choice behaviour at smaller visual angles. The fact that the presence of the achromatic stimulus could not be learned by the bees is not consistent with the well-documented learning of achromatic black and white patterns by bees (see Wehner 1981; Srinivasan 1994 for reviews). If bees are thus capable of learning a large, black disc on a white background and vice versa (Zerrahn 1934; Hertz 1937) why could they not learn to detect the achromatic stimulus used in our experiments at larger visual angles? A possible explanation is that a higher intensity contrast (intensity contrast of a stimulus against the background is calculated as the sum of the absorbed quanta in the three receptor types, relative to the background) is necessary for an achromatic stimulus to be learned at such visual angles. This explanation would be in line with the traditional view that intensity is the parameter by which patterns are perceived. The explanation we favour, however, is that a higher amount of green contrast is what is necessary for an achromatic stimulus to be detected and learned. This suggestion is based on the fact that intensity is de®nitely absent as a perceptual dimension in honeybee colour vision (Brandt and Vorobyev 1997; Giurfa et al. 1997) and the bee achromatic channel is provided by the green photoreceptor type. For black stimuli against a white background, for instance, the amount of green contrast is 14, i.e. much higher than the value of 2.4 (see Table 1) provided by our achromatic disc against the grey background. Thus, increasing the green contrast of achromatic stimuli would allow their learning and detection, even at larger visual angles. This hypothesis can be explicitly tested and a threshold from which learning and detection of achromatic targets at larger visual angles are possible, can therefore be found. If such a threshold exists, it lies de®nitely above the value of 2.4 provided by our achromatic disc. The dependence of the percentage of correct choices on the angular size of the achromatic disc agrees well with the predictions of a linear model that assumes that detection is mediated by the units having centre-surround receptive ®elds described by Gaussian functions

of equal size (Ku‚er 1953). This indicates that the achromatic visual pathway in the honeybee may be mediated by neurones with centre-surround receptive ®elds. Since the estimated width of the central part of the receptive ®eld is approximately twice the width of the angular sensitivity function of a single ommatidium, it is likely that signals of several adjacent ommatidia interact. A more precise characterisation of the angular distribution of ommatidia connected to the centre and surround parts of receptive ®eld would require experiments with stimuli specially designed for this purpose. Although we can explain the results of our present experiment using a simple linear model, this model cannot explain the results of our previous experiments (Giurfa et al. 1996). The linear model predicts that the detectability of the stimuli can be improved by increasing their contrast (see Eq. A8 in Appendix). Thus, stimuli having a higher contrast should be detectable from a further distance than those having a lower one, and a stimulus having a sucient contrast should be detected even if it covers an area less than that of one ommatidium. This prediction is not consistent with the fact that stimuli having a green contrast varying between 0.7 and 4.1 (see Table 1 in Giurfa et al. 1996, Giurfa and Vorobyev 1997) are detected with a probability higher than 60% only if they subtend a visual angle equal or larger than 5°, i.e. a circular stimulus must cover at least seven ommatidia in order to be detected (Giurfa et al. 1996). Such a threshold is independent of the contrast and can be explained by the existence of neurones which respond only if they receive signals from adjacent ommatidia simultaneously, rather than by summing their signals. This means that the response of these neurones is signi®cantly non-linear. Do these non-linear neurones receive signals from linear neurones with centre surround receptive ®elds or are the centre-surround neurones signi®cantly non-linear? Behavioural and physiological experiments may in future allow us to provide an answer to this question. Acknowledgements We especially thank Daniel Osorio, Eric Warrant and an anonymous referee for suggestions, and valuable corrections on the manuscript. We also thank Robert Brandt, Natalie Hempel and Randolf Menzel for corrections, fruitful discussions and valuable contributions to our work. Thanks are due to Josue NuÂnÄez, Walter Farina, HeÂctor Verna and Fernando Grosclaude for their support at the campus of the University of Buenos Aires, where this work was partially done. Martin Giurfa was supported by the Alexander von Humboldt Foundation and by the Berlin Branderburgische Akademie der Wissenschaften (Programme RULE). Misha Vorobyev was supported by the Deutsche Forschungsgemeinschaft (AZ Me365/20-1).

Appendix Response of the centre-surround receptive ®eld to a circular stimulus A linear model describes the response of a neurone to a stimulus as:

109

Z R…0x ; 0y † ˆ

F …Ux ; Uy †G…Ux ; ÿ0x ; Uy ÿ 0y †dUx ; dUy ; …A1†

where 0x ; 0y denote the angular co-ordinates of the receptive ®eld of the neurone, Ux ; Uy correspond to the coordinates of the eye, R…0x ; 0y † is the response of the neurone, G…Ux ; Uy † is the response function of the neurone and F …Ux ; Uy † describes the angular distribution of the quantum ¯ux of the stimulus. Integration is performed over the area of stimulation (Fiorentini et al. 1990). When G…Ux ; Uy † is positive, the stimulation of the point Ux ; Uy excites the neurone, and when it is negative the neurone is inhibited. Neurones with both excitatory and inhibitory centre may be present in the visual pathways. This can be described by a model with an average eciency of stimulation independent of the sign of R…0x ; 0y †. We assume that the eciency of the stimulus, W, is given simply by the average density of the squared response, i.e. Z 1 …R…0x ; 0y ††2 d0x d0y ; …A2† W ˆ S where S is the area of stimulation. Fourier transform simpli®es Eqs. A1 and A2. Let R…xx ; xy † be a Fourier transform of the receptor response R…0x ; 0y †, then, R…xx ; xy † ˆ F…xx ; xy † G…xx ; xy †;

…A3†

Where F…xx ; xy ) and G…xx ; xy † denote Fourier transforms of the angular distribution of the quantum ¯ux of the stimulus, F …Ux ; Uy †, and of the response function of the neurone, G…Ux ; Uy †, respectively. Consequently, Eq. A2 can be written as: Z 2 1 F…xx ; xy †G…xx ; xy † dxx ; dxy : …A4† W ˆ S The response of a neurone with a Gaussian centresurround receptive ®eld is given by: " # …U2x ; U2y † Ac G…Ux ; Uy † ˆ Exp ÿ 2prc2 2r2c " # …A5† …U2x ; U2y † As Exp ÿ ; ÿ 2pr2s 2r2s where rc ; rs describe the width of the centre and surround, respectively, Ac and As the weight of the centre and surround (Fig. 5a). In the case of a neurone which does not respond to uniform stimulation Ac ˆ As ˆ A. The Fourier transform of the response function then is given by:    2 2 2 rc G…xx ; xy † ˆ A Exp ÿ…xx ‡ xy † 2   …A6† 2 2 2 rs ÿExp ÿ…xx ‡ xy † : 2

Consider a circular stimulus with centre at …U0x ; U0y †, radius R, and constant quantum ¯ux H, presented on a background having quantum ¯ux B. Let 2 2 …Ux ÿ U0x † ‡ …Uy ÿ U0y † ˆ r2 , then the angular distribution of the quantum ¯ux of the stimulus, F(r), is equal to H + B if r < R, otherwise it is equal to B. Let x2x ‡ x2y ˆ x2 , then the Fourier transform of F …Ux ; Uy † is given by: 2pH R J1 …xR† Exp‰ixx U0x ‡ ixy U0y Š; …A7† x p for x 6ˆ 0, where i ˆ ÿ1; J1 …xR† denotes the Bessel function of the ®rst order. Substitution of Eqs. A6 and A7 into Eq. A4 gives: F…xx ; xy † ˆ

W ˆ 4pH

2

Z1 0



ÿ Exp ÿ



x2 r2c Exp ÿ 2

x

2

r2s

2

2

 …A8† 2

…JI …xR†† dx: x

Eq. A8 can be simpli®ed by substituting xR ˆ t : W ˆ 4pH

2

Z1 0



  2 2  2 t2 dc2 t d …JI …t††2 ÿ Exp ÿ s dt; Exp ÿ 2 2 t …A9†

where dc ˆ rRc and ds ˆ rRs . Thus the eciency of the response depends on the ratio of the radius of the stimuli to the sizes of the centre and surround parts of receptive ®elds, dc , and ds , respectively, and it is proportional to the square of the quantum ¯ux of the stimulus, H. The eciency of response can be related to the probability of detection of a stimulus, which in turn can be converted into a predicted percentage of correct choices. The probability of detection, P, is equal to zero if the eciency, W, is equal to zero, and equal to one in the case of high eciency. P can be approximated with sucient accuracy by non-linear functions with two parameters, threshold T, which is equal to the value of W corresponding to P ˆ 0.5, and a, a parameter characterising the slope of the probability of the detection curve. Here we use the following approximation:    W W P ˆ Erf a Log if > 1; T T and

   W P ˆ Erf ÿa Log T

if

W < 1; T

…A10†

where, Erf denotes the error function. The percentage of correct choices, Pcorr is equal to 50% if a stimulus cannot be detected (P ˆ 0) and it saturates at some level Psat (Psat < 100%) if a stimulus

110

is detected with P ˆ l. Thus, the following equation relates the probability of detection with the percentage of correct choices: Pcorr ˆ 50% ‡ P…Psat ÿ 50%†:

…A11†

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