Vision Res. Vol. 32, No. 10, pp. 1837-1843, 1992 Printed in Great Britain. All rights reserved
0042.6989/92 $5.00 + 0.00 Copyright T? 1992 Pergamon Press Ltd
Pattern Recognition in Honeybees: Multidimensional Scaling Reveals a City-Block Metric BERNHARD
RONACHER*
Received 10 February 1992; in revised form 15 April 1992
Bees were trained to discriminate ring-patterns which varied in number of rings and in size. Transfer-tests revealed size discrimination to be largely independent of pattern type and vice versa. A multidimensional scaling procedure, using Minkowski metrics as models, was applied in order to determine the bee’s “perceptual metric”. The city-block metric, and not the Euclidean metric, provided the best description of the data. Apparently, the bee’s perceptual system derives the overall dissimilarity of complex ring-patterns additively from the component differences. These results are discussed with regard to “holistic” and “analytic” processing modes postulated for the perception of human subjects. Pattern recognition bee Hymenoptera
Multidimensional Insects
scaling (MDS)
INTRODUCTION Basic tasks of a perceptual system are object recognition and object localization. To be able to identify objects, a perceptual system has to detect and analyze those properties of an object that permit the discrimination, andeven more importantly-an efficient classification by the CNS (see e.g. Treisman, 1986; Suga, 1988; Herrnstein, 1990). To facilitate the classification of a greater number of objects, it is indispensable to be able to determine similarities between objects (see also Carnap, 1928; Shepard, 1987). Mathematical models for similarities are metrics, assuming that “perceptual differences” can be interpreted as distances in an abstract vector space, the “‘perceptual parameter space”. The axes of this vector space are the “perceptual parameters” which are extracted by the nervous system (Torgerson, 1958; Shepard, 1964, 1987; Ronacher, 1979a, b). By comparing how these basic operations-extracting features and assessing similarities--are performed in differently organized perceptual systems, we can learn more about principal rules in the design of perceptual systems. Honeybees were chosen for a comparison with vertebrates due to their very differently organized nervous system and to their excellent learning capacities. Honeybees are able to discriminate and classify patterns according to different parameters; the relevance of different parameters for the discrimination depends on the differences present during the training sessions (Wehner, 1968. 197 la; Ronacher, 1979a; cf. also *Institut fiir Zoologie II der Universitat Erlangen. Germany.
Erlangen,
Staudtstr.
5, 8520
City-block
metric
Analytic
processing
Honey-
Mackintosh, 1974). By means of discrimination training procedures, several candidates for “perceptual parameters” of the bee were established (Ronacher, 1979a, 1980, 1983; for a review see Wehner, 1981). However, in order for the construction of a perceptual parameter space to make sense, one has to show that the animals are able to ascertain consistent similarity relations between different perceptual parameters. For the honeybee this has been verified for several parameters (size, lightness, ring-patterns, colors) (Ronacher, 1979a). In a kind of “cross-modality-matching” experiment (cf. Stevens, 1959), for example it was possible to find a size difference which is, for the bee’s perception, equivalent to a certain difference in contrast. This equivalency is transitive, i.e. it remains valid even when a third parameter is introduced, and therefore is a true equivalence relation. This proof of transitivity is one of the prerequisites for the construction of a perceptual parameter space (Ronacher, 1979a). Moreover, it constitutes an interesting parallel to the perceptual organization of vertebrates (cf. Stevens, 1959, 1969). The next question then is: what kind of metric describes the distances in this perceptual space. In other words, how do the animals determine the distance between any two points in that space from the component distances on the axes. Most investigators of insect vision, if considering this question at all, tacitly assumed an Euclidean combination rule (e.g. Wehner, 1971b; but see von Helversen, 1970, 1972). There are, however, no a priori reasons justifying this assumption, which imposes a considerable theoretical restriction on the mathematical structure (Ronacher. 1979a, b). 1837
183X
BERNHARD
Indeed, in experiments on pattern recognition with human subjects, a city-block metric often provides a much better description of the data than the Euclidean metric (see e.g. Shepard, 1964; Garner, 1974; Ronacher & Bautz, 1985; Ronacher & Si.il3,1990). The applicability of either the city-block or the Euclidean metric is considered a criterion for the use of different processing strategies by the observer (Garner, 1974). Interestingly, in a two-dimensional similarity scaling experiment on the bee’s pattern recognition, with size and brightness as parameters, the city-block (and not the Euclidean) metric was most applicable (Ronacher, 1979b). Recently, this question was tackled for color similarity scaling with bees (Backhaus, Menzel & KreiDl, 1987). In this study, the city-block metric again provided the better description compared to the Euclidean metric. This result is particularly interesting, since for human observers colors are considered to be perceptually “integral” parameters which consistently lead to an Euclidean metric in similarity scaling experiments (Garner, 1974; Garner & Felfoldy, 1970; Handel & Imai, 1972). Thus, it was of interest to determine the bee’s “perceptual metric” for another combination of visual stimuli in order to test whether the city-block metric could be more generally valid for the honeybee’s visual perception. Ring-patterns were chosen due to the existence of comparable data for humans (see Discussion).
METHODS
The training and testing procedure, as well as the experimental apparatus and the stimuli, are described in detail elsewhere (Ronacher, 1979a), and therefore shall be only briefly summarized here. Training and testing were performed on a horizontal white plane (60 cm in dia) which was illuminated from above by a 150 W tungsten lamp (light intensity approx. 1600 lx, for the spectral emittance of the lamp see Ronacher, 1979a). A single, individually marked bee was trained to discriminate between a pair of ring-patterns which differed in size and in number of (concentric) rings (see Fig. 1). For example, the bee was rewarded by a drop of sugar water when landing on a one-ring pattern
-b-
0
\
/
b-
a
FIGURE 1. Scheme of the tests for the determination of the perceptual metric. a, a’ denote perceptual differences for test pairs differing in size; b, b’ for ring-pattern differences; c, c’ are the perceptual differences of stimulus pairs differing on both parameters. To determine the perceptual differences from the observed choice frequencies, the calibration curve in Fig. 2(b) was used.
RONACHER
of 50mm dia; landings on the alternative, a three-ring pattern of 20 mm dia, were not rewarded. As soon as the bee had reached a stable discrimination level of over 80% for the training pair, tests were begun. In these tests, the bee was confronted with a changed situation, one or, in most cases, both patterns now differed from the training situation (transfer-tests). During a test the bee was never rewarded for selecting a test pattern (at the end of a 5-10 min test, however, the bee received a drop of sugar water on the positive training stimulus which was then placed in the midst of the test area). Only actual landings on the test patterns were counted as a “choice”, i.e. the bee had to touch the test pattern with its legs. Typically a test visit yielded between 30-120 choices (depending on the overall similarity with the training situation). Results are expressed as choice frequencies [CF = x*100/(x +y), x, 4’ representing the number of decisions for pattern X, Y]. All choice frequency values shown thereafter were measured in tests with pairs of patterns, which differed either in size, or in ring-pattern, or in both (cf. Fig. 1). Training and test stimuli
The training and test stimuli were black-and-white ring-patterns of high contrast, consisting of l-4 concentric rings; additionally, in some experiments uniform black discs were used (abbreviations: lR, 2R, 3R, 4R, D). The ring-patterns were constructed so that the proportion of black and white areas was 1: 1, in order to keep the total reflectance constant (cf. Ronacher, 1979a). As a consequence of this requirement the widths of the rings in a pattern varied, see examples in Fig. 1. A second variable was the size of the patterns, with outer diameters of 50, 40, 32, 25 or 20 mm having been used (the size is indicated by indices in the abbreviations). With different individuals, five different training combinations were used (+ and - indicate which of the patterns was rewarded and which not): (D”O+ : 2Rm--), (3Rz0+ : lRsO-), (lRN+ :3RZo-), (3Rz0+ :DSo-), ( lRzO+ : 3RSo-). As a control [Fig. 2(a)] a training pair without a size difference was also used. These different training combinations were applied in order to control for spontaneous preferences which could distort choice behavior (cf. Wehner, 198 1). Spontaneous preferences, however, were not very strong, and could be easily overcome by the training. The bees behaved rather similarly after these different trainings, all individuals discriminating size differences as well as patterns of equal size that differed in the number of rings (cf. Fig. 3). Therefore the data of different trainings were pooled [see however, Fig. 4(d) for data of individuals]. Determination
of the “best” Minkowski
metric
The perceptual differences determined for these combinations were evaluated with a two-dimensional scaling procedure, using Minkowski metrics as models for perceptual differences. The most appropriate Minkowski metric was determined from the data of 10 bees together, as well as from the data of each individual.
CITY-BLOCK
METRIC
IN BEES
PATTERN
1x39
RECOGNITION
choice frequencies of tests with different sizes, a, a’ (or different pattern types b, b’, respectively). All choice frequency values were converted into perceptual distances by means of the “calibration curve” [see below and Fig. 2(b)]. RESULTS
Deriving “perceptual d@erences" ,from choice frequencies
Number
of
‘Calibration
curve’
/’
I
I
25
50
Perceptual (orbltrory
It is important to note that the choice frequencies (CF) do not directly reflect the stimulus differences as perceived by the bee (henceforth termed perceptual diflerences U): as the stimulus difference increases, the choice frequency necessarily reaches a ceiling level (100%) whereas the perceptual difference, of course, does not. Several attempts have been made to deal with the problem of inferring perceptual differences from discrimination frequencies measured in behavioral tests. Jander (1968) and Wehner (1969) used a Probit transformation (see also Hassenstein, 1958) whereas von Helversen (1972) tried to determine a “calibration curve” h(U) = CF (based on the assumption of Fechner’s law). Here, too, a “calibration curve” shall be
rmgs
r
units)
FIGURE 2. Discrimination of ring-patterns after training with a black disc (50 mm dia, rewarded) against a gray disc of same size (unrewarded). Abscissa, type of ring-pattern (lR, 2R, 3R, 5R), or black disc (0 on abscissa); ordinate, choice frequency. The pattern that was tested against others is indicated on the right of each curve. 3 bees, n = 1470. (b) “Calibration curve” for perceptual differences. Ordinate, choice frequency; abscissa, perceptual difference in arbitrary units. Thick line, calibration curve, derived for size and brightness; stippled curves, corresponding standard deviations, data from Ronacher (1979b). *Results from same evaluation for data with ring-patterns. Further explanations in text.
By interpreting perceptual differences of the type a, b, c (see Fig. 1) as distances, the Minkowski metrics in the two-dimensional case can be written as c = (ar + &)‘I’.
(N = number
= $ [(a; + bj)“’ - ci]* ,=I
of data triples
,,j
discrimination
(a)
0
90
4
3
2
I
Number
of
rings
Shape
discrimination
(b)
(1)
This formula satisfies the metric axioms for r 3 1, and comprises the special cases of the city-block metric (r = 1), of the Euclidean metric (r = 2), and of the dominance metric (Y---fco). The “best” Minkowski metric is characterized by that exponent r for which the average difference between observed perceptual distances of type c and a prediction of c according to equation (1) becomes minimum. For this the function SQ(r) was defined, SQ(r)
Size
90
difference
(2)
a,, hi, c,)
and the minimum of this function was determined [Fig. 4(c), for a detailed description of this procedure see Ronacher & Bautz, 19851. For assessing the best metric, in all cases the data of the type a, b (see Fig. 1) were taken as mean values of
50
’ 10
I
I
I
I
20
30
40
50
Dtometer
(mm)
FIGURE 3. (a) Size discrimination was largely independent of pattern type. Geometrically similar pairs of ring-patterns of 20 and 50 mm dia were tested. Abscissa, type of pattern (lR, 2R, 3R, 4R) or black discs (0 on abscissa); ordinate, choice frequency. Data of four individuals, The symbols indicate different types of training [x (3R*” + : lR’“-); 0 (lR”+ :3RZo-); n (1R20+ :3RSo-). Arrow points to the curve of the individual mentioned in text. (b) Pattern discrimination was independent of size for several individuals. Abscissa, size of respective test pairs; ordinate, choice frequency. Data of 3 individuals (x , 0, *) that were tested with lR:2R, 1R: 3R or 1R:4R. Individuals were trained on (3RZo+:lRSo-): f, or on (IR5”+:3RZ0-): 0, *,
1840
BERNHARD
100
metric
City-block
I
(0)
/
I ?5f-
r’
i
/
/
/
/
RONACHER
/
Euclidean
metric
/
75
/ / / /
= E 2 g
50
E 0
25
/’ +
0
,
I
/
0
I
I
I
25
50
75
c
j/ 0.5
1.0
I
100
f
0
a
,
/’ J
I
I
1
25
5a
75
100
expected
c
I
I
I
1
1.5
2.0
2.5
3.0
Exponent
r
expected
1
2 Exponent
r
FKXJRE 4. (a) Evaluation of multidimens~o~~ differences ~c~~~~ing to the city-block metric. Data of 10 bees, based on 10,870 choices. Abscissa, expected values for complex distance, determined by Form& (1) with r = 1, i.e. a + b, Ordinate, measured complex perceptual difference c. Dashed line, bisectrix; thick line, regression line (regression coefficient 0.858). Horizontal and vertical bars indicate standard deviations for some values (the largest and two typical deviations). These. deviations were estimated, fo~~o~n~ the rules of error ~rupagat~o~ (Bauie, 1959), from the standard deviations of the choice frequew~ values and the deviations of the ‘Wibration” curve of Fig. Z(b). {b) ~va~~t~on of same data according to the Eueiidean metric. In this case the expected values were determined by (a2 + @)‘:t. Regression coefficient 0.860. (cc) Determination of the best Minkowski metric, by means of the SQ-function [see Methods, formula (2)j. (d) Exponent of the respective best Minkowski metric for individual bees. Each segment of a column represents the best metric determined From the data of an individual; the height of the se@nents represents the number of measured values cont~buti~~ to this evaluation. Black columns indicate individuals with larger deviations in the ratings of type b, b’ (see text).
used. This curve was, however, determined on a somewhat different theoretical basis, namely the validity of the metric axioms (Ronacher, 1979b). The procedure is based on the assumption that perceptual differences which relate to a single perceptual parameter can be combined additively (Ui3 = Uzz+ Uz3, for stimuli 1, 2, and 3). However, when measuring choice frequencies, this additivity will not hold for values over 70%, i.e. in general: CF,, < CF,, + CF,, . The deviations from additivity in this inequality are due to the appI~~at~on of the function h. Assuming that h is linear for smaI1 values of U, one can infer the function h from these deviations in a recurrent procedure (for details see Ronacher, 1979b). This assumption of linearity of h for small values is justified by the observation that with small stimulus values the additivity also holds for choice frequencies,
This has been verified in detail for the parameters size and contrast (Ronacher, 19?9a, 1980), and appears to also be valid for differences in ring-patterns [cf. parallel curves in Fig. 2(a)]. The result of this calculation was a hyperbolic curve [thick CUPX in Fig. 2(b)]. Singe the values obtained with rung-patterns [* in Fig. Z(b)] also match this curve, the same calibration curve’ was used here. The effect of this calibration curve is, however, very similar to that of the Probit transformation {see below).
Beds, Krantz and Tversky (t968) and Tversky and Krantz (1970) established criteria for the ~ppii~bility of ~inkowski metrics: the main two are “intradimens~ona~ subtractivity” and “‘interdimensional additivity” (cf. also Dunn, 1983).
CITY-BLOCK
METRIC
IN BEES PATTERN
The first criterion, “intradimensional subtractivity”, is the requirement that distances along a perceptual parameter can be combined additively. This has already been verified for size (Ronacher, 1979a, 1980) and ring-patterns [Fig. 2(a)]. The second important condition for the applicability of Minkowski metrics is the independence of perceptual parameters (“interdimensional additivity”). This was tested in the following way: size discrimination was tested with (geometrically similar) patterns of different size (e.g. 1R50:lR20, 2RSo:2Rz0, or 3RSo:3R2’). The choice frequencies for these pairs were similar [curves parallel to the abscissa in Fig. 3(a)]. Size discrimination was thus largely independent of the pattern type. For most individuals the pattern discrimination was also independent of the size of test patterns [Fig. 3(b), tests were e.g. 1R20: 3RZo, 1Rso: 3R5’]. Only two individuals showed a larger deviation between tests with small and tests with large ring-patterns. Since the evaluation of the metric for these individuals did not reveal substantial differences [black columns in Fig. 4(d)], their data are included in Fig. 4(a-c) (for similar effects with human observers see Ronacher & Bautz, 1985). Thus the data apparently fulfill the second criterion as well. However, a further possibility had to be tested: it is conceivable that the bees had used only a single cue to discriminate these patterns. Indeed, some authors proposed that the bees evaluate the contour-length-ratio or contour-density-ratio (see Wehner, 198 1, for review). This kind of evaluation would produce the independence mentioned above as a “byproduct”, and would, of course, preclude the application of a multidimensional scaling procedure. The single-cue hypothesis can, however, be unequivocally ruled out on the basis of several observations. For example, in some individuals a difference was found in speed at which size discrimination and discrimination of equal-sized ring-patterns was acquired (further arguments will be presented in detail elsewhere, Ronacher, 1992). Thus, the bees used at least two cues to discriminate these ring-patterns, and since both criteria appear to hold, the application of Minkowski metrics is possible. Determination qf the best Minkowski metric In Fig. 4(a, b) the data of 10 bees (based on 10,870 choices) are presented in two evaluations, for the cityblock and the Euclidean metric. In both diagrams, measured values for distances of the type c are plotted against the expected values, which were calculated from a and h values according to formula (1) for the city-block metric (exponent r = 1) or for the Euclidean metric (r = 2). The procedure shall be exemplified with a single value [arrows in Fig. 4(a, b)]: for tests of the type a, i.e. size discrimination (cf. Fig. l), one individual produced choice frequencies of 77.5, 78.2, 82, and 78.4% [tested for black discs, lR-, 2R- and 3R-patterns, respectively, see curve marked with an arrow in Fig. 3(a); mean value 79.0%]. The discrimination of 1R : 3R-patterns yielded 78.3, 78.8 and 82.6% (tests of type b with 20, 32 and
RECOGNITION
1841
50 mm dia) [arrow in Fig. 3(b), mean value 79.9%]. The choice frequency for a test of type c, 1RSo: 3R*‘, was 92.3%. Transformation by means of the calibration curve [Fig. 2(b)] yields the following values a = 33, b = 34.5, c = 63.5, and the application of formula (1) yields an expected value of 67.5 for the city-block metric of 47.7 for the Euclidean metric (a + b), and [(a’ + b2)“*]. For this data triple the solution of equation (1) would result in r = 1.10. It is immediately apparent that the city-block metric is a quite satisfactory match for the data [compare solid regression line with the dotted bisectrix in Fig. 4(a)]. In contrast, the expected values for c with the Euclidean metric are too small in almost all cases. This is confirmed by Fig. 4(c) in which the best Minkowski metric was sought, i.e. that Minkowski metric for which the SQvalue [formula (2)] is minimum. This minimum is located at r = 1.02 [arrow in Fig. 4(c)]. As a control, the choice frequency data were also converted by the Probit transformation (Jander, 1968) instead of the calibration curve of Fig. 2(b). The best exponent, however, remained unaffected (r = 1.03). In Fig. 4(d) the best exponents are evaluated separately for individuals. Each column (or segment of a column) represents 1 bee, the different heights of the columns symbolize the number of measured values obtained per individual (data of the above mentioned two animals with larger deviations in the ratings of type b, b’ are marked by black columns). For all bees except 1, the city-block metric provided a much better description of the data than the Euclidean metric. The sole exception is caused by a single value (the two measurements obtained with this individual yielded an r of 1.15 and 1.82, respectively). Since for other individuals, too, single values occasionally were matched by the Euclidean metric [cf. Fig. 4(b)], this result certainly should not be interpreted as an indication for the existence of interindividual differences in the best Minkowski metric.
DISCUSSION The aim of this study was to determine the metric which best describes multidimensional perceptual differences of an insect. Earlier studies have already established several congruences between the perceptual capacities of the bee and of vertebrates: the feasability of “cross modality matches”, and the transitivity of the resulting equivalence relation (Ronacher, 1979a); the derivation of perceptual distances from “just noticeable differences” (Ronacher, 1979b, 1980; cf. also Backhaus & Menzel, 1987; Menzel & Backhaus, 1989); the ability to attend to certain parameters and to ignore others, depending on the training task (Ronacher, 1979a, 1980, 1992; cf. also Wehner, 1968, 1971a, 1975, 1981; Anderson, 1972; Schnetter, 1972; Klosterhalfen, Fischer & Bitterman, 1978) and the possibility to construct a perceptual parameter space and to describe similarity relations by metrics (Ronacher, 1979a, b; Backhaus et al., 1987).
1842
BERNHARD
In multidimensional scaling experiments with humans, a distinction has been drawn between “integral” (or “unitary”) stimuli, which are said to be subjected to “holistic” processing, and “separable” stimuli, which are said to be processed “analytically”. The description of multidimensional scaling data by the Euclidean or the city-block metric, respectively, is taken as an important criterion for holistic vs analytic processing (for review see Garner, 1974). Examples for integral stimuli are hue, saturation and brightness of colours (cf. Introduction); examples for a separable parameter combination are size and brightness (Attneave, 1950; Garner, 1977; see also Ronacher & Bautz, 1985; Ronacher & SiiD, 1990). With bees, the city-block metric was found to apply for size and brightness of discs (Ronacher, 1979bthe best exponent for these data is 1.09), as well as for colors (Backhaus ez al., 1987). The latter result was unexpected since, with humans, multidimensional scaling procedures with colors always led to an Euclidean metric (see above). Therefore, it was of interest to perform similarity scaling experiments with bees for other parameter combinations in order to test whether the city-block metric could be more generally valid for the bee’s perceptual system. Ring-patterns (of different sizes) were chosen because for humans they appear to have an intermediate position between highly separable and highly integral stimuli: in a similar experiment (cf. Fig. 1) with humans, the data of 70% of the subjects yielded an Euclidean metric (Ronacher, 1992). The bee’s data for ring-patterns are quite well described by a city-block metric (see Fig. 4, the best exponent 1.02 being not significantly different from 1.00) thus indicating that the overall dissimilarity is derived additively from the component differences. Thus, for the honeybee’s perceptual system the city-block metric provides a good description for three parameter combinations, which-for humans-range from separable to highly integral. It is thus conceivable that the city-block metric is generally valid for the bee’s perceptual system-a hypothesis which should now be tested for further parameter combinations. Recently, Shepard (1987) in his article “Toward a universal law of generalization for psychological science”, tried to relate the two forms of preferred perceptual metrics (Euclidean and city-block) to the optimization of object classification during the evolutionary history of nervous systems. Following Shepard’s line of reasoning, it is tempting to speculate that these types of experiments reveal a more fundamental difference between the differently organized perceptual systems of insects and vertebrates. REFERENCES Anderson, A. (1972). The ability of honey bees to generalise visual stimuli. In Wehner, R. (Ed.), Information processing in the visual system of arthropods (pp. 207-212). Berlin: Springer. Attneave, F. (1950). Dimensions of similarity. American Journal of Psychology, 63, 5 16556.
Backhaus, W. & Menzel, R. (1987). Color distance derived from a receptor model of color vision in the honeybee. Biological Cybernetits, 55, 321-331.
RONACHER Backhaus, W., Menzel, R. & Kreilll, S. (1987). Multidimensional scaling of color similarities in bees. Biological Cvhrmrtics. 56. 2933304.
Baule, B. (1959). Die Mathematik des Naturf0rscher.s und hgenieurs. Band II. Ausgleichs-und Ndherungsrechnung. Leipzig: Hirzel. Beals, R., Krantz, D. H. & Tversky, A. (1968). Foundations of multidimensional scaling. Psychological Review, 75, 127-142. Carnap, R. (1928). Der iogische Aufbau der Welt. Berlin: Weltkreisverlag. Dunn, J. C. (1983). Spatial metrics of integral and separable dimensions. Journal of Experimental Psychology, Human Perception and Performance,
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Garner, W. R. (1974). The processing of information and structure. London: Wiley. Garner, W. R. (1977). The effect of absolute size on the separability of the dimensions of size and brightness. Bulletin of the Psychonomic Society, 9, 380-382.
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Hassenstein, B. (1958). Die Starke von optokinetischen Reaktionen auf verschiedene Mustergeschwindigkeiten. Zeitschrzfi fur Nuturforschung, 13b, l-6. von Helversen, 0. (1970). Zur spektralen Unterschiedsempfindlichkeit der Honigbiene. Thesis, Universitat Freiburg i.Br. von Helversen, 0. (1972). The relationship between difference in stimuli and choice frequency in training experiments with the honey bee. In Wehner, R. (Ed.), Information processing in the visual system of arlhropods (pp. 323-334). Berlin: Springer. Herrnstein, R. L. (1990). Levels of categorization. In Edelman, G. M., Gall, W. E. & Cowan, W. M. (Eds), Signal and sense. Local and global order in perceptual maps (pp. 385413). New York: Wiley-Liss. Jander, R. (1968). Uber die Ethometrie von Schliisselreizen, die Theorie der telotaktischen Wahlhandlung und das Potenzprinzip der terminalen Cumulation. Zeitschrifi fur Vergleichende Physiologic, 59, 3 19-356.
Klosterhalfen, S., Fischer, W. & Bitterman, M. E. (1978). Modification of attention in honey bees. Science, 201, 1241-1242. Mackintosh, N. J. (1974). The psychology of animal learning. New York: Academic Press. Menzel, R. & Backhaus, W. (1989). Color vision in honey bees: Phenomena and physiological mechanisms. In Stavenga, D. & Hardie, R. (Eds), Facets of vision (pp. 281-297). Berlin: Springer. Ronacher, B. (1979a). Aquivalenz zwischen Grdllen- und HelligkeitsUnterschieden im Rahmen der visuellen Wahrnehmung der Honigbiene. Biological Cybernetics, 32, 63. 75. Ronacher, B. (1979b). Beitrag einzelner Parameter zum wahrnehmungsgemaBen Unterschied von zusammengesetzten Reizen bei der Honigbiene. Biological Cybernetics, 32, 77-83. Ronacher, B. (1980). Ein einfacher Zusammenhang zwischen der Aquivalenzbeziehung und der Unterschiedsempfindlichkeit fur zwei Musterparameter bei der Honigbiene. Biological Cyberneiics, 36, 5161.
Ronacher, B. (1983). Unabhlngigkeit der Bewertung zweier Musterparameter von deren Unterschiedlichkeitsgrad bei der Dressur. Biological Cybernetics, 46, 173-l 82. Ronacher, B. (1992). Influence of unrewarded stimuli on the classitication of visual patterns by the honeybee. Ethology. Submitted. Ronacher, B. & Bautz, W. (1985). Human pattern recognition: Individually different strategies in analyzing complex stimuli. Biological Cybernetics, 51, 249-261.
Ronacher, B. & StiO, H. (1990). Perception of size and lightness of human observers: Two criteria for holistic and analytic processing show no correlation in individuals. Biological Cybernetics, 64, 107-115.
Schnetter, B. (1972). Experiments on pattern discrimination in honey bees. In Wehner, R. (Ed.), Informationprocessing in the visual system of arthropods (pp. 195200). Berlin: Springer
CITY-BLOCK
METRIC
IN BEES
Shepard, R. N. (1964). Attention and the metric structure of the stimulus space. Journal of Mathematical Psychology, I, 54-87. Shepard, R. N. (1987). Toward a universal law of generalization for psychological science. Science, 237, 13 17-l 323. Stevens, S. S. (1959). Cross-modality validation of subjective scales for loudness, vibration, and electric shock. Journal of Experimental Psychology, 57, 201-209. Stevens, S. S. (1969). On predicting exponents for cross-modality matches. Perception and Psychophysics, 6, 251-256. Suga, N. (1988). What does single-unit analysis in the auditory cortex tell us about information processing in the auditory system? In Racik, P. & Singer, W. (Eds), Neurobiology of neocortex (pp. 331-349). New York: Wiley. Torgerson, W. S. (1958). Theory and methods of scaling. New York: Wiley. Treisman, A. (1986). Properties, parts, and objects. In Boff, K., Kaufmann, L. & Thomas, J. (Eds), Handbook of perception and human performance (pp. I-71). New York: Wiley. Tversky, A. & Krantz, D. H. (1970). The dimensional representation and the metric structure of similarity data. Journal of Mathematical Psychology, 7, 572-596. Wehner, R. (1968). Die Bedeutung der Streifenbreite fur die optische Winkelmessung der Biene (Apis mellifica). Zeitschrzft ftir Vergleichende Physiologie, 58. 322-343.
PATTERN
Wehner,
1843
RECOGNITION
R. (1969). Der Mechanismus
der optischen
Winkelmessung
bei der Biene Apis mellifica). Zoologischer Anzeiger (Suppl. 33), Verhandlungen der Deutschen Zoologischen Gesellschaft, 586-592. Wehner, R. (1971a). The generalization of directional visual stimuli in the honey bee, Apis mellifera. Journal of Insect Physiology, 17, 1579-1591. Wehner, R. (1971b). Formensehen bei Insekten. Orientierungsphysiologische Untersuchungen zur Datenverarbeitung in optischen Systemen. Verhandlungen der Deutschen Zoologischen Gesellschaft. 65, 251-266. Wehner, R. (1975). Pattern recognition. In Horridge, G. A. (Ed.), The compound eye and vision qf insects (pp. 755113). Oxford: Clarendon Press. Wehner, R. (1981). Spatial vision in arthropods. In Autrum, H., Jung, R., Loewenstein, W. R., MacKay, D. M. & Teuber, H. L. (Eds), Comparariue physiology and evolution of vision in inoertebrates. Handbook of sensory physiology. Volume V11/6C (pp. 287-616). Berlin: Springer.
Acknowledgements-I thank J. Singer and H. Beck for their help with the experiments, Otto von Helversen for critically reading the manuscript, and the DFG for financial support (Ro 547/4-1,2).
0042.6989/92 $5.00 + 0.00 Copyright T? 1992 Pergamon Press Ltd
Pattern Recognition in Honeybees: Multidimensional Scaling Reveals a City-Block Metric BERNHARD
RONACHER*
Received 10 February 1992; in revised form 15 April 1992
Bees were trained to discriminate ring-patterns which varied in number of rings and in size. Transfer-tests revealed size discrimination to be largely independent of pattern type and vice versa. A multidimensional scaling procedure, using Minkowski metrics as models, was applied in order to determine the bee’s “perceptual metric”. The city-block metric, and not the Euclidean metric, provided the best description of the data. Apparently, the bee’s perceptual system derives the overall dissimilarity of complex ring-patterns additively from the component differences. These results are discussed with regard to “holistic” and “analytic” processing modes postulated for the perception of human subjects. Pattern recognition bee Hymenoptera
Multidimensional Insects
scaling (MDS)
INTRODUCTION Basic tasks of a perceptual system are object recognition and object localization. To be able to identify objects, a perceptual system has to detect and analyze those properties of an object that permit the discrimination, andeven more importantly-an efficient classification by the CNS (see e.g. Treisman, 1986; Suga, 1988; Herrnstein, 1990). To facilitate the classification of a greater number of objects, it is indispensable to be able to determine similarities between objects (see also Carnap, 1928; Shepard, 1987). Mathematical models for similarities are metrics, assuming that “perceptual differences” can be interpreted as distances in an abstract vector space, the “‘perceptual parameter space”. The axes of this vector space are the “perceptual parameters” which are extracted by the nervous system (Torgerson, 1958; Shepard, 1964, 1987; Ronacher, 1979a, b). By comparing how these basic operations-extracting features and assessing similarities--are performed in differently organized perceptual systems, we can learn more about principal rules in the design of perceptual systems. Honeybees were chosen for a comparison with vertebrates due to their very differently organized nervous system and to their excellent learning capacities. Honeybees are able to discriminate and classify patterns according to different parameters; the relevance of different parameters for the discrimination depends on the differences present during the training sessions (Wehner, 1968. 197 la; Ronacher, 1979a; cf. also *Institut fiir Zoologie II der Universitat Erlangen. Germany.
Erlangen,
Staudtstr.
5, 8520
City-block
metric
Analytic
processing
Honey-
Mackintosh, 1974). By means of discrimination training procedures, several candidates for “perceptual parameters” of the bee were established (Ronacher, 1979a, 1980, 1983; for a review see Wehner, 1981). However, in order for the construction of a perceptual parameter space to make sense, one has to show that the animals are able to ascertain consistent similarity relations between different perceptual parameters. For the honeybee this has been verified for several parameters (size, lightness, ring-patterns, colors) (Ronacher, 1979a). In a kind of “cross-modality-matching” experiment (cf. Stevens, 1959), for example it was possible to find a size difference which is, for the bee’s perception, equivalent to a certain difference in contrast. This equivalency is transitive, i.e. it remains valid even when a third parameter is introduced, and therefore is a true equivalence relation. This proof of transitivity is one of the prerequisites for the construction of a perceptual parameter space (Ronacher, 1979a). Moreover, it constitutes an interesting parallel to the perceptual organization of vertebrates (cf. Stevens, 1959, 1969). The next question then is: what kind of metric describes the distances in this perceptual space. In other words, how do the animals determine the distance between any two points in that space from the component distances on the axes. Most investigators of insect vision, if considering this question at all, tacitly assumed an Euclidean combination rule (e.g. Wehner, 1971b; but see von Helversen, 1970, 1972). There are, however, no a priori reasons justifying this assumption, which imposes a considerable theoretical restriction on the mathematical structure (Ronacher. 1979a, b). 1837
183X
BERNHARD
Indeed, in experiments on pattern recognition with human subjects, a city-block metric often provides a much better description of the data than the Euclidean metric (see e.g. Shepard, 1964; Garner, 1974; Ronacher & Bautz, 1985; Ronacher & Si.il3,1990). The applicability of either the city-block or the Euclidean metric is considered a criterion for the use of different processing strategies by the observer (Garner, 1974). Interestingly, in a two-dimensional similarity scaling experiment on the bee’s pattern recognition, with size and brightness as parameters, the city-block (and not the Euclidean) metric was most applicable (Ronacher, 1979b). Recently, this question was tackled for color similarity scaling with bees (Backhaus, Menzel & KreiDl, 1987). In this study, the city-block metric again provided the better description compared to the Euclidean metric. This result is particularly interesting, since for human observers colors are considered to be perceptually “integral” parameters which consistently lead to an Euclidean metric in similarity scaling experiments (Garner, 1974; Garner & Felfoldy, 1970; Handel & Imai, 1972). Thus, it was of interest to determine the bee’s “perceptual metric” for another combination of visual stimuli in order to test whether the city-block metric could be more generally valid for the honeybee’s visual perception. Ring-patterns were chosen due to the existence of comparable data for humans (see Discussion).
METHODS
The training and testing procedure, as well as the experimental apparatus and the stimuli, are described in detail elsewhere (Ronacher, 1979a), and therefore shall be only briefly summarized here. Training and testing were performed on a horizontal white plane (60 cm in dia) which was illuminated from above by a 150 W tungsten lamp (light intensity approx. 1600 lx, for the spectral emittance of the lamp see Ronacher, 1979a). A single, individually marked bee was trained to discriminate between a pair of ring-patterns which differed in size and in number of (concentric) rings (see Fig. 1). For example, the bee was rewarded by a drop of sugar water when landing on a one-ring pattern
-b-
0
\
/
b-
a
FIGURE 1. Scheme of the tests for the determination of the perceptual metric. a, a’ denote perceptual differences for test pairs differing in size; b, b’ for ring-pattern differences; c, c’ are the perceptual differences of stimulus pairs differing on both parameters. To determine the perceptual differences from the observed choice frequencies, the calibration curve in Fig. 2(b) was used.
RONACHER
of 50mm dia; landings on the alternative, a three-ring pattern of 20 mm dia, were not rewarded. As soon as the bee had reached a stable discrimination level of over 80% for the training pair, tests were begun. In these tests, the bee was confronted with a changed situation, one or, in most cases, both patterns now differed from the training situation (transfer-tests). During a test the bee was never rewarded for selecting a test pattern (at the end of a 5-10 min test, however, the bee received a drop of sugar water on the positive training stimulus which was then placed in the midst of the test area). Only actual landings on the test patterns were counted as a “choice”, i.e. the bee had to touch the test pattern with its legs. Typically a test visit yielded between 30-120 choices (depending on the overall similarity with the training situation). Results are expressed as choice frequencies [CF = x*100/(x +y), x, 4’ representing the number of decisions for pattern X, Y]. All choice frequency values shown thereafter were measured in tests with pairs of patterns, which differed either in size, or in ring-pattern, or in both (cf. Fig. 1). Training and test stimuli
The training and test stimuli were black-and-white ring-patterns of high contrast, consisting of l-4 concentric rings; additionally, in some experiments uniform black discs were used (abbreviations: lR, 2R, 3R, 4R, D). The ring-patterns were constructed so that the proportion of black and white areas was 1: 1, in order to keep the total reflectance constant (cf. Ronacher, 1979a). As a consequence of this requirement the widths of the rings in a pattern varied, see examples in Fig. 1. A second variable was the size of the patterns, with outer diameters of 50, 40, 32, 25 or 20 mm having been used (the size is indicated by indices in the abbreviations). With different individuals, five different training combinations were used (+ and - indicate which of the patterns was rewarded and which not): (D”O+ : 2Rm--), (3Rz0+ : lRsO-), (lRN+ :3RZo-), (3Rz0+ :DSo-), ( lRzO+ : 3RSo-). As a control [Fig. 2(a)] a training pair without a size difference was also used. These different training combinations were applied in order to control for spontaneous preferences which could distort choice behavior (cf. Wehner, 198 1). Spontaneous preferences, however, were not very strong, and could be easily overcome by the training. The bees behaved rather similarly after these different trainings, all individuals discriminating size differences as well as patterns of equal size that differed in the number of rings (cf. Fig. 3). Therefore the data of different trainings were pooled [see however, Fig. 4(d) for data of individuals]. Determination
of the “best” Minkowski
metric
The perceptual differences determined for these combinations were evaluated with a two-dimensional scaling procedure, using Minkowski metrics as models for perceptual differences. The most appropriate Minkowski metric was determined from the data of 10 bees together, as well as from the data of each individual.
CITY-BLOCK
METRIC
IN BEES
PATTERN
1x39
RECOGNITION
choice frequencies of tests with different sizes, a, a’ (or different pattern types b, b’, respectively). All choice frequency values were converted into perceptual distances by means of the “calibration curve” [see below and Fig. 2(b)]. RESULTS
Deriving “perceptual d@erences" ,from choice frequencies
Number
of
‘Calibration
curve’
/’
I
I
25
50
Perceptual (orbltrory
It is important to note that the choice frequencies (CF) do not directly reflect the stimulus differences as perceived by the bee (henceforth termed perceptual diflerences U): as the stimulus difference increases, the choice frequency necessarily reaches a ceiling level (100%) whereas the perceptual difference, of course, does not. Several attempts have been made to deal with the problem of inferring perceptual differences from discrimination frequencies measured in behavioral tests. Jander (1968) and Wehner (1969) used a Probit transformation (see also Hassenstein, 1958) whereas von Helversen (1972) tried to determine a “calibration curve” h(U) = CF (based on the assumption of Fechner’s law). Here, too, a “calibration curve” shall be
rmgs
r
units)
FIGURE 2. Discrimination of ring-patterns after training with a black disc (50 mm dia, rewarded) against a gray disc of same size (unrewarded). Abscissa, type of ring-pattern (lR, 2R, 3R, 5R), or black disc (0 on abscissa); ordinate, choice frequency. The pattern that was tested against others is indicated on the right of each curve. 3 bees, n = 1470. (b) “Calibration curve” for perceptual differences. Ordinate, choice frequency; abscissa, perceptual difference in arbitrary units. Thick line, calibration curve, derived for size and brightness; stippled curves, corresponding standard deviations, data from Ronacher (1979b). *Results from same evaluation for data with ring-patterns. Further explanations in text.
By interpreting perceptual differences of the type a, b, c (see Fig. 1) as distances, the Minkowski metrics in the two-dimensional case can be written as c = (ar + &)‘I’.
(N = number
= $ [(a; + bj)“’ - ci]* ,=I
of data triples
,,j
discrimination
(a)
0
90
4
3
2
I
Number
of
rings
Shape
discrimination
(b)
(1)
This formula satisfies the metric axioms for r 3 1, and comprises the special cases of the city-block metric (r = 1), of the Euclidean metric (r = 2), and of the dominance metric (Y---fco). The “best” Minkowski metric is characterized by that exponent r for which the average difference between observed perceptual distances of type c and a prediction of c according to equation (1) becomes minimum. For this the function SQ(r) was defined, SQ(r)
Size
90
difference
(2)
a,, hi, c,)
and the minimum of this function was determined [Fig. 4(c), for a detailed description of this procedure see Ronacher & Bautz, 19851. For assessing the best metric, in all cases the data of the type a, b (see Fig. 1) were taken as mean values of
50
’ 10
I
I
I
I
20
30
40
50
Dtometer
(mm)
FIGURE 3. (a) Size discrimination was largely independent of pattern type. Geometrically similar pairs of ring-patterns of 20 and 50 mm dia were tested. Abscissa, type of pattern (lR, 2R, 3R, 4R) or black discs (0 on abscissa); ordinate, choice frequency. Data of four individuals, The symbols indicate different types of training [x (3R*” + : lR’“-); 0 (lR”+ :3RZo-); n (1R20+ :3RSo-). Arrow points to the curve of the individual mentioned in text. (b) Pattern discrimination was independent of size for several individuals. Abscissa, size of respective test pairs; ordinate, choice frequency. Data of 3 individuals (x , 0, *) that were tested with lR:2R, 1R: 3R or 1R:4R. Individuals were trained on (3RZo+:lRSo-): f, or on (IR5”+:3RZ0-): 0, *,
1840
BERNHARD
100
metric
City-block
I
(0)
/
I ?5f-
r’
i
/
/
/
/
RONACHER
/
Euclidean
metric
/
75
/ / / /
= E 2 g
50
E 0
25
/’ +
0
,
I
/
0
I
I
I
25
50
75
c
j/ 0.5
1.0
I
100
f
0
a
,
/’ J
I
I
1
25
5a
75
100
expected
c
I
I
I
1
1.5
2.0
2.5
3.0
Exponent
r
expected
1
2 Exponent
r
FKXJRE 4. (a) Evaluation of multidimens~o~~ differences ~c~~~~ing to the city-block metric. Data of 10 bees, based on 10,870 choices. Abscissa, expected values for complex distance, determined by Form& (1) with r = 1, i.e. a + b, Ordinate, measured complex perceptual difference c. Dashed line, bisectrix; thick line, regression line (regression coefficient 0.858). Horizontal and vertical bars indicate standard deviations for some values (the largest and two typical deviations). These. deviations were estimated, fo~~o~n~ the rules of error ~rupagat~o~ (Bauie, 1959), from the standard deviations of the choice frequew~ values and the deviations of the ‘Wibration” curve of Fig. Z(b). {b) ~va~~t~on of same data according to the Eueiidean metric. In this case the expected values were determined by (a2 + @)‘:t. Regression coefficient 0.860. (cc) Determination of the best Minkowski metric, by means of the SQ-function [see Methods, formula (2)j. (d) Exponent of the respective best Minkowski metric for individual bees. Each segment of a column represents the best metric determined From the data of an individual; the height of the se@nents represents the number of measured values cont~buti~~ to this evaluation. Black columns indicate individuals with larger deviations in the ratings of type b, b’ (see text).
used. This curve was, however, determined on a somewhat different theoretical basis, namely the validity of the metric axioms (Ronacher, 1979b). The procedure is based on the assumption that perceptual differences which relate to a single perceptual parameter can be combined additively (Ui3 = Uzz+ Uz3, for stimuli 1, 2, and 3). However, when measuring choice frequencies, this additivity will not hold for values over 70%, i.e. in general: CF,, < CF,, + CF,, . The deviations from additivity in this inequality are due to the appI~~at~on of the function h. Assuming that h is linear for smaI1 values of U, one can infer the function h from these deviations in a recurrent procedure (for details see Ronacher, 1979b). This assumption of linearity of h for small values is justified by the observation that with small stimulus values the additivity also holds for choice frequencies,
This has been verified in detail for the parameters size and contrast (Ronacher, 19?9a, 1980), and appears to also be valid for differences in ring-patterns [cf. parallel curves in Fig. 2(a)]. The result of this calculation was a hyperbolic curve [thick CUPX in Fig. 2(b)]. Singe the values obtained with rung-patterns [* in Fig. Z(b)] also match this curve, the same calibration curve’ was used here. The effect of this calibration curve is, however, very similar to that of the Probit transformation {see below).
Beds, Krantz and Tversky (t968) and Tversky and Krantz (1970) established criteria for the ~ppii~bility of ~inkowski metrics: the main two are “intradimens~ona~ subtractivity” and “‘interdimensional additivity” (cf. also Dunn, 1983).
CITY-BLOCK
METRIC
IN BEES PATTERN
The first criterion, “intradimensional subtractivity”, is the requirement that distances along a perceptual parameter can be combined additively. This has already been verified for size (Ronacher, 1979a, 1980) and ring-patterns [Fig. 2(a)]. The second important condition for the applicability of Minkowski metrics is the independence of perceptual parameters (“interdimensional additivity”). This was tested in the following way: size discrimination was tested with (geometrically similar) patterns of different size (e.g. 1R50:lR20, 2RSo:2Rz0, or 3RSo:3R2’). The choice frequencies for these pairs were similar [curves parallel to the abscissa in Fig. 3(a)]. Size discrimination was thus largely independent of the pattern type. For most individuals the pattern discrimination was also independent of the size of test patterns [Fig. 3(b), tests were e.g. 1R20: 3RZo, 1Rso: 3R5’]. Only two individuals showed a larger deviation between tests with small and tests with large ring-patterns. Since the evaluation of the metric for these individuals did not reveal substantial differences [black columns in Fig. 4(d)], their data are included in Fig. 4(a-c) (for similar effects with human observers see Ronacher & Bautz, 1985). Thus the data apparently fulfill the second criterion as well. However, a further possibility had to be tested: it is conceivable that the bees had used only a single cue to discriminate these patterns. Indeed, some authors proposed that the bees evaluate the contour-length-ratio or contour-density-ratio (see Wehner, 198 1, for review). This kind of evaluation would produce the independence mentioned above as a “byproduct”, and would, of course, preclude the application of a multidimensional scaling procedure. The single-cue hypothesis can, however, be unequivocally ruled out on the basis of several observations. For example, in some individuals a difference was found in speed at which size discrimination and discrimination of equal-sized ring-patterns was acquired (further arguments will be presented in detail elsewhere, Ronacher, 1992). Thus, the bees used at least two cues to discriminate these ring-patterns, and since both criteria appear to hold, the application of Minkowski metrics is possible. Determination qf the best Minkowski metric In Fig. 4(a, b) the data of 10 bees (based on 10,870 choices) are presented in two evaluations, for the cityblock and the Euclidean metric. In both diagrams, measured values for distances of the type c are plotted against the expected values, which were calculated from a and h values according to formula (1) for the city-block metric (exponent r = 1) or for the Euclidean metric (r = 2). The procedure shall be exemplified with a single value [arrows in Fig. 4(a, b)]: for tests of the type a, i.e. size discrimination (cf. Fig. l), one individual produced choice frequencies of 77.5, 78.2, 82, and 78.4% [tested for black discs, lR-, 2R- and 3R-patterns, respectively, see curve marked with an arrow in Fig. 3(a); mean value 79.0%]. The discrimination of 1R : 3R-patterns yielded 78.3, 78.8 and 82.6% (tests of type b with 20, 32 and
RECOGNITION
1841
50 mm dia) [arrow in Fig. 3(b), mean value 79.9%]. The choice frequency for a test of type c, 1RSo: 3R*‘, was 92.3%. Transformation by means of the calibration curve [Fig. 2(b)] yields the following values a = 33, b = 34.5, c = 63.5, and the application of formula (1) yields an expected value of 67.5 for the city-block metric of 47.7 for the Euclidean metric (a + b), and [(a’ + b2)“*]. For this data triple the solution of equation (1) would result in r = 1.10. It is immediately apparent that the city-block metric is a quite satisfactory match for the data [compare solid regression line with the dotted bisectrix in Fig. 4(a)]. In contrast, the expected values for c with the Euclidean metric are too small in almost all cases. This is confirmed by Fig. 4(c) in which the best Minkowski metric was sought, i.e. that Minkowski metric for which the SQvalue [formula (2)] is minimum. This minimum is located at r = 1.02 [arrow in Fig. 4(c)]. As a control, the choice frequency data were also converted by the Probit transformation (Jander, 1968) instead of the calibration curve of Fig. 2(b). The best exponent, however, remained unaffected (r = 1.03). In Fig. 4(d) the best exponents are evaluated separately for individuals. Each column (or segment of a column) represents 1 bee, the different heights of the columns symbolize the number of measured values obtained per individual (data of the above mentioned two animals with larger deviations in the ratings of type b, b’ are marked by black columns). For all bees except 1, the city-block metric provided a much better description of the data than the Euclidean metric. The sole exception is caused by a single value (the two measurements obtained with this individual yielded an r of 1.15 and 1.82, respectively). Since for other individuals, too, single values occasionally were matched by the Euclidean metric [cf. Fig. 4(b)], this result certainly should not be interpreted as an indication for the existence of interindividual differences in the best Minkowski metric.
DISCUSSION The aim of this study was to determine the metric which best describes multidimensional perceptual differences of an insect. Earlier studies have already established several congruences between the perceptual capacities of the bee and of vertebrates: the feasability of “cross modality matches”, and the transitivity of the resulting equivalence relation (Ronacher, 1979a); the derivation of perceptual distances from “just noticeable differences” (Ronacher, 1979b, 1980; cf. also Backhaus & Menzel, 1987; Menzel & Backhaus, 1989); the ability to attend to certain parameters and to ignore others, depending on the training task (Ronacher, 1979a, 1980, 1992; cf. also Wehner, 1968, 1971a, 1975, 1981; Anderson, 1972; Schnetter, 1972; Klosterhalfen, Fischer & Bitterman, 1978) and the possibility to construct a perceptual parameter space and to describe similarity relations by metrics (Ronacher, 1979a, b; Backhaus et al., 1987).
1842
BERNHARD
In multidimensional scaling experiments with humans, a distinction has been drawn between “integral” (or “unitary”) stimuli, which are said to be subjected to “holistic” processing, and “separable” stimuli, which are said to be processed “analytically”. The description of multidimensional scaling data by the Euclidean or the city-block metric, respectively, is taken as an important criterion for holistic vs analytic processing (for review see Garner, 1974). Examples for integral stimuli are hue, saturation and brightness of colours (cf. Introduction); examples for a separable parameter combination are size and brightness (Attneave, 1950; Garner, 1977; see also Ronacher & Bautz, 1985; Ronacher & SiiD, 1990). With bees, the city-block metric was found to apply for size and brightness of discs (Ronacher, 1979bthe best exponent for these data is 1.09), as well as for colors (Backhaus ez al., 1987). The latter result was unexpected since, with humans, multidimensional scaling procedures with colors always led to an Euclidean metric (see above). Therefore, it was of interest to perform similarity scaling experiments with bees for other parameter combinations in order to test whether the city-block metric could be more generally valid for the bee’s perceptual system. Ring-patterns (of different sizes) were chosen because for humans they appear to have an intermediate position between highly separable and highly integral stimuli: in a similar experiment (cf. Fig. 1) with humans, the data of 70% of the subjects yielded an Euclidean metric (Ronacher, 1992). The bee’s data for ring-patterns are quite well described by a city-block metric (see Fig. 4, the best exponent 1.02 being not significantly different from 1.00) thus indicating that the overall dissimilarity is derived additively from the component differences. Thus, for the honeybee’s perceptual system the city-block metric provides a good description for three parameter combinations, which-for humans-range from separable to highly integral. It is thus conceivable that the city-block metric is generally valid for the bee’s perceptual system-a hypothesis which should now be tested for further parameter combinations. Recently, Shepard (1987) in his article “Toward a universal law of generalization for psychological science”, tried to relate the two forms of preferred perceptual metrics (Euclidean and city-block) to the optimization of object classification during the evolutionary history of nervous systems. Following Shepard’s line of reasoning, it is tempting to speculate that these types of experiments reveal a more fundamental difference between the differently organized perceptual systems of insects and vertebrates. REFERENCES Anderson, A. (1972). The ability of honey bees to generalise visual stimuli. In Wehner, R. (Ed.), Information processing in the visual system of arthropods (pp. 207-212). Berlin: Springer. Attneave, F. (1950). Dimensions of similarity. American Journal of Psychology, 63, 5 16556.
Backhaus, W. & Menzel, R. (1987). Color distance derived from a receptor model of color vision in the honeybee. Biological Cybernetits, 55, 321-331.
RONACHER Backhaus, W., Menzel, R. & Kreilll, S. (1987). Multidimensional scaling of color similarities in bees. Biological Cvhrmrtics. 56. 2933304.
Baule, B. (1959). Die Mathematik des Naturf0rscher.s und hgenieurs. Band II. Ausgleichs-und Ndherungsrechnung. Leipzig: Hirzel. Beals, R., Krantz, D. H. & Tversky, A. (1968). Foundations of multidimensional scaling. Psychological Review, 75, 127-142. Carnap, R. (1928). Der iogische Aufbau der Welt. Berlin: Weltkreisverlag. Dunn, J. C. (1983). Spatial metrics of integral and separable dimensions. Journal of Experimental Psychology, Human Perception and Performance,
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Garner, W. R. (1974). The processing of information and structure. London: Wiley. Garner, W. R. (1977). The effect of absolute size on the separability of the dimensions of size and brightness. Bulletin of the Psychonomic Society, 9, 380-382.
Gamer, W. R. & Felfoldy, G. L. (1970). integrality of stimulus dimensions in various types of information processing. Cog&ice Psychology, I, 225-241.
Handel, S. & Imai, S. (1972). The free classification of analyzable and unanalyzable stimuli. Perception and Psychophysics, 1.2, 108-l 16.
Hassenstein, B. (1958). Die Starke von optokinetischen Reaktionen auf verschiedene Mustergeschwindigkeiten. Zeitschrzfi fur Nuturforschung, 13b, l-6. von Helversen, 0. (1970). Zur spektralen Unterschiedsempfindlichkeit der Honigbiene. Thesis, Universitat Freiburg i.Br. von Helversen, 0. (1972). The relationship between difference in stimuli and choice frequency in training experiments with the honey bee. In Wehner, R. (Ed.), Information processing in the visual system of arlhropods (pp. 323-334). Berlin: Springer. Herrnstein, R. L. (1990). Levels of categorization. In Edelman, G. M., Gall, W. E. & Cowan, W. M. (Eds), Signal and sense. Local and global order in perceptual maps (pp. 385413). New York: Wiley-Liss. Jander, R. (1968). Uber die Ethometrie von Schliisselreizen, die Theorie der telotaktischen Wahlhandlung und das Potenzprinzip der terminalen Cumulation. Zeitschrifi fur Vergleichende Physiologic, 59, 3 19-356.
Klosterhalfen, S., Fischer, W. & Bitterman, M. E. (1978). Modification of attention in honey bees. Science, 201, 1241-1242. Mackintosh, N. J. (1974). The psychology of animal learning. New York: Academic Press. Menzel, R. & Backhaus, W. (1989). Color vision in honey bees: Phenomena and physiological mechanisms. In Stavenga, D. & Hardie, R. (Eds), Facets of vision (pp. 281-297). Berlin: Springer. Ronacher, B. (1979a). Aquivalenz zwischen Grdllen- und HelligkeitsUnterschieden im Rahmen der visuellen Wahrnehmung der Honigbiene. Biological Cybernetics, 32, 63. 75. Ronacher, B. (1979b). Beitrag einzelner Parameter zum wahrnehmungsgemaBen Unterschied von zusammengesetzten Reizen bei der Honigbiene. Biological Cybernetics, 32, 77-83. Ronacher, B. (1980). Ein einfacher Zusammenhang zwischen der Aquivalenzbeziehung und der Unterschiedsempfindlichkeit fur zwei Musterparameter bei der Honigbiene. Biological Cyberneiics, 36, 5161.
Ronacher, B. (1983). Unabhlngigkeit der Bewertung zweier Musterparameter von deren Unterschiedlichkeitsgrad bei der Dressur. Biological Cybernetics, 46, 173-l 82. Ronacher, B. (1992). Influence of unrewarded stimuli on the classitication of visual patterns by the honeybee. Ethology. Submitted. Ronacher, B. & Bautz, W. (1985). Human pattern recognition: Individually different strategies in analyzing complex stimuli. Biological Cybernetics, 51, 249-261.
Ronacher, B. & StiO, H. (1990). Perception of size and lightness of human observers: Two criteria for holistic and analytic processing show no correlation in individuals. Biological Cybernetics, 64, 107-115.
Schnetter, B. (1972). Experiments on pattern discrimination in honey bees. In Wehner, R. (Ed.), Informationprocessing in the visual system of arthropods (pp. 195200). Berlin: Springer
CITY-BLOCK
METRIC
IN BEES
Shepard, R. N. (1964). Attention and the metric structure of the stimulus space. Journal of Mathematical Psychology, I, 54-87. Shepard, R. N. (1987). Toward a universal law of generalization for psychological science. Science, 237, 13 17-l 323. Stevens, S. S. (1959). Cross-modality validation of subjective scales for loudness, vibration, and electric shock. Journal of Experimental Psychology, 57, 201-209. Stevens, S. S. (1969). On predicting exponents for cross-modality matches. Perception and Psychophysics, 6, 251-256. Suga, N. (1988). What does single-unit analysis in the auditory cortex tell us about information processing in the auditory system? In Racik, P. & Singer, W. (Eds), Neurobiology of neocortex (pp. 331-349). New York: Wiley. Torgerson, W. S. (1958). Theory and methods of scaling. New York: Wiley. Treisman, A. (1986). Properties, parts, and objects. In Boff, K., Kaufmann, L. & Thomas, J. (Eds), Handbook of perception and human performance (pp. I-71). New York: Wiley. Tversky, A. & Krantz, D. H. (1970). The dimensional representation and the metric structure of similarity data. Journal of Mathematical Psychology, 7, 572-596. Wehner, R. (1968). Die Bedeutung der Streifenbreite fur die optische Winkelmessung der Biene (Apis mellifica). Zeitschrzft ftir Vergleichende Physiologie, 58. 322-343.
PATTERN
Wehner,
1843
RECOGNITION
R. (1969). Der Mechanismus
der optischen
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bei der Biene Apis mellifica). Zoologischer Anzeiger (Suppl. 33), Verhandlungen der Deutschen Zoologischen Gesellschaft, 586-592. Wehner, R. (1971a). The generalization of directional visual stimuli in the honey bee, Apis mellifera. Journal of Insect Physiology, 17, 1579-1591. Wehner, R. (1971b). Formensehen bei Insekten. Orientierungsphysiologische Untersuchungen zur Datenverarbeitung in optischen Systemen. Verhandlungen der Deutschen Zoologischen Gesellschaft. 65, 251-266. Wehner, R. (1975). Pattern recognition. In Horridge, G. A. (Ed.), The compound eye and vision qf insects (pp. 755113). Oxford: Clarendon Press. Wehner, R. (1981). Spatial vision in arthropods. In Autrum, H., Jung, R., Loewenstein, W. R., MacKay, D. M. & Teuber, H. L. (Eds), Comparariue physiology and evolution of vision in inoertebrates. Handbook of sensory physiology. Volume V11/6C (pp. 287-616). Berlin: Springer.
Acknowledgements-I thank J. Singer and H. Beck for their help with the experiments, Otto von Helversen for critically reading the manuscript, and the DFG for financial support (Ro 547/4-1,2).
