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Multidimensional scaling of color similarity in bees

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Abstract

A multiple choice experiment with free flying bees trained to a color signal is described which allows for multidimensional scaling of color similarity. The choice proportions are analysed by metric (Torgerson 1958) and non-metric (Kruskal 1964a, b) multidimensional scaling. The light reflected from the twelve color signals used differed in spectral composition, intensity, and the proportion of white light. Only two scales are necessary to reconstruct the experimental data. The interpretation of the scale values by Helmholtz-coordinates, derived from the chromaticity diagram for bees, shows that the main perceptual parameters are hue and saturation (or blue/greenness and UV/blue-greenness, respectively). Brightness is ignored by the bees in this choice situation. The total color difference is related to the differences on the two perceptual parameters by the city-block metric (Minkowski exponentp=1).

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References

  • Ahrens HJ (1974) Multidimensionale Skalierung. Methodik, Theorie und empirische Gültigkeit mit Anwendungen aus der differentiellen Psychologie und Sozialpsychologie. Beltz, Weinheim

    Google Scholar 

  • Backhaus W, Menzel R (1984) Multidimensional scaling of the colour space of honeybees. Verh Dtsch Zool Ges 77:230

    Google Scholar 

  • Backhaus W, Menzel R (1987) Color distance derived from a receptor model of color vision in the honeybee. Biol Cybern 55:321–331

    Google Scholar 

  • Daumer K (1956) Reizmetrische Untersuchung des Farbensehens der Bienen. Z Vergl Physiol 38:413–478

    Google Scholar 

  • Davison ML (1983) Multidimensional scaling. Wiley, New York

    Google Scholar 

  • Frisch K v (1914) Der Farbensinn und Formensinn der Bienen. Zool Jb Abt Allg Zool Physiol 35:1

    Google Scholar 

  • Guilford JP (1937) Scale values derived from the method of choices. Psychometrika 2:139–150

    Google Scholar 

  • Helm CE (1964) Multidimensional ratio scaling analysis of perceived color relations. J Opt Soc Am 54:256–262

    Google Scholar 

  • Helversen O v (1972) Zur spektralen Unterschiedsempfindlichkeit der Honigbiene. J Comp Physiol 80:439–472

    Google Scholar 

  • Hotelling H (1933) Analysis of a complex of statistical variables into principale components. J Educ Psychol 24:417–441, 498–520

    Google Scholar 

  • Indow T, Ohsumi K (1972) Multidimensional mapping of sixty Munsell colors by nonmetric procedure. In: Vos JJ, et al. (eds) Color metrics. AIC, Holland

    Google Scholar 

  • Krantz DH (1967) Rational distance functions for multidimensional scaling. J Math Psychol 4:226–245

    Google Scholar 

  • Kruskal JB (1964a) Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika 29:1–29

    Google Scholar 

  • Kruskal JB (1964b) Nonmetric multidimensional scaling: A numerical method. Psychometrika 29:115–131

    Google Scholar 

  • Kruskal JB, Wish M (1978) Multidimensional scaling. Sage, Beverly Hills, CA

    Google Scholar 

  • Labhart T (1974) Behavioral analysis of light intensity discrimination and spectral sensitivity in the honey bee,Apis mellifera. J Comp Physiol 95:203–216

    Google Scholar 

  • Lieke E (1987) Honeybees have a perceptual dimension of color saturation. J Comp Physiol (in press)

  • Menzel R (1967) Untersuchungen zum Erlernen von Spektralfarben durch die Honigbiene (Apis mellifica). Z Vergl Physiol 56:22–62

    Google Scholar 

  • Menzel R, Greggers U (1985) Natural phototaxis and its relationship to colour vision in honeybees. J Comp Physiol 157:311–321

    Google Scholar 

  • Menzel R, Lieke E (1983) Antagonistic color effects in spatial vision of honeybees. J Comp Physiol 141:389–393

    Google Scholar 

  • Nash JC (1979) Compact numerical methods for computers. Hilger, Bristol

    Google Scholar 

  • Messick SJ, Abelson RP (1956) The additive constant problem in multidimensional scaling. Psychometrika 21:1–17

    Google Scholar 

  • Sixtl F (1982) Meßmethoden der Psychologie. Theoretische Grundlagen und Probleme. 2. Edn. Beltz, Weinheim

    Google Scholar 

  • Thurstone LL (1927) A law of comparative judgment. Psychol Rev 34:273–286

    Google Scholar 

  • Torgerson WS (1951) A theoretical and empirical investigation of multidimensional scaling. Ph.D. Thesis, Princeton University

  • Torgerson WS (1958) Theory and methods of scaling. Wiley, New York

    Google Scholar 

  • Überla K (1982) Faktorenanalyse. Eine systematische Einführung für Psychologen, Mediziner, Wirtschafts- und Sozialwissenschaftler. 2. Edn. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Werner A, Menzel R (1984) Color discrimination and receptor color space in honeybees. Verh Dtsch Zool Ges 77:229

    Google Scholar 

  • Zielinski R (1978) Erzeugung von Zufallszahlen. Program-mierung und Test auf Digitalrechnern. Deutsch, Frankfur/Main

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Backhaus, W., Menzel, R. & Kreißl, S. Multidimensional scaling of color similarity in bees. Biol. Cybernetics 56, 293–304 (1987). https://doi.org/10.1007/BF00319510

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