Journal of Comparative Physiology A

, Volume 203, Issue 12, pp 983–997 | Cite as

The path to colour discrimination is S-shaped: behaviour determines the interpretation of colour models

  • Jair E. Garcia
  • Johannes Spaethe
  • Adrian G. DyerEmail author
Original Paper


Most of our current understanding on colour discrimination by animal observers is built on models. These typically set strict limits on the capacity of an animal to discriminate between colour stimuli imposed by physiological characteristics of the visual system and different assumptions about the underlying mechanisms of colour processing by the brain. Such physiologically driven models were not designed to accommodate sigmoidal-type discrimination functions as those observed in recent behavioural experiments. Unfortunately, many of the fundamental assumptions on which commonly used colour models are based have been tested against empirical data for very few species and many colour vision studies solely rely on physiological measurements of these species for predicting colour discrimination processes. Here, we test the assumption of a universal principle of colour discrimination only mediated by physiological parameters using behavioural data from four closely related hymenopteran species, considering two frequently used models. Results indicate that there is not a unique function describing colour discrimination by closely related bee species, and that this process is independent of specific model assumptions; in fact, different models produce comparable results for specific test species if calibrated against behavioural data.


Sigmoidal Vision Bee Receptor noise Hexagon 



The authors acknowledge Professor Leo Fleishman for discussions and comments on a previous version of the manuscript, and Dr. Lalina Muir for careful editing. We also thank the two anonymous reviewers and editors for valuable feedback on our study.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material

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  1. Avargués-Weber A, de Brito Sanchez MG, Giurfa M, Dyer AG (2010) Aversive reinforcement improves visual discrimination learning in free-flying honeybees. PLoS One 5(e15):370. doi: 10.1371/journal.pone.0015370 Google Scholar
  2. Avargués-Weber A, Giurfa M (2014) Cognitive components of color vision in honey bees: how conditioning variables modulate color learning and discrimination. J Comp Physiol A 200:449–461CrossRefGoogle Scholar
  3. Backhaus W (1991) Color opponent coding in the visual system of the honeybee. Vis Res 31:1381–1397CrossRefPubMedGoogle Scholar
  4. Backhaus W (1998) Physiological and psychophysical simulations of color vision in humans and animals. In: Backhaus W, Reinhold K, Werner JS (eds) Color vision: perspectives from different disciplines. Walter de Gruyter, Berlin, pp 45–75CrossRefGoogle Scholar
  5. Benes ES (1969) Behavioral evidence for color discrimination by the whiptail lizard, Cnemidophorus tigris. Copeia 1969:707–722CrossRefGoogle Scholar
  6. Bobeth H (1979) Dressurversuche zum Farbensehen der Bienen: Die Sättigung von Spektralfarben. PhD thesis, Albert-Ludwigs-Universität zu Freigburg i.BrGoogle Scholar
  7. Brandt R, Vorobyev M (1997) Metric analysis of threshold spectral sensitivity in the honeybee. Vis Res 37:425–439. doi: 10.1016/S0042-6989(96)00195-2 CrossRefPubMedGoogle Scholar
  8. Briscoe AD, Chittka L (2001) The evolution of color vision in insects. Annu Rev Entomol 46:471–510CrossRefPubMedGoogle Scholar
  9. Bukovac Z, Shrestha M, Garcia JE, Burd M, Dorin A, Dyer AG (2017) Why background colour matters to bees and flowers. J Comp Physiol A 203:369–380. doi: 10.1007/s00359-017-1175-7 CrossRefGoogle Scholar
  10. Bukovac Z, Dorin A, Dyer AG (2013) A-bees see: a simulation to assess social bee visual attention during complex search tasks. In: Lio’ P, Miglino O, Nicosia G, Nolfi G, Pavone M (eds) Advances in artificial life ECAL 2013. Proceedings of the twelfth European conference on the synthesis and simulation of living systems, Taormina, September 2013. MIT Press, Cambridge, Complex adaptive systems, pp 276–283Google Scholar
  11. Burns JG, Dyer AG (2008) Diversity of speed-accuracy strategies benefits social insects. Curr Biol 18:R953–R954CrossRefPubMedGoogle Scholar
  12. Champ CM, Vorobyev M, Marshall NJ (2016) Colour thresholds in a coral reef fish. R Soc Open Sci 3(160):399. doi: 10.1098/rsos.160399 Google Scholar
  13. Chittka L (1992) The colour hexagon: a chromaticity diagram based on photoreceptor excitations as a generalized representation of colour opponency. J Comp Physiol A 170:533–543Google Scholar
  14. Crawley MJ (2012) The R book, 2nd edn. Wiley, ChichesterCrossRefGoogle Scholar
  15. Daumer K (1956) Reizmetrische Untersuchung des Farbensehens der Bienen. Z Vergleich Physiol 38:413–478Google Scholar
  16. Dyer AG (2006) Discrimination of flower colours in natural settings by the bumblebee species Bombus terrestris (Hymenoptera: Apidae). Entomol Gen 28:257–268CrossRefGoogle Scholar
  17. Dyer AG, Arikawa K (2014) A hundred years of color studies in insects: with thanks to Karl von Frisch and the workers he inspired. J Comp Physiol A 200:409–410CrossRefGoogle Scholar
  18. Dyer AG, Boyd-Gerny S, McLoughlin S, Rosa MG, Simonov V, Wong BB (2012) Parallel evolution of angiosperm colour signals: common evolutionary pressures linked to hymenopteran vision. Proc R Soc B 279:3606–3615. doi: 10.1098/rspb.2012.0827 CrossRefPubMedPubMedCentralGoogle Scholar
  19. Dyer AG, Chittka L (2004a) Biological significance of distinguishing between similar colours in spectrally variable illumination: Bumblebees (Bombus terrestris) as a case study. J Comp Physiol A 190:105–114. doi: 10.1007/s00359-003-0475-2 CrossRefGoogle Scholar
  20. Dyer AG, Chittka L (2004b) Fine colour discrimination requires differential conditioning in bumblebees. Naturwissenschaften 91:224–227CrossRefPubMedGoogle Scholar
  21. Dyer AG (2012) Psychophysics of honey bee color processing in complex environments. In: Galizia CG, Eisenhardt D, Giurfa M (eds) Honeybee neurobiology and behaviour. Springer, Heidelberg, pp 303–314CrossRefGoogle Scholar
  22. Dyer AG, Garcia JE (2014) Color difference and memory recall in free-flying honeybees: forget the hard problem. Insects 5:629–638. doi: 10.3390/insects5030629 CrossRefPubMedPubMedCentralGoogle Scholar
  23. Dyer AG, Neumeyer C (2005) Simultaneous and successive colour discrimination in the honeybee (Apis mellifera). J Comp Physiol A 191:547–57. doi: 10.1007/s00359-005-0622-z CrossRefGoogle Scholar
  24. Dyer AG, Paulk AC, Reser DH (2011) Colour processing in complex environments: insights from the visual system of bees. Proc R Soc B 278:952–959. doi: 10.1098/rspb.2010.2412 CrossRefPubMedGoogle Scholar
  25. Dyer AG, Spaethe J, Prack S (2008) Comparative psychophysics of bumblebee and honeybee colour discrimination and object detection. J Comp Physiol A 194:617–627. doi: 10.1007/s00359-008-0335-1 CrossRefGoogle Scholar
  26. Efron B, Tibshirani RJ (1993) An introduction to the bootstrap. Chapman & Hall, New YorkCrossRefGoogle Scholar
  27. Fleishman LJ, Perez CW, Yeo AI, Cummings KJ, Dick S, Almonte E (2016) Perceptual distance between colored stimuli in the lizard Anolis sagrei: comparing visual system models to empirical results. Behav Ecol Sociobiol 70:541–555. doi: 10.1007/s00265-016-2072-8 CrossRefGoogle Scholar
  28. von Frisch K (1914) Der Farbensinn und Formensinn der Biene. Zool Jahrb Abt allg Zool Physiol Tiere 37:1–187Google Scholar
  29. Garcia JE, Hung YS, Rosa MG, Endler JA, Dyer AG (2017) Improved color constancy in honeybees enabled by parallel visual projections from dorsal ocelli. PNAS. doi: 10.1073/pnas.1703454114 Google Scholar
  30. Giurfa M (2004) Conditioning procedure and color discrimination in the honeybee Apis Mellifera. Naturwissenschaften 91:228–231CrossRefPubMedGoogle Scholar
  31. Giurfa M (2007) Behavioral and neural analysis of associative learning in the honeybee: a taste from the magic well. J Comp Physiol A 193:801–824. doi: 10.1007/s00359-007-0235-9 CrossRefGoogle Scholar
  32. Grimm V, Revilla E, Berger U, Jeltsch F, Mooij WM, Railsback SF, Thulke HH, Weiner J, Wiegand T, DeAngelis DL (2005) Pattern-oriented modeling of agent-based complex systems: lessons from ecology. Science 310:987–991. doi: 10.1126/science.1116681 CrossRefPubMedGoogle Scholar
  33. Hall P, Hart JD (1990) Bootstrap test for difference between means in nonparametric regression. JASA 85:1039–1049CrossRefGoogle Scholar
  34. von Helmholtz H (1970) Physiological optics. In: MacAdam D (ed) Sources of color science. MIT Press, Cambridge, pp 84–100Google Scholar
  35. von Helversen O (1972a) Zur spektralen der Honigbiene. J Comp Physiol 80:439–472CrossRefGoogle Scholar
  36. von Helversen O (1972b) The relationship between difference in stimuli and choice frequency in training experiments with the honeybee. In: Wehner R (ed) Information processing in the visual systems of arthropods. Springer, Berlin, pp 323–334CrossRefGoogle Scholar
  37. Hempel de Ibarra N, Vorobyev M, Menzel R (2014) Mechanisms, functions and ecology of colour vision in the honeybee. J Comp Physiol A 200:411–433. doi: 10.1007/s00359-014-0915-1 CrossRefGoogle Scholar
  38. Howard J, Blakeslee B, Laughlin S (1987) The intracellular pupil mechanism and photoreceptor signal: noise ratios in the fly Lucilia cuprina. Proc R Soc B 231:415–435CrossRefGoogle Scholar
  39. Kelber A (2016) Colour in the eye of the beholder: receptor sensitivities and neural circuits underlying colour opponency and colour perception. Curr Opin Neurobiol 41:106–112. doi: 10.1016/j.conb.2016.09.007 CrossRefPubMedGoogle Scholar
  40. Kemp D, Herberstein M, Fleishman L, Endler J, Bennett A, Dyer A, Hart N, Marshall J, Whiting M (2015) An integrative framework for the appraisal of coloration in nature. Am Nat 185:705–724CrossRefPubMedGoogle Scholar
  41. Komatsu H, Ideura Y (1993) Relationships between color, shape, and pattern selectivities of neurons in the inferior temporal cortex of the monkey. J Neurophysiol 70:677–694PubMedGoogle Scholar
  42. van der Kooi CJ, Elzenga JTM, Staal M, Stavenga DG (2016) How to colour a flower: on the optical principles of flower coloration. Proc R Soc B 283:1–9Google Scholar
  43. Koshitaka H, Kinoshita M, Vorobyev M, Arikawa K (2008) Tetrachromacy in a butterfly that has eight varieties of spectral receptors. Proc R Soc B 275:947–954CrossRefPubMedPubMedCentralGoogle Scholar
  44. Kulikowski J, Walsh V (1991) On the limits of colour detection and discrimination. In: Kulikowski J, Walsh V, Murray I (eds) Limits of vision. MacMillan Press, London, pp 202–220Google Scholar
  45. Lehrer M (1999) Dorsoventral asymmetry of colour discrimination in bees. J Comp Physiol A 184:195–206. doi: 10.1007/s003590050318 CrossRefGoogle Scholar
  46. Lind O, Kelber A (2009) Avian colour vision: effects of variation in receptor sensitivity and noise data on model predictions as compared to behavioural results. Vis Res 49:1939–1947. doi: 10.1016/j.visres.2009.05.003 CrossRefPubMedGoogle Scholar
  47. Longden KD (2016) Central brain circuitry for color vision modulated behaviors. Curr Biol 26:R981–R988CrossRefPubMedGoogle Scholar
  48. Lythgoe JN (1979) The ecology of vision. Oxford University Press, New YorkGoogle Scholar
  49. MacAdam DL (1942) Visual sensitivities to color differences in daylight. J Opt Soc Am 32:247–273. doi: 10.1364/JOSA.32.000247 CrossRefGoogle Scholar
  50. MacAdam DL (1943) Specification of small chromaticity differences. J Opt Soc Am 33:18–26. doi: 10.1364/JOSA.33.000018 CrossRefGoogle Scholar
  51. MacAdam DL (1985) Color measurement theme and variations, 2nd edn. Springer, BerlinGoogle Scholar
  52. Martínez-Harms J, Vorobyev M, Schorn J, Shmida A, Keasar T, Homberg U, Schmeling F, Menzel R (2012) Evidence of red sensitive photoreceptors in Pygopleurus israelitus (Glaphyridae: Coleoptera) and its implications for beetle pollination in the southeast Mediterranean. J Comp Physiol A 198:451–463CrossRefGoogle Scholar
  53. Morawetz L, Spaethe J (2012) Visual attention in a complex search task differs between honeybees and bumblebees. J Exp Biol 215:2515–2523CrossRefPubMedGoogle Scholar
  54. Neumeyer C (1992) Tetrachromatic color vision in goldfish: evidence from color mixture experiments. J Comp Physiol A 171:639–649. doi: 10.1007/BF00194111 CrossRefGoogle Scholar
  55. Newhall SM, Burnham RW, Clark JR (1957) Comparison of successive with simultaneous color matching. J Opt Soc Am 47:43–54. doi: 10.1364/JOSA.47.000043 CrossRefGoogle Scholar
  56. Olsson P, Lind O, Kelber A (2015) Bird colour vision: behavioural thresholds reveal receptor noise. J Exp Biol 218:184–193CrossRefPubMedGoogle Scholar
  57. Paine CET, Marthews TR, Vogt DR, Purves D, Rees M, Hector A, Turnbull LA (2012) How to fit nonlinear plant growth models and calculate growth rates: an update for ecologists. Methods Ecol Evol 3:245–256. doi: 10.1111/j.2041-210X.2011.00155.x CrossRefGoogle Scholar
  58. Peitsch D, Fietz A, Hertel H, Souza J, Ventura D, Menzel R (1992) The spectral input systems of hymenopteran insects and their receptor-based colour vision. J Comp Physiol A 170:23–40. doi: 10.1007/bf00190398 CrossRefPubMedGoogle Scholar
  59. Pinheiro J, Bates D, DebRoy S, Sarkar D, R Core Team (2016) nlme: linear and nonlinear mixed effects models. R package version 3.1-125Google Scholar
  60. Pommerening A, Muszta A (2016) Relative plant growth revisited: towards a mathematical standardisation of separate approaches. Ecol Model 320:383–392CrossRefGoogle Scholar
  61. R Core Team (2016) R: A language and environment for statistical computing. R foundation for statistical computing, Vienna, Austria.
  62. Renoult JP, Kelber A, Schaefer HM (2017) Colour spaces in ecology and evolutionary biology. Biol Rev 92:292–315. doi: 10.1111/brv.12230 CrossRefPubMedGoogle Scholar
  63. Reser DH, Wijesekara Witharanage R, Rosa MGP, Dyer AG (2012) Honeybees (Apis mellifera) learn color discriminations via differential conditioning independent of long wavelength (green) photoreceptor modulation. PLoS One 7(e48):577. doi: 10.1371/journal.pone.0048577 Google Scholar
  64. Shepard R (1987) Toward a universal law of generalization for psychological science. Science 237:1317–1323. doi: 10.1126/science.3629243 CrossRefPubMedGoogle Scholar
  65. Shrödinger E (1926) Thresholds of color differences. In: MacAdam DL (ed) Sources of color science. MIT Press, Cambridge, pp 183–193Google Scholar
  66. Skorupski P, Chittka L (2010) Differences in photoreceptor processing speed for chromatic and achromatic vision in the bumblebee, Bombus terrestris. J Neurosci 30:3896–3903CrossRefPubMedGoogle Scholar
  67. Sommerlandt FMJ, Spaethe J, Rössler W, Dyer AG (2016) Does fine color discrimination learning in free-flying honeybees change mushroom-body calyx neuroarchitecture? PLoS One 11:1–17. doi: 10.1371/journal.pone.0164386 CrossRefGoogle Scholar
  68. Spaethe J, Streinzer M, Eckert J, May S, Dyer AG (2014) Behavioural evidence of colour vision in free flying stingless bees. J Comp Physiol A 200:485–486CrossRefGoogle Scholar
  69. Stavenga D, Smits R, Hoenders B (1993) Simple exponential functions describing the absorbance bands of visual pigments. Vis Res 33:1011–1017CrossRefPubMedGoogle Scholar
  70. Tabanick BG, Fidell L (2007) Using multivariate statistics, 5th edn. Pearson Allyn and Bacon, BostonGoogle Scholar
  71. Telles FJ, Kelber A, Rodríguez-Gironés MA (2016) Wavelength discrimination in the hummingbird hawkmoth Macroglossum stellatarum. J Exp Biol 219:553–560CrossRefPubMedGoogle Scholar
  72. Thoen HH, How MJ, Chiou TH, Marshall J (2014) A different form of color vision in mantis shrimp. Science 343:411–413. doi: 10.1126/science.1245824 CrossRefPubMedGoogle Scholar
  73. Vorobyev M, Brandt R (1997) How do insect pollinators discriminate colors? Israel J Plant Sci 45:103–113CrossRefGoogle Scholar
  74. Vorobyev M, Brandt R, Peitsch D, Laughlin SB, Menzel R (2001) Colour thresholds and receptor noise: behaviour and physiology compared. Vis Res 41:639–653. doi: 10.1016/s0042-6989(00)00288-1 CrossRefPubMedGoogle Scholar
  75. Vorobyev M, Osorio D (1998) Receptor noise as a determinant of colour thresholds. Proc R Soc B 265:351–358CrossRefPubMedPubMedCentralGoogle Scholar
  76. Wright AA (1972) Psychometric and psychophysical hue discrimination functions for the pigeon. Vis Res 12:1447–1464. doi: 10.1016/0042-6989(72)90171-X CrossRefPubMedGoogle Scholar
  77. Wyszecki G, Stiles W (1982) Color science concepts and methods, quantitative data and formulae, 2nd edn. Wiley, New YorkGoogle Scholar
  78. Yang EC, Lin HC, Hung YS (2004) Patterns of chromatic information processing in the lobula of the honeybee, Apis Mellifera L. J Insect Physiol 50:913–925CrossRefPubMedGoogle Scholar
  79. Zuur AF, Ieno EN, Saveliev AA (2009) Mixed effects models and extensions in ecology with R. Springer, New YorkCrossRefGoogle Scholar
  80. Zwietering MH, Jongenburger I, Rombouts FM, van't Riet K (1990) Modeling of the bacterial growth curve. Appl Environ Microbiol 56:1875–1881PubMedPubMedCentralGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Bio-Inspired Digital Sensing (BIDS) Lab, School of Media and CommunicationRMIT UniversityMelbourneAustralia
  2. 2.Department of Behavioral Physiology and SociobiologyBiozentrum, University of WuerzburgWuerzburgGermany

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