The Mathematics, Nanostructure, and Evolution of Color-Producing Biological Arrays

Richard O. Prum and Rodolfo H. Torres

Why is it blue? - Fourier Analysis
Poster on Fourier analysis

This interdisciplinary work is devoted to the study of the anatomy and nanostructure of structurally colored tissues of living organisms, and to the analysis of the physical and mathematical modeling of the optical phenomena that produce such coloration. The mathematical tools employed relate to the understanding of quasi-order in physical and geometrical configurations through Fourier analysis techniques. The methods applied follow in part an electromagnetic scattering theoretical model described by G. Benedek (Theory of transparency of the eye, Applied Optics, 1971). The Fast Fourier Transform (FFT) of transmission electron micrographs of biological tissues is employed to characterize the spatial periodicity in variation in refractive index of nanostructured material.
The analysis of evolutionary transitions among nanostructural classes and their forms of coloration have important implications for the study of the function of such biological arrays in communication, mate selection, and other research areas in biology.

 

Media Coverage

Non-technical description of this work and related ones can be found in the following media coverage and related topics
(you may need to be a subscriber to the corresponding publication to access some of articles)

 

Publications

  • Prum, R. O., Torres, R. H., Williamson, S., and Dyck, J. 1998. Coherent light scattering by blue bird feather barbs. Nature 396: 28-29.
  • Prum, R. O., Torres, R. H., Williamson, S., and Dyck, J. 1999. Two-dimensional Fourier analysis of the spongy medullary keratin of structurally coloured feather barbs. Proceedings of the Royal Society, London: Biological Sciences (B) 266: 13-22.
  • Prum, R. O., Torres, R. H., Kovach, C., Williamson, S., and Goodman, S. M. 1999. Coherent Light Scattering by Nanostructured Collagen Arrays in the Caruncles of the Malagasy Asities (Eurylaimidae: Aves). Journal of Experimental Biology 202: 3507-3522.
  • Prum, R. O., and Torres, R. H. 2001. Azul de ave. Un color estructural. Investigación y Ciencia (Spanish edition of Scientific American) 299: 36-37.
  • Prum, R. O., Andersson, and S. F., Torres, R. H. 2003. Coherent scattering of ultraviolet light by avian feather barbs. Auk 120:163-170.
  • Prum, R. O., and Torres, R. H. 2003. Structural colouration of avian skin: Convergent evolution of coherently scattering dermal collagen arrays. Journal of Experimental Biology 206: 2409-2429.
  • Prum, R. O., and Torres, R. H. 2003. A Fourier tool for the analysis of coherent light scattering by bio-optical nanostructures. Integrative and Comparative Biology 43: 591-610.
  • Prum, R. O., and Torres, R. H. 2004. Structural colouration of mammalian skin: Convergent evolution of coherently scattering dermal collagen arrays. Journal of Experimental Biology 207: 2157-2172.
  • Prum, R. O., Cole, J. A., and Torres, R. H. 2004. Blue integumentary structural colours in dragonflies (Odonata) are not produced by incoherent Tyndall scattering. Journal of Experimental Biology 207: 3999-4009.
  • Torres, R. H. and Prum, R. O. 2005. Análisis espectral de nanoestructuras en tejidos biológicos. Matematicalia 1 no. 2: Matematicalia website.
  • Prum, R. O., T. Quinn, and Torres, R. H. 2006. Anatomically Diverse Butterfly Scales Produce Structural Colors by Coherent Scattering. Journal of Experimental Biology 209: 748-765.

 

Contact Information

 

 

Support and Disclaimer

This research has been supported in part by the National Science Foundation under the following Grants: DEB-9318273, DMS-9696267, DMS-0070514, DBI-0078376, DMS-0112375, DMS-0400423

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.