The Mathematics, Nanostructure, and Evolution of
Color-Producing Biological Arrays
Richard O. Prum and Rodolfo H. Torres
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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.
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)
Lawrence Journal World
Science on Line
Nature (Science Update)
Nature, Photonic structures in Biology
Nature (UV News Feature)
New York Times
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: http://www.matematicalia.net/.
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.
- Richard O. Prum, William Robertson Coe Professor of Ornithology
- Mail: Ecology and Evolutionary Biology
Peabody Museum of Natural History
New Haven, CT 06520-8105
- Office: Environmental Science Center (ESC) 164
- Phone: (203) 432-9423
- Fax: (203) 432-5176
- E-mail: firstname.lastname@example.org
- Rodolfo H. Torres, Professor of Mathematics
- Mail: Department of Mathematics
University of Kansas
405 Snow Hall
1460 Jayhawk Blvd
Lawrence, KS 66045
- Office: 623 Snow Hall
- Phone: (785) 864-7310
- Fax: (785) 864-5255
- E-mail: email@example.com
- URL: http://torres.faculty.ku.edu/
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.