scientific correspondence

1. Peterson, M. D. The Jefferson Image in the American Mind
181–187 (Oxford Univ. Press, New York, 1960).
2. Malone, D. Jefferson the President: First Term, 1801–1805
Appendix II, 494–498 (Little Brown, Boston, MA, 1970).
3. Brodie, F. M. Thomas Jefferson: An Intimate History (Norton,New York, 1974).
4. Ellis, J. J. American Sphinx: The Character of Thomas Jefferson(Knopf, New York, 1997).
5. Callender, J. T. Richmond Recorder 1 September 1802. [Cited in:Gordon-Reed, A. Thomas Jefferson and Sally Hemings: An American
Controversy (Univ. Press of Virginia, Charlottesville, 1997)].
6. Woodson, M. S. The Woodson Source Book 2nd edn(Washington, 1984).
7. Hammer, M. F. Mol. Biol. Evol. 11, 749–761 (1994).
8. Whitfield, L. S., Sulston, J. E. & Goodfellow, P. N. Nature 378,379–380 (1995).
9. Seielstad, M. T. et al. Hum. Mol. Genet. 3, 2159–2161 (1994).
10. Zerjal, T. et al. Am. J. Hum. Genet. 60, 1174–1183 (1997).
11. Mathias, N., Bayes, M. & Tyler-Smith, C. Hum. Mol. Genet. 3,115–123 (1994).
12. Kwok, C. et al. J. Med. Genet. 33, 465–468 (1996).
13. Kayser, M. et al. Int. J. Legal Med. 110, 125–133 (1997).
14. Jobling, M. A., Bouzekri, N. & Taylor, P. G. Hum. Mol. Genet. 7,643–653 (1998).

a×107
5

1.125

4.5

0.750

3.50.375

32.5

020.375

1.50.750

11.125

28

1635
1430

1225

10820

615

410

2

5

0.50.375 0.750 1.125

Spatial frequency (nm—1 × 10—2)

The structural colours of avian feather
barbs are created by the scattering of lightfrom the spongy matrix of keratin and airin the medullary layer of the barbs1–5. However, the precise physical mechanism for theproduction of these colours is still controversial1,3,4,6. Here we use a two-dimensional(2D) Fourier analysis of the spatial variation in refractive index of the blue feather
barbs of the plum-throated cotinga (Cotingamaynana, Cotingidae) to show that thecolour is produced by constructive interference between light waves scattered coherently by the nanostructured keratin–airmatrix of the barbs.
Mechanisms proposed to explain the production of structural colours of feather barbsb4

1.125 0.750 0.375 0Coherent light scatteringby blue feather barbs

80% Reflectance*6 Gildersleeve Wood, Charlottesville,Virginia 22903, USAe-mail: eafoster@aol.com†Department of Genetics,
University of Leicester,
Adrian Building, University Road,Leicester LE1 7RH, UK‡Department of Statistics,
University of Oxford,
South Parks Road, Oxford OX1 3TG, UK§MGC Department of Human Genetics,
Leiden University, PO Box 9503,
2300 RA Leiden, The Netherlands¶Department of Biochemistry,
University of Oxford,
South Parks Road, Oxford OX1 3QU, UK

quasi-random array of scatterers, coherentscattering is predicted only for light waves
with a wavelength of twice that of the largest
components of the Fourier transform of thespatial variation in refractive index7. We
performed a discrete 2D Fourier analysis ofdigitized transmission electron micrographsof cross-sections of the medullary keratin
from the blue feather barbs of C. maynana
to examine whether it has periodic spatial
variation in refractive index. The spongy
medullary layer of C. maynana barbs consists of a matrix of keratin bars with air vacuoles of strikingly uniform diameter andspacing2. The matrix has no planes of symmetry and is randomly orientated to thesurface of the feather. The 2D Fourier power
spectrum of the medullary keratin matrix
shows a nearly circular ring around the origin 0.0059 nm⫺1 in diameter (Fig. 1a). Thisring indicates that the tissue has a highlyordered, nanoscale spatial variation in
refractive index that is nearly uniform in all
directions.
Reflection spectra of the blue feather
barbs display a peak between 500 and 520
nanometres (Fig. 1b). We used the 2D
Fourier power spectrum to predict thereflectance spectrum of these barbs. The% Total Fourier power

Eugene A. Foster*, M. A. Jobling†,
P. G. Taylor†, P. Donnelly‡, P. de Knijff§,
Rene Mieremet§, T. Zerjal¶, C. Tyler-Smith¶fall into two classes, according to whether
the vacuoles in medullary keratin scatter
light coherently (with a relationshipbetween the phases of waves scattered bydifferent surfaces) or incoherently. In theRayleigh and Mie scattering models4,6, thecolours are produced by incoherent scattering of smaller visible wavelengths by anarray of spatially independent air vacuoles in
the medullary keratin. Alternatively, in theconstructive interference model, the colours
are produced by interactions between lightwaves scattered coherently by the keratin–air
matrix1–3,5. Out-of-phase waves will destructively interfere and cancel out, whereas inphase waves will constructively reinforce
one another and be reflected coherently. The
phase relationships of scattered waves aredetermined by the size and spatial distribution of the scatterers1,2,7. Periodic spatial
relationships between scatterers will produce consistent path-length differencesamong scattered waves and reinforce a limited set of wavelengths.
To investigate how the structural colourof feather barbs is produced, we apply anelectromagnetic theory of coherent lightscattering7 that was developed to explain
the transparency of the human cornea. In a

Spatial frequency (nm—1 × 10—2)

Jefferson could possibly have illegitimately
fathered an ancestor of the presumed maleline descendant of Eston. But in the absenceof historical evidence to support such possibilities, we consider them to be unlikely.

0300 350 400 450 500 550 600 650 700

Wavelength (nm)Figure 1 Two-dimensional Fourier power spectrum and observed and predicted reflectance spectra of a bluefeather barb of Cotinga maynana. a, 2D Fourier power spectrum of the spongy medullary keratin matrix of ablue feather barb. b, Observed reflectance spectrum of a blue feather barb (black squares, right axis) and predicted reflectance spectrum (bars, left axis) based on the 2D Fourier power spectrum (a). The discrete Fouriertransform describes how a signal or image is composed of different periodic component waves10. A 2D Fourieranalysis was conducted using the 2D Fast Fourier Transform algorithm in MATLAB11 on a digitized 500-pixel2
image of a transmission electron micrograph (magnification, ⫻ 29,000)2. The image was processed in MATLAB
using variance rescaling with block processing and median filtering11. The 2D Fourier power spectrum (a)resolves the spatial variation in optical density in the tissue into its periodic components in any direction in theplane from all points. The size and direction of any component spatial frequency is given by the length anddirection of a vector from the origin to that point. The squared amplitude of the component is given by thecolour (scale bar on the right). The ring indicates a highly ordered, nanoscale fluctuation in optical density
moving in any direction in the plane of the tissue at a spatial frequency of about 0.0059 nm⫺1. Reflectance of
blue feather barbs (b, squares, right axis) was measured using a Zeiss microspectrophotometer at 30 wavelengths between 400 and 700 nm12. The predicted reflectance spectrum (b, bars, left axis) expresses the percentage of the total power distributed among the components of the 2D Fourier power spectrum over alldirections. The predicted reflection spectrum was calculated using the radial average of one quadrant of the2D Fourier power spectrum with half-pixel width intervals, normalizing the volume under the rotated radial average function to one, calculating the volume under radial sections of the radial average Fourier power function,multiplying these volumes by twice the mean refractive index (1.283), estimated from the micrographs using
the refractive indices of keratin (1.54) and air (1.00)2, and plotting these values as wavelengths in nanometres.
Nature © Macmillan Publishers Ltd 1998

NATURE | VOL 396 | 5 NOVEMBER 1998 | www.nature.com

scientific correspondence
predicted reflectance spectrum shows apeak at 435 nanometres with descending
slopes towards both ends of the visible
spectrum (Fig. 1b), which agrees well withthe observed reflectance spectrum in hue(position of peak) and chroma (shape ofpeak). Most of the total power in the Fourier power spectrum is concentrated at spatial frequencies that will produce coherent
scattering of light waves that are close tothe observed blue hue. The correspondence
between the peaks of the observed and predicted reflection spectra (about 75nanometres) is striking as there are no reasons, apart from structural colour production, to expect these spatial frequencies topredominate.
In the Mie and Rayleigh scattering models, the medullary keratin scatters incoherently (which means the scatterers must beseparated by distances larger than the wavelength of visible light)8. However, the ringlike Fourier power spectrum demonstrates
that the scatterers in medullary keratin arespatially periodic on a scale smaller thanvisible wavelengths, so scattering is coherent. Furthermore, the air vacuoles in the
medullary keratin of C. maynana and otherstructurally coloured feather barbs3,5 are too
close together to scatter visible light incoherently. Finally, the Rayleigh model predicts that the reflectance spectrum should
increase continuously into the ultraviolet1,
but the distinct peak in the reflection spectrum shows this prediction to be false (Fig.
1b). Rayleigh scattering has been the traditional explanation of this phenomenon fornearly a century4, and remains widely citedin ornithological texts and reference works9,but our results indicate that the Rayleighmodel and other incoherent scatteringmodels are not suitable explanations.
Our analysis of the spatial variation in
the refractive index of medullary keratinshows that this tissue is a highly ordered
nanostructure of the appropriate size to
produce the observed hue by constructive interference. The similarity in nanostructure between the medullary keratinof C. maynana and other structurally
coloured feather barbs indicates that constructive interference probably also causes
the production of the structural greens,blues, violets and ultraviolet colours inother feather barbs1–5.

3. Dyck, J. Proc. Int. Ornithol. Congr. 16, 426–437 (1976).
4. Fox, D. L. Animal Biochromes and Structural Colors (Univ.
California Press, Berkeley, 1976).
5. Durrer, H. in Biology of the Integument Vol. 2. Vertebrates (eds
Bereiter-Hahn, J., Matoltsky, A. G. & Richards, K. S.) 239–247(Springer, Berlin, 1986).
6. Finger, E. Naturwissenschaften 82, 570–573 (1995).
7. Benedek, G. B. Appl. Optics 10, 459–473 (1971).
8. Bohren, C. F. & Huffman, D. R. Absorption and Scattering ofLight by Small Particles (Wiley, New York, 1983).
9. Gill, F. B. Ornithology (Freeman, New York, 1995).
10. Briggs, W. L. & Henson, V. E. The DFT (Society for Industrial
and Applied Mathematics, Philadelphia, 1995).
11. MATLAB Reference Guide (Mathworks, Natick, MA, 1992).
12. Dyck, J. Anser (suppl.) 3, 57–75 (1978).

The specimen (Fig. 1) is from UCMP
locality V65238 in the Lance Formation,Lancian North American Land Mammal
Age, Maastrichtian, latest Cretaceous, Niobrara County, Wyoming. The mandibularsymphysis is deeply concave, with a nearlyU-shaped cross-section at the posterior endof the fragment, and has a rounded anterior
margin (Fig. 1). The left and right dentaries
are fused completely without a suture. Smallbone fibres indicate that the individual wasat or close to adult size, so the characters are
not juvenile states. The labial surface of themandibular symphysis has a highly vascularized appearance, produced by numerous
foramina (openings), canals and grooves forneurovascular tissue (Fig. 1c), like thosepresent in the area in which a horny covering, or rhamphotheca, is attached to the jaw
in living amniotes.
A completely fused and edentulous(toothless) mandibular symphysis is present
only in turtles, oviraptorids, ornithomimids, caenagnathid theropods and neornithine birds. The pair of lingual mediansymphysial foramina next to the sagittal
plane is found in most neornithines, including Anseriformes, Galliformes, Psittaciformes and other orders, but is absent inhesperornithiforms, oviraptorids and turtles. Caenagnathid theropods have lateralgrooves, lateral occlusal grooves, lingualridges, longitudinal vascular grooves, meckelian grooves and median tubercles9, which8

A lower jaw from a
Cretaceous parrot
All known Cretaceous bird fossils representing modern higher taxa are from the aquaticgroups Anseriformes1–3, Gaviiformes4,5,
Procellariiformes1 and Charadriiformes1,6.
Here I describe a toothless avian dentary
symphysis (fused jawbone) from the latest
Cretaceous of Wyoming, United States. Thissymphysis appears to represent the oldest
known parrot and is, to my knowledge, thefirst known fossil of a ‘terrestrial’ modern
bird group from the Cretaceous. The existence of this fossil supports the hypothesis,
based on molecular divergence data7,8, thatmost or all of the major modern bird groups
were present in the Cretaceous.
acmacbdmc

Richard O. Prum*†, Rodolfo H. Torres‡,
Scott Williamson†, Jan Dyck§*Natural History Museum, and Departments of†Ecology and Evolutionary Biology, and‡Mathematics, University of Kansas,
Lawrence, Kansas 66045, USAe-mail: prum@ukans.edu§Institute of Population Biology,
Universitetsparken 15,
DK-2100 Copenhagen, Denmark
1. Dyck, J. Biol. Skrift. 18, 1–67 (1971).
2. Dyck, J. Z. Zellforsch. 115, 17–29 (1971).

NATURE | VOL 396 | 5 NOVEMBER 1998 | www.nature.com

1cmFigure 1 Mandibular symphysis of the Lance Formation parrot (University of California Museum of Paleontology, specimen UCMP 143274). a, Dorsal view. The two large median foramina (m) on the lingual surface 3.0
millimetres from the posteroventral edge of the symphysis are equidistant from the midline, with very shortgrooves posterior to them. b, Ventral view. c, Dorsolateral view, showing anterior accessory canal opening(ac) and large labial foramina; the right tomial crest is slightly concave, curving ventrally, and the left is wornand does not have a concave dorsal margin. d, Posterior view, showing meckelian canal (mc). Anterior is tothe left in a–c.
Nature © Macmillan Publishers Ltd 199829