This table is adapted from Montgomerie (2006) and lists all spectral descriptors that are computed by the summary function in pavo.

Color variable Names used Formula Reference
Brightness Total brightness, total reflectance, spectral intensity \[B_1=B_T=\int_{\lambda_{min}}^{\lambda_{max}} R_i = \sum_{\lambda_{min}}^{\lambda_{max}} R_i\] Andersson (1999),Andersson et al. (2002),Örnborg et al. (2002),Andersson, Örnborg, and Andersson (1998),Smiseth et al. (2001),Saks, McGraw, and Horak (2003),Pryke, Lawes, and Andersson (2001),Shawkey et al. (2003)
Mean brightness \[B_2=\frac{\sum_{\lambda_{min}}^{\lambda_{max}} R_i}{n_w}=\frac{B_1}{n_w}\] Delhey et al. (2003),Siefferman and Hill (2005)
Intensity \[B_3=R_{max}\] Andersson (1999),Keyser and Hill (2000),Keyser and Hill (1999)
Saturation Chroma, reflectance ratio, spectral purity \[S_1= \frac{\sum_{\lambda_a}^{\lambda_b} R_i}{\sum_{\lambda_{min}}^{\lambda_{max}} R_i} = \frac{\sum_{\lambda_a}^{\lambda_b} R_i}{B_1}\] Örnborg et al. (2002),Andersson, Örnborg, and Andersson (1998),Smiseth et al. (2001),Siefferman and Hill (2005),Peters et al. (2004),Shawkey et al. (2003)
Spectral saturation \[S_2 = \frac{R_{max}}{R_{min}}\] Andersson (1999)
Chroma \[S_3 = \frac{\sum_{\lambda_{R_{max}}-50}^{\lambda_{R_{max}}+50} R_i}{B_1}\] Shawkey et al. (2003)
Spectral purity \[S_4 = \lvert b\text{max}_{neg}\lvert\] Andersson (1999)
Chroma \[S_5=\sqrt{(B_r-B_g)^2+(B_y-B_b)^2}\] Saks, McGraw, and Horak (2003)
Constrast, amplitude \[S_6 = R_{max} - R_{min}\] Keyser and Hill (2000),Keyser and Hill (1999)
Spectral saturation \[S_7 = \frac{\left(\sum_{\lambda_{320}}^{\lambda_{R_{mid}}} R_i - \sum_{\lambda_{R_{mid}}}^{\lambda_{700}} R_i\right)}{B_1}\] Andersson et al. (2002),Pryke, Lawes, and Andersson (2001)
Chroma \[S_8=\frac{R_{max}-R_{min}}{B_2}\] Andersson et al. (2002),Smiseth et al. (2001)
Carotenoid chroma \[S_9=\frac{R_{\lambda_{700}}-R_{\lambda_{450}}}{R_{\lambda_{700}}}\] Peters et al. (2004)
Peaky chroma \[S_{10}=\lvert b\text{max}_{neg} \lvert\frac{R_{max}-R_{min}}{B_2}\] Örnborg et al. (2002)
Hue Hue, peak wavelength, spectral location \[H_1=\lambda_{R_{max}}\] Andersson (1999),Örnborg et al. (2002),Andersson, Örnborg, and Andersson (1998),Delhey et al. (2003),Smiseth et al. (2001),Keyser and Hill (2000),Siefferman and Hill (2005),Shawkey et al. (2003)
Hue \[H_2 = \lambda_{b\text{max}_{neg}}\] Andersson, Örnborg, and Andersson (1998),Smiseth et al. (2001)
Hue \[H_3 = \lambda_{R_{mid}}\] Andersson et al. (2002),Smiseth et al. (2001),Pryke, Lawes, and Andersson (2001)
Hue \[H_4 = \arctan\left(\frac{B_y-B_b}{B_r-B_g}\right)\] Saks, McGraw, and Horak (2003)
Hue \[H_5 = \lambda_{b\text{max}_{pos}}\] Keyser and Hill (1999)
  • \(R_i\): percentage (or proportional) reflectance at the \(i\)th wavelength
  • \(\lambda_{max}\), \(\lambda_{min}\): upper and lower (respectively) limits of wavelengths
  • \(n_w\): number of wavelength intervals used to calculate \(B_T\)
  • \(R_{max}\), \(R_{min}\): maximum and minimum percent reflectances, respectively
  • \(\lambda_{R_{max}}\): wavelength at maximum reflectance
  • \(b\text{max}_{neg}\), \(b\text{max}_{pos}\): maximum negative and positive slopes of reflectance curve in a region of interest
  • \(B_r\), \(B_y\), \(B_g\), \(B_b\): total brightness in red (\(r=625-700\,nm\)), yellow (\(y=550-625\,nm\)), green (\(g=475-550\,nm\)) and blue (\(b=400-475\,nm\)) segments of the spectrum
  • \(\lambda_{R_{mid}}\): wavelength at the reflectance midpoint between \(R_{max}\) and \(R_{min}\) (i.e., \(\frac{R_{max}+R_{min}}{2}\))

References

Andersson, Staffan. 1999. “Morphology of UV Reflectance in a Whistling-Thrush: Implications for the Study of Structural Colour Signalling in Birds.” Journal of Avian Biology 30 (2): 193–204. https://doi.org/10.2307/3677129.

Andersson, Staffan, Jonas Örnborg, and Malte Andersson. 1998. “Ultraviolet Sexual Dimorphism and Assortative Mating in Blue Tits.” Proceedings of the Royal Society of London B: Biological Sciences 265 (1395): 445–50. https://doi.org/10.1098/rspb.1998.0315.

Andersson, Staffan, Sarah R. Pryke, Jonas Örnborg, Michael J. Lawes, and Malte Andersson. 2002. “Multiple Receivers, Multiple Ornaments, and a Trade‐off Between Agonistic and Epigamic Signaling in a Widowbird.” The American Naturalist 160 (5): 683–91. https://doi.org/10.1086/342817.

Delhey, Kaspar, Arild Johnsen, Anne Peters, Staffan Andersson, and Bart Kempenaers. 2003. “Paternity Analysis Reveals Opposing Selection Pressures on Crown Coloration in the Blue Tit (Parus Caeruleus).” Proceedings of the Royal Society of London B: Biological Sciences 270 (1528): 2057–63. https://doi.org/10.1098/rspb.2003.2460.

Keyser, Amber J., and Geoffrey E. Hill. 1999. “Condition–Dependent Variation in the Blue–Ultraviolet Coloration of a Structurally Based Plumage Ornament.” Proceedings of the Royal Society of London B: Biological Sciences 266 (1421): 771–77. https://doi.org/10.1098/rspb.1999.0704.

———. 2000. “Structurally Based Plumage Coloration Is an Honest Signal of Quality in Male Blue Grosbeaks.” Behavioral Ecology 11 (2): 202–9. https://doi.org/10.1093/beheco/11.2.202.

Montgomerie, Robert. 2006. “Analyzing Colors.” In Bird Coloration, Volume 1: Mechanisms and Measurements, edited by Geoffrey E. Hill and Kevin J. McGraw, 1:640. Bird Coloration. Harvard University Press.

Örnborg, Jonas, Staffan Andersson, Simon C. Griffith, and Ben C. Sheldon. 2002. “Seasonal Changes in a Ultraviolet Structural Colour Signal in Blue Tits, Parus Caeruleus.” Biological Journal of the Linnean Society 76 (2): 237–45. https://doi.org/10.1111/j.1095-8312.2002.tb02085.x.

Peters, A., A. G. Denk, K. Delhey, and B. Kempenaers. 2004. “Carotenoid-Based Bill Colour as an Indicator of Immunocompetence and Sperm Performance in Male Mallards.” Journal of Evolutionary Biology 17 (5): 1111–20. https://doi.org/10.1111/j.1420-9101.2004.00743.x.

Pryke, Sarah R., Michael J. Lawes, and Staffan Andersson. 2001. “Agonistic Carotenoid Signalling in Male Red-Collared Widowbirds: Aggression Related to the Colour Signal of Both the Territory Owner and Model Intruder.” Animal Behaviour 62 (4): 695–704. https://doi.org/10.1006/anbe.2001.1804.

Saks, Lauri, Kevin McGraw, and Peeter Horak. 2003. “How Feather Colour Reflects Its Carotenoid Content.” Functional Ecology 17 (4): 555–61. https://doi.org/10.1046/j.1365-2435.2003.00765.x.

Shawkey, Matthew D., Anne M. Estes, Lynn M. Siefferman, and Geoffrey E. Hill. 2003. “Nanostructure Predicts Intraspecific Variation in Ultraviolet–Blue Plumage Colour.” Proceedings of the Royal Society of London B: Biological Sciences 270 (1523): 1455–60. https://doi.org/10.1098/rspb.2003.2390.

Siefferman, Lynn, and Geoffrey E. Hill. 2005. “UV-Blue Structural Coloration and Competition for Nestboxes in Male Eastern Bluebirds.” Animal Behaviour 69 (1): 67–72. https://doi.org/10.1016/j.anbehav.2003.12.026.

Smiseth, Per T., Jonas Örnborg, Staffan Andersson, and Trond Amundsen. 2001. “Is Male Plumage Reflectance Correlated with Paternal Care in Bluethroats?” Behavioral Ecology 12 (2): 164–70. https://doi.org/10.1093/beheco/12.2.164.