Using Reflectance Ratios to Study Animal Coloration

Abstract

Reflectance spectrophotometry is used to quantify animal coloration and compare it across individuals, populations or species. While principles of colour perception, pigment-based colour production, and some structural-based colour production, all conform to reflectance differences on a ratio scale, reflectance is usually measured on a linear scale. Processing reflectance spectra on a linear scale distorts colour information (e.g. averaging linear spectra overestimates mean brightness), and computing receiver-independent colour metrics using linear reflectance can bias results (e.g. it underestimates differences in saturation and brightness among dark colours). Working with reflectance spectra on a ratio scale obviates those issues and improves several aspects of colour analysis, from better visualization of reflectance spectra and control of measurement error, to better colour metrics.

Appendices

Appendix 1

Chromatic and achromatic contrasts (CC and AC, respectively) between pairs of adjacent spectra in Figs. 1 and 2 were calculated, in units of just noticeable differences, using the visual model of Vorobyev et al. (1998; see also Siddiqi et al. 2004) as implemented in the R package pavo (v0.5-1, functions vismodel and coldist ; Maia et al. 2013). CC is computed using quantum catches from single-cones, and AC using quantum catches from double-cones. Visual model settings were as follow: average UV avian sensitivity, regular daylight illumination, von Kries correction, absolute quantum catches according to Fechner law, and the remaining options set to default (contrasts are identical whether modelling with or without von Kries correction, applying Fechner law or not).

To illustrate how we would approximately perceive hue and saturation of the spectra in Figs. 1 and 2, we used the function spec2rgb in pavo . The resulting coordinates in RGB (red–green–blue) colour space were converted to coordinates in the HSL (hue–saturation–lightness) colour space, and the lightness coordinates set to an identical, arbitrary value to illustrate chromatic differences while holding brightness constant.

To illustrate how we would approximately perceive colour brightness of the spectra in Figs. 1 and 2, we measured emitted light of a greyscale, from black to white at intervals of 5 % lightness, on a computer monitor with an Ocean Optics USB4000 spectrophotometer, calibrating emission spectra with black and white measurements on the same monitor. We then chose the tone of grey whose mean log light emission across the human-visible wavelengths (ca. 400–700 nm) best matched those of each spectrum in Figs. 1 and 2.

Appendix 2

We used the data of Taysom et al. (2010) on pigment-based red to yellow colour of Australasian parrots, but here flattened reflectance values lower than 1 % in the original spectra to 1 %, and used geometric rather than arithmetic means to average across the spectra of each individual and then across the different individuals of each species and sex (see the section ‘Recommendations’ in the main text). We calculated the achromatic contrast between the mean spectrum of males and females for each species, using the visual models of Vorobyev et al. (1998) as implemented in pavo (Maia et al. 2013) with the same settings as described before. For comparison with these achromatic contrasts, we computed absolute values of the difference between the sexes in receiver-independent metrics of brightness: mean reflectance on a linear (% reflectance) or on a ratio (log₁₀ % reflectance) scale of reflectance, across the bird-visible frequency range (ca. 300–700 nm). Mean brightness for each species (horizontal axes in Fig. 3) was computed as the mean of male and female log₁₀ % reflectance across their visible frequency range.

Appendix 3

We used 8911 reflectance spectrophotometry measurements of plumage colours, made on museum skins of 135 species of finches in the family Estrildidae. For most species male and female specimens were measured, usually three specimens per species/sex, and multiple measurements of colour were made that include all the main body parts. This dataset will be described in detail elsewhere.

Here we applied visual models to estimate colour saturation of these spectra as the distance to the achromatic centre of an avian tetrahedral colour space (Endler and Mielke 2005; Stoddard and Prum 2008). Reflectance values lower than 1 % were flattened to 1 %, and spectra were then analysed using the avian visual model of Vorobyev et al. (1998) as implemented in pavo (functions vismodel and tcs ; Maia et al. 2013). Visual model settings were as follow: average UV avian sensitivity, regular daylight illumination, von Kries correction, relative quantum catches according to Fechner law (i.e. log-transforming quantum catches, for the x-axis of Fig. 4) or relative quantum catches without Fechner law (i.e. not log-transforming, for the y-axis of Fig. 4), and the remaining options set to default.