Erratum to: Using Reflectance Ratios to Study Animal Coloration

Abstract

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 used 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), either applying or not applying Fechner law. 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). Settings for the visual model without Fechner law (y-axes in Fig. 4) were as follows: average UV avian sensitivity, regular daylight illumination, von Kries correction, relative quantum catches, no Fechner law (i.e. not log-transforming quantum catches), and the remaining options set to default. For visual models with Fechner law (x-axes in Fig. 4) we first ran a model similar to the above but with Fechner law applied (i.e. log-transforming quantum catches), and with absolute rather than relative quantum catches. Then, as explained below, we rescaled log-transformed quantum catches to a biologically interpretable scale before normalization (i.e. dividing the signal of each photoreceptor cone type by the sum of signals of the four cone types) to obtain relative quantum catches. Rescaling log-transformed quantum catches is necessary because, as discussed by Stoddard and Prumm (2008; page 4 of the appendix), log-transformation changes colour spaces artefactually in a way that strongly depends on the arbitrary, unitless scale chosen for absolute quantum catches (from 0 for no stimulation of the photoreceptor, to an arbitrary value for stimulation by 100 % reflectance). Relative differences among log-transformed quantum catches are unaffected by the scale used or by the logarithmic base chosen, but the absolute values change so that normalizing log-quantum catches directly produces meaningless colour spaces. For example, software for analysis of spectral colour usually quantify quantum catches from 0 to an arbitrary value of 1; the resulting log-transformed quantum catches have negative values that, upon normalization, distort colour to the point that the relative strength of signals from the four cone types is reversed. The conceptual problem is that log-transformed quantum catches have no intrinsic minimum (as log(0) tends to minus infinity, though low values should be flattened because they reach beyond the perceptual range of animals and because The online version of the original article can be found under doi:10.1007/s11692-015-9328-5.