Birds' eggshells are renowned for their striking colours and varied patterns. Although often considered exceptionally diverse, we report that avian eggshell coloration, sampled here across the full phylogenetic diversity of birds, occupies only 0.08-0.10% of the avian perceivable colour space. The concentrations of the two known tetrapyrrole eggshell pigments (protoporphyrin and biliverdin) are generally poor predictors of colour, both intra- and interspecifically. Here, we show that the constrained diversity of eggshell coloration can be accurately predicted by colour mixing models based on the relative contribution of both pigments and we demonstrate that the models' predictions can be improved by accounting for the reflectance of the eggshell's calcium carbonate matrix. The establishment of these proximate links between pigmentation and colour will enable future tests of hypotheses on the functions of perceived avian eggshell colours that depend on eggshell chemistry. More generally, colour mixing models are not limited to avian eggshell colours but apply to any natural colour. Our approach illustrates how modelling can aid the understanding of constraints on phenotypic diversity.

Department of Psychology Hunter College and the Graduate Center The City University of New York 695 Park Avenue New York NY 10065 USA

Department of Zoology and Laboratory of Ornithology Palacký University 17 listopadu 50 Olomouc 77146 Czech Republic

School of Biological Sciences University of Adelaide Adelaide South Australia 5005 Australia

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