Abstract
We analyzed the egg shape in bird family Corvidae using a polynomial model and a compound ovoid model. We constructed a geometric model that reflects the relationship between cloacal and infundibular arcs, and the length and the diameter of the egg. Specifically, we quantified the shape of the egg via seven indices: the traditional index of elongation and six novel indices. Morphological parameters of bird eggs within three genera of Corvids (Corvus, Pica, and Garrulus) revealed that although there was overlap with their minimum and maximum values, the mean values remained different. Cluster analysis, using suggested indices and polynomial equations based on the absolute length and diameter of eggs, demonstrated different values within three main groups: the Hooded Crow, Carrion Crow, and Common Raven group, the European Jackdaw and Eurasian Jay group, and the Rook and Eurasian Magpie group. This is best explained by the variation in the elongation indices, suggesting that spheroid eggs are the optimal for clutches of 1-2 eggs or more than 5 eggs. Geometrical schemes, formulas of compound ovoid, and polynomial equations generated for seven species of corvids are supplied, which provide evidence of species-specific patterns of egg shapes.
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