Geometrical standards in shapes of avian eggs

Abstract

The original technique of description of avian eggs on the basis of the geometry of asymmetrical oval (ovoid) is suggested. Specific properties of this figure allow to create a system of 80 basic ovoid standards, each given an appropriate name, digital and letter coding, and distinct quantitative characteristics. Combining infundibular zones (blunt poles) of basic ovoids in pairs gives 80 standards of symmetric pseudo-ovoids, 44 of which are found in birds. The same procedure applied to different ovoids produces 375 standards of asymmetrical pseudo-ovoids. This totality can be divided into six groups. Use of such system of standards enables us to identify real shapes of avian eggs, to analyze relation of morphometric parameters to incubatory properties of eggs, and also to carry out comparisons and generalizations of other authors' data. Each standard is quantitatively characterized by means of indexes (namely, indices of infundibular, cloacal, and lateral zones; index of asymmetry, elongation index, complementarity index, interporal index, arc radiuses, length and diameter).

Mathematical interpretation of artificial ovoids and avian egg shapes (part I)

“…Some authors tried to concentrate on limited species (Murray et al, 2013;Avila, 2014;Mieszkalski, 2014), while others present the results obtained from a large number of species (Deeming & Ruta, 2014;Nedomová & Buchar, 2014;Stoddard et al, 2017). The method of photographic analysis was elaborated and presented in Mytiai & Matsyura (2017, 2018, Deeming (2018), and Biggins et al (2018). Proceeding from the above, we were interested how similar the egg-shaped curves constructed by mathematicians, architects and builders are to the profiles of real bird eggs.…”

Accurately quantifying the shape of birds’ eggs

“…Although their approach is rather different, Mityay et al. (), Mityay, Strigunov, and Matsyura () and Mytiai and Matsyura () also suggest a variety of indices based on the radii of circles. They are not fully consistent in naming these nor in the formulae.…”

“…In particular, the “index of asymmetry” in Mityay et al. () is R P / R B , the reciprocal of Polar Asymmetry, but the “index of asymmetry” in Mytiai and Matsyura () is different: it is ( R B − R P )/ D . A selection of indices from Mytiai and Matsyura () is included in Table .…”

“…For an asymmetrical egg, b k will be less than b i , with larger values of these indices corresponding to greater asymmetry. The other two indices, blunt‐end convexity and sharp‐end convexity, seek to measure the pointedness of each end separately and so are similar in spirit to Mytiai and Matsyura's () infundibular and cloacal.…”

“…The other two indices, blunt-end convexity and sharp-end convexity, seek to measure the pointedness of each end separately and so are similar in spirit to Mytiai and Matsyura's (2017) infundibular and cloacal. Mänd et al (1986) propose an index which compares the egg volume, V, to that of a prolate ellipsoid (i.e.…”