Usage of the iterative photo-computing method in specifying of bird egg radiuses curvature


I.S. Mytiai, A.V. Matsyura

The egg shape, as a description datum about adult bird is an important object for research work closely allied with the bird adaptation to brood under different environmental conditions. Besides, it is possible to use this approach as an additional research instrument for general bird evolution study, ecological proximity, taxonomy, etc. Moreover, at the same time egg shape profile is the mostly suitable characteristic for intravital study above-mentioned aspects.

Keywords: Egg shape; photo-computing method; egg radius; curvature

Anderson, M. (1978). Optimal egg shape in waders. Ornis Fennica, 55, 105-109.
Âvila, D. D. (2014). Aplicaciôn de las funciones elipticas de Fourier para la description de la forma de los liuevos de las aves. Rev. Biol. Trop, 62(4), 1469-1480.
Baker, D. E. (2002). A geometric method for determining shape of bird eggs. The Auk, 119, 1179-1186.;2.
Ban, M., Barta, Z., Munoz, A. R., Takasu, F., Nakamura, H., & Moskat, C. (2011). The analysis of common cuckoo’s egg shape in relation to its hosts’ in two geographically distant areas. Journal of Zoology, 284(2), 77-150.
Biggins, J. D., Thompson, J. E., & Birkhead, T. R. (2018). Accurately quantifying the shape of birds’ eggs. Ecology and Evolution, 1-11.
Barta, Z., & Székely, T. (1997). The optimal shape of avian eggs. Functional Ecol, 11, P. 656-662.
Bridge, E. S., Boughton, R. K., Aldredge, R. A., Harrison, T. E., Bowman, R., & Schoech, S. J. (2007). Measuring egg size using digital photography: testing Hoyt`s method using Florida Scrub-Jay eggs. Journal of Field Ornithology, 78,109-116. DOI: 10.1111/j.1557-9263.2006.00092.x
Cundy, H., & Rollett A. (1989). Mathematical Models. Third Edition. Stradbroke, Tarquin Pub.
Dixon, R. (1991). Mathographics. New York, Dover.
Deeming, D. C., & Ruta, M. (2014). Egg shape changes at the theropod-bird transition, and a morphometric study of amniote eggs. R. Soc. Open Sci, 1. doi:10.1098/rsos.140311
Deeming, D. C. (2018). Effect of composition on shape of bird eggs. Journal of Avian Biology, 49(1), 1-7. doi: 10.1111/jav.01528.
Frantsevich, L. (2010). Planimetry of the egg shape parameters. Available from: Accessed on 10.11.2018. (In Russian)
Führer-Nagy, G. (2002). Mathematical modeling of bird egg curves. Aquila, 107/108, 67-73.
Heck, A. (2010). Mathematical Brooding over an Egg. Convergence, DOI:10.4169/loci002842.
Johnson, L. S., Leyhe, J. E., & Werner, C. (2001). The shape of eggs in different-size clutches of the/ House Wren (Troglodytes aedon). Can. J. Zool, 79, 1527-1531.
Iwamoto, T. (2011). Many Shapes of Bird's Eggs. Available from: Accessed on 25.10.2018
Hutchinson, J. M. C. (2000). Three into two doesn’t go: two-dimensional models of bird eggs, snail shells and plant roots // Biological Journal of the Linnean Society, 70, 161-187. doi:10.1006/bijl.1999.0395
Gemperle, M. E., Preston, F. W. (1955). Variation of shape in the eggs of the common tern in the clutch-sequence. Auk, 72, 184-198.
Köller, J. (2000). Mathematische Basteleien. Availble from: Accessed on 04.10.2018
Kostin, Y. V. (1977). About methodology of oomorphological researches and unification of descriptions of oological material. In Metodiki issledovaniya produktivnosti i struktury vidov ptits v predelakh ikh arealov. (Methods of the study of the productivity and structure of bird species within their areals.) Vilnius (In Russian)
Mao, K. M., Murakami, A., Iwasawa, A., & Yoshizaki, N. (2007). The asymmetry of avian egg-shape: an adaptation for reproduction on dry land. J Anat, 210(6), 741-748. doi:10.1111/j.1469-7580.2007.00737.x
Mattas, ??. (2001). Uraovani tvar u ptaaich vajec. Sylvia, 37, 17-25.
Mieszkalski, L. (2014). Method of mathematical modelling Of the surface of the egg shell shape, egg yolk and air chamber of chicken eggs. Agricultural Engineering, 3(151), 93-104.
Mytiai, I. S. (2003). New method for the complex estimation of a form of the egg. Branta, 6, 179-192. (In Russian)
Mytia??, ??. S. (2008). Using modern technologies in researching of bird eggs. Zaporozhye National University Journal. Series Biology, 175-183. (In Russian)
Mytiai, I. S., & Matsyura, A. V. (2017). Geometrical standards in shapes of avian eggs. Ukrainian Journal of Ecology, 7(3), 264-282. doi: 10.15421/2017_78
Möller, H. (2009). Das 2:3-Ei-ein praktikables Eimodell. Available from: Accessed on 05.11.2018
Myand, R. (1988). Intrapopulational variability of bird eggs. Tallin, Valgu (In Russian)
Murray, C. M., Piller, K. R., & Merchant, M. (2013). Salinity and Egg Shape Variation: A Geometric Morphometric Analysis // Journal of Herpetology, 47(1), 15-23.
Narushin, V. G. (2001). Shape geometry of the avian egg. J. Agric. Engin. Res, 79, 441-448.
Nedomová, Š., & Buchar, J. (2014). Goose eggshell geometry. Res. Agr. Eng, 60, 100-106.
Nishiyama, Y. (2010). The Mathematics of Egg Shape. Available from: Accessed on 15.11.2018
Paganelli, C. V., Olszowka, A., & Ar, A. (1974). The avian egg: surface area, volume, and density. The Condor, 76, 319-325.
Petrovi??, ??., & Obradovi??, ??. (2010). The complement of the hugelschaffer’s ?onstruction of the egg curve. Avalable from: Accessed on 20.11.2018.
Preston, F. W. (1953). The shapes of birds egg. The Auk, 70, 160-182.
Preston, F. W. (1957a). Two New Devices for Measuring the Shapes of Birds' Eggs. The Auk, 74, 386-388.
Preston, F. W. (1968). The shapes of birds eggs: mathematical aspects. The Auk, 85, 454-463.
Reid, W. S., Buckley, D. J., Hunt, J. R., & Prices, K. (1974). A digital instrument for egg shape index measurement. Canadian Journal of Animal Science, 55, 87-92.
Stoddard, M. C., Yong, E. H., Akkaynak, D., Sheard, C., Tobias, J. A., & Mahadevan, L. (2017). Avian egg shape: form, function, and evolution. Science, 356, 1249-1254.
Todd, P. H., & Smart, I. H. M. (1984). The shape of birds’ eggs. J. Theor. Biol, 106, 239-243.
Troscianko, J. (2014). A simple tool for calculating egg shape, volume and surface area from digital images. Ibis, 156(4), 874-878.
Yamamoto, N. (2016). We Find an Equation of Egg Shaped Curve. Available from: Accessed on 02.11.2018


Share this article