Accurately quantifying the shape of birds' eggs

Abstract

Describing the range of avian egg shapes quantitatively has long been recognized as difficult. A variety of approaches has been adopted, some of which aim to capture the shape accurately and some to provide intelligible indices of shape. The objectives here are to show that a (four-parameter) method proposed by Preston (1953, The Auk, 70, 160) is the best option for quantifying egg shape, to provide and document an R program for applying this method to suitable photographs of eggs, to illustrate that intelligible shape indices can be derived from the summary this method provides, to review shape indices that have been proposed, and to report on the errors introduced using photographs of eggs at rest rather than horizontal.

Keywords: asymmetry; elongation; guillemot; pointedness; pyriform; shape indices; shape parameters.

Figure 1

The values of the three shape indices for eggs of varied shapes. All egg images are scaled to have the same length. Key: (1) White‐breasted Kingfisher (Halcyon smyrnensis); (2) Adélie penguin (Pygoscelis adeliae); (3) Dalmatian Pelican (Pelecanus crispus); (4) Greater Flamingo (Phoenicopterus roseus); (5) Southern Brown Kiwi (Apteryx australis); (6) Little Grebe (Tachybaptus ruficollis); (7) Royal Tern (Thalasseus maximus); (8) King Penguin (Aptenodytes patagonicus); (9) Pheasant‐tailed Jacana (Hydrophasianus chirurgus); (10) Common Guillemot (Uria aalge)

Figure 2

Graphical explanation of the symbols occurring in the text: $L$ is the length of the egg; $D$ is the largest latitudinal diameter; $P$ is the length from the latitude of maximum diameter to the more distant pole; $d$ is the equatorial diameter; $R_{\mathrm{B}}$ and $R_{\mathrm{P}}$ are the radii of the largest circles within the egg and touching the blunt and pointed pole, respectively; and $b_i$ and $b_k$ are the latitudinal diameter half way between the latitude of largest diameter and the blunt and pointed pole — $b_i$ is the larger of the two

Figure 3

The actual egg shape of C126 is the black outline; the Preston fit is in red. The error, as defined at Equation (6), is 0.00091. The length of the egg has been scaled to be one. The two circles are the largest possible that touch the end of the egg and are wholly within the (Preston fit to the) egg. Then, the Polar Asymmetry (PA) is the ratio of the diameter of the larger (blue) to the smaller (green) circle. Po is the pointedness. El is the Elongation. T is the equatorial diameter

Figure 4

The actual egg shape of C126 is the black outline; the Baker fit is in red. The error, as defined at Equation (6), is 0.0116. The values of Po, 1/El, and T based on the Baker fit are indicated. The Polar Asymmetry (PA) is very large because of the very small circle at the more pointed end

Figure 5

Boxplots comparing the error defined at Equation (6) (multiplied by 1,000) for the methods of Carter (1968), given in Supporting Information Equation (SEq1), the methods of Baker (2002) and Troscianko (2014), given in Equations (4) and (5), the method of Carter and Morley Jones (1970), described in Supporting Information Equation (SEq6), labeled CMJ, and the method of Preston (1953) given in Equation (2). The results are for 132 eggs of various species: 18 Uria aalge, 16 Uria lomvia, 7 Alca torda, 11 Aptenodytes patagonicus, 10 Lanius collurio, 10 Phalacrocorax carbo, 10 Gallus gallus domesticus, 10 Spheniscus humboldti, 10 Eudyptes pachyrhynchus, 30 Larus fuscus. The heavy line is the median, the boxes extend between the upper and lower quartiles, the whiskers extend to the minimum and maximum