DOI: 10.5061/dryad.f4qrfj719
title: Egg-shape data of six species of poultry

description: We digitized the side profiles of 2221 eggs of six species of
 poultry, two species of Anatidae (Anas platyrhynchos domesticus
 and Anser cygnoides domesticus) and four species of Phasianidae
 (Alectoris chukar domesticus, Coturnix
 japonica domesticus, Gallus gallus domesticus,
 and Phasianus colchicus domesticus), and used an
 explicit re-expression of Preston’s equation (referred to as EPE
 hereinafter) to fit the planar coordinates of each egg profile. By using
 the estimated parameters, we calculated the volume and surface area of
 each egg. The black_white.rar file saves the black and white .bmp images
 at 600 dpi for the 2221 egg profiles. The edge_data.zip file includes the
 planar coordinates (in cm) of each of the 2221 egg profiles, and the
 EPE.csv file includes the estimated parameters and goodness-of-fit of the
 EPE, and the egg surface area and volume calculated by the surface area
 and volume equations of the solid of revolution based on the EPE for each
 egg. In addition, the EPE.csv file also provided the measured volumes of
 120 A. cygnoides eggs, and 366 P.
 colchicus eggs using the graduated cylinders. For each species of
 poultry, we boiled 120 eggs that were randomly sampled, and then measured
 the mass of albumen, yolk, and shell of boiled eggs. The results were
 saved in the EPE.csv file.
description: We
 selected six species of poultry for study because of the availability in
 large numbers of their eggs: two species of Anatidae (<em>Anas
 platyrhynchos domesticus</em> and <em>Anser cygnoides
 domesticus</em>), and four species of Phasianidae
 (<em>Alectoris chukar domesticus, Coturnix japonica domesticus,
 Gallus gallus domesticus</em>, and <em>Phasianus</em>
 <em>colchicus</em> <em>domesticus</em>). For each
 species, 351−390 eggs were selected for detailed study.
 We used an adjustable
 tabletop phone-mount to hold a smartphone (Huawei P30Pro, Huawei,
 Dongguan, China) to photograph eggs of <em>A.
 </em><em>platyrhynchos</em><em>, A. cygnoides, C.
 japonica</em>, and <em>G. gallus</em>, and another
 smartphone (Redmi K40S, Xiaomi, Kunshan, China) to photograph eggs of
 <em>A. chukar</em> and <em>P.
 colchicus</em>. Over
 2200 eggs (2221 in total, &gt;360 of each of the six species on
 average) were photographed at a constant scale to determine the
 representative 2-D egg-profiles of each species. To focus the camera on
 the center of each egg, we estimated the midpoint of the length of each
 profile. In addition, we prepared a test tube rack and a small beaker as a
 concave base to support each egg to make the mid-line of each profile
 orthogonal to the tabletop phone mount. In addition, we measured each
 egg’s length to provide a correction factor for the actual size from its
 image size. The egg
 images were converted to black and white .bmp files with Photoshop
 (version 13.0; Adobe, San Jose, CA, USA). The Matlab (version ≥ 2009a;
 MathWorks, Natick, MA, USA) procedures developed by Shi et al. (2018) and
 Su et al. (2019) were used to extract the planar coordinates of each egg
 profile. Each egg profile was characterized by 2000 approximately
 equidistantly spaced coordinates using the ‘adjdata’ function of the
 ‘biogeom’ package (version 1.3.5; Shi et al., 2022) in R (version 4.2.0; R
 Core Team, 2022). And then we used a re-expression of Preston’s equation
 (referred to as EPE hereinafter; Shi et al., 2023) to fit the planar
 coordinate data of the egg profiles. The ‘fitEPE’ function in the ‘biogeom’ package
 (version 1.3.5) in R (version 4.2.0) was used to fit the data points to
 estimate the values of <em>a, b, c<sub>1</sub>,
 c<sub>2</sub></em>, and
 <em>c<sub>3</sub></em> (i.e., the parameters of
 the EPE) by minimizing the residual sum of squares (RSS) between the
 observed and predicted y-values using the Nelder-Mead optimization method.
 After obtaining the estimated parameters of the EPE, we used the surface
 area and volume equations for the solid of revolution
 (Narushin et al.,
 2022) based on the EPE to
 calculate the egg surface area and volume for each egg of the 2221
 eggs. We measured the V of 120
 <em>A. cygnoides</em> eggs using a 1000 mL glass graduated
 cylinder with a diameter of 6.7 cm, and the V of 366 <em>P.
 colchicus</em> eggs
 using a 250 mL glass graduated cylinder with a diameter of 4 cm. We
 photographed 360 <em>A. cygnoides</em> eggs and 367
 <em>P. colchicus</em> eggs. Because it is time-consuming to
 measure the V of an egg using the graduated cylinder method, we randomly sampled
 120 <em>A.
 cygnoides</em> eggs
 and all <em>P. colchicus</em> eggs (apart from a broken egg in
 the experiment), and measured the volumes using the graduated cylinders. The predicted volumes were compared to those
 measured using graduated cylinders for a total of 120 + 366 = 486 eggs,
 comprising 120 of <em>A. cygnoides</em> and 366 of
 <em>P. colchicus</em>.
 In addition, for each of the
 six species of poultry, we boiled 120 eggs, and then measured the mass of
 albumen, yolk, and shell of boiled eggs using an electronic balance (Type:
 ML 204; Mettler Toledo Company, Greifensee, Switzerland; measurement
 accuracy 0.0001 g). The results were saved in the EPE.csv
 file. The above contents were cited from Shi et al.
 (2023). References 
 Narushin, V. G., Romanov, M.
 N., Mishra, B., & Griffin, D. K. (2022). Mathematical progression
 of avian egg shape with associated area and volume determinations.
 <em>Annals of the New York Academy of Sciences</em>, 1513:
 65–78. R Core Team. (2022). R: A language and
 environment for statistical computing. Vienna, Austria: R Foundation for
 Statistical Computing. Shi, P., Chen, L., Quinn, B.K., Yu, K., Miao, Q.,
 Guo, X., Lian, M., Gielis, J., & Niklas, K.J. (2023). A simple way
 to calculate the volume and surface area of avian eggs.
 <em>Annals of the
 New York Academy of Sciences</em>, in press. 
 Shi, P., Gielis, J., Quinn, B. K., Niklas,
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