# Egg-shape data of six species of poultry
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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 of each of the 2221 eggs, 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 of the data and file structure

In the black_white.rar file, there are 2221 .bmp images at 600 dpi. The image size was scaled to its actual size using the ratio of its actual egg length measured to the egg length in the scanned image. This means that the image size in a .bmp file is equal to the actual size of an egg profile. 

In the edge_data.zip file, there are 2221 .csv files. In each .csv file, there are two columns, which record the x- and y-coordinates in cm for an arbitrary egg’s side profile.

In the EPE.csv file, there are 22 columns.
(1) Image saves the code of each of the 2221 eggs. The number before the hyphen represents the species code, and the number after the hyphen represents the individual code of an egg. For the number before the hyphen, 1 and 2 represent Anas platyrhynchos domesticus, and Anser cygnoides domesticus, respectively; 5, 3, 4 and 7 represent Alectoris chukar domesticus, Coturnix japonica domesticus, Gallus gallus domesticus, and Phasianus colchicus domesticus, respectively.
(2) x0 and y0 represent the coordinates of the center of an egg profile (in cm), and theta represent the angle between the midline of the egg profile and the x-axis. 
(3) a, b, c1, c2 and c3 represent the estimated values of the parameters of the explicit Preston equation (see Shi et al. [2023] for details), where the units of a and b are cm, and c1, c2, and c3 are unitless.
(4) scan.length, scan.width and scan.area represent the scanned egg length (in cm), maximum width (in cm) and planar area (in cm2).
(5) RSS represents the residual sum of squares in y-coordinates in cm2. 
(6) sample.size represents the sample size.
(7) RMSE represents the root-mean-square error in cm.
(8) V and S represent the predicted egg volume (in cm3) and surface area (in cm2) using the volume and surface area equations based on the explicit Preston equation with estimated parameters, respectively.
(9) Volume represents the volume (in cm3) measured using the graduated cylinder.
(10) Albumen represents the mass of albumen for a boiled egg in g.
(11) Yolk represents the mass of yolk for a boiled egg in g.
(12) Shell represents the mass of shell for a boiled egg in g. 

Reference(s)
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. Annals of the New York Academy of Sciences, in press.

