Studying avian egg shape and other aspects of its morphology has recently undergone a renaissance. Yet, most studies rely solely on two metrics for the quantification of egg shape: elongation and asymmetry. The difficulty of additionally quantifying the curvature of an eggshell has yielded many attempts including those with complex equations and spatial modeling techniques based on digitized images. These have lacked an independent single-variable metric, hampering comparative studies. We propose a metric for one common quality of egg shape, conicality, which is notably variable in diverse species’ calcareous shells including shorebirds and non-avian theropods. This metric utilizes multiple measurements of the slope along an eggs profile to produce a distribution of angular measurements, which can be analyzed with a Kurtosis (K) value. This metric was tested with sets of computer modeled and 3D printed egg forms, where elongation, the percentage of conicality, and the relative curvature of the shell profile were controlled. For applicability to natural eggs and their diversity across taxa, the Kurtosis value was used to quantify the gradient of conicality across a focal avian family, Alcidae, where the Kurtosis value successfully identified the most conical eggs using qualitative descriptions from well-established literature. Given the significance of egg morphology and profile curvature to structural integrity, surface-area to volume ratio, egg mobility/stability, nesting behavior, and embryonic development, our proposed measure of conicality could prove a useful variable to the study of avian and non-avian egg-producing species. 

This data was collected to compare relative the conicality of Alcidae eggs. Before this study, there was no single independent metric for quantifying how much a bird’s egg resembled a cone, specifically to what extent the pointed part of an egg has a straight-lined profile. This characteristic is common in shorebirds, and has been studied ad-hoc in Alcidae. It has been linked to egg stability, movement, and reduced egg loss in some species. The data set was used to compare Alcid species with anecdotally conical eggs with those of more rounded shell form. The conicality value (K) was made with of repeated angular measures of the shell profile assembled into a histogram that produced a kurtosis measure. This allowed for the identification of those species with highly conical eggs, including the genus Uria, (U. lomvia, and U. aalge). 

Angular measurements along a pointed quadrant of the egg's profile were taken from photos of museum specimens, from the Smithsonian collection and American Museum of Natural History. Each measurement was taken relative to the radial line of symmetry, between ~10 pixels along the profile, at every pixel. These angular measurements were assembled into bins of 2 degrees, and a kurtosis value of the distribution was extracted as a measure of the extent of which the pointed side of an egg matched a cone.