DOI: 10.5061/dryad.zcrjdfn7s
title: Data from: The shape of avian eggs: assessment of a novel metric for quantifying eggshell conicality

description: 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. 
description: 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 <i>Uria</i>, (<i>U.
 lomvia</i>, and <i>U. aalge</i>). 
 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.