Comparison of a universal (but complex) model for avian egg shape with a simpler model. Issue 1 (31st May 2022) - Shi, Peijian; Gielis, Johan; Niklas, Karl J.
Abstract: Recently, a universal equation by Narushin, Romanov, and Griffin (hereafter, the NRGE) was proposed to describe the shape of avian eggs. While NRGE can simulate the shape of spherical, ellipsoidal, ovoidal, and pyriform eggs, its predictions were not tested against actual data. Here, we tested the validity of the NRGE by fitting actual data of egg shapes and compared this with the predictions of our simpler model for egg shape (hereafter, the SGE). The eggs of nine bird species were sampled for this purpose. NRGE was found to fit the empirical data of egg shape well, but it did not define the egg length axis (i.e., the rotational symmetric axis), which significantly affected the prediction accuracy. The egg length axis under the NRGE is defined as the maximum distance between two points on the scanned perimeter of the egg's shape. In contrast, the SGE fitted the empirical data better, and had a smaller root‐mean‐square error than the NRGE for each of the nine eggs. Based on its mathematical simplicity and goodness‐of‐fit, the SGE appears to be a reliable and useful model for describing egg shape. Abstract : A recent study has provided a universal mathematical equation for avian egg shape. However, its validity in fitting the actual data of egg shapes has not been tested. Here, we tested its validity using actual data of egg shapes, and compared it with a simplified version of the Gielis equation. The simplified Gielis equation was found to have a more concise mathematical expression and better describe avian egg shape.