Preston's universal formula for avian egg shape

Abstract

ABSTRACT Nearly 70 years ago, Preston published a pioneering study in which he provided formulae for the shapes of birds' eggs. One of these formulae is universal in that it provides an almost perfect representation for all eggs, even pyriform ones, and is better than all other formulae published since. This essentially perfect representation of egg shape is obtained by estimating the parameters in Preston's universal formula by least squares, using hundreds of measurements of the egg's radii along its entire length. Preston's universal formula can also be used to obtain an equation for avian egg shape that uses just 5 measurements (the length and 4 appropriately spaced diameters). The equation based solely on these 5 measurements provides an egg shape that is virtually indistinguishable from one based on hundreds of measurements. We demonstrate the usefulness of Preston's formulations using digital photographs of eggs. Our perspective is that, despite a number of subsequent approaches, Preston's original one has not been bettered and should be the standard for studying avian egg shape. LAY SUMMARY The shapes of birds' eggs vary considerably, from the archetypal ovoid shape of the hen's egg, through those that are almost spherical, to eggs that are pointed at one or both ends. In the 1950s, the engineer and amateur ornithologist Frank W. Preston published methods for measuring and quantifying avian egg shape. Unfortunately, his equations proved rather inaccessible to ornithologists and have largely been ignored. As a result, there has been a succession of papers claiming to have solved the problem of quantifying avian egg shape, including some with titles that imply that their approach is better than anything previously published, but without testing the validity of their claims. Here, we show that all of these papers were trying to solve a problem that Preston had resolved long ago. All methods of estimating egg shape published since the 1950s are all, to varying extents, less accurate than Preston's original formulation. Preston provides the most perfect formula for “the most perfect thing,” a bird's egg. RESUMEN Hace casi setenta años, Preston publicó un estudio pionero en el que proporcionaba fórmulas para las formas de los huevos de las aves. Una de estas fórmulas es universal porque proporciona una representación casi perfecta de todos los huevos, incluso los piriformes, y es mejor que todas las demás fórmulas publicadas desde entonces. Esta representación esencialmente perfecta de la forma del huevo se obtiene estimando los parámetros en la fórmula universal de Preston mediante mínimos cuadrados, usando cientos de medidas de los radios del huevo a lo largo de toda su longitud. La fórmula universal de Preston también puede ser usada para obtener una ecuación para la forma del huevo aviar que utiliza solo cinco medidas (la longitud y cuatro diámetros espaciados adecuadamente). La ecuación basada únicamente en estas 5 medidas proporciona una forma de huevo que es prácticamente indistinguible de una basada en cientos de medidas. Demostramos la utilidad de las formulaciones de Preston utilizando fotografías digitales de huevos. Nuestra perspectiva es que, a pesar de una serie de enfoques posteriores, el enfoque original de Preston no ha sido mejorado y debería ser el estándar para estudiar la forma del huevo aviar.