Preston's universal formula for avian egg shape

Lay Summary center dot 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. center dot 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. center dot 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. center dot 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. 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.

Automated summary

Bird eggs have varying shapes, and Frank W. Preston's formula from 70 years ago provides the most accurate representation for their shapes. By estimating the parameters using least squares method and using a few measurements, Preston's formula can obtain virtually perfect representations of egg shape. Digital photographs of eggs confirm the effectiveness of Preston's formula, which should be the standard for studying avian egg shapes.