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.