Scientists find a universal formula for bird egg shape

It has long been said that the egg is the most perfect thing – in fact, in 1862, Thomas Wentworth Higginson said: “I think that, if required on pain of death to name instantly the most perfect thing in the universe, I should risk my fate on a bird’s egg.” It’s a recognisable shape, and an example of evolutionary adaptation to the most diverse range of environmental conditions and situations. The shape has long attracted the attention of mathematicians, engineers, and biologists from an analytical point of view, and now a team of researchers from the University of Kent have discovered a formula that can describe any bird’s egg existing in nature.

What is it about the egg shape that makes it so interesting? It is large enough to incubate an embryo, small enough to exit the body in the most efficient way, not roll away once it has been laid, and it’s structurally sound enough to bear weight. It is generally effective in extremes of heat and humidity, incubation with or without body heat, in or out of nests, and clean and highly-infected environments. There’s a reason that the egg structure is a feature of over 10,500 living bird species.

Analysis of all egg shapes has used four geometric figures: the sphere, ellipsoid, ovoid (literally ‘egg-shaped’) and pyriform (conical or pear-shaped). Until now, a geometric characterisation of the latter shape has belied accurate description by scientists. As Professor Darren Griffin, senior co-author of the University of Kent, said: “As a main parameter in oomorphology, the shape of a bird’s egg has, to date, escaped a universally applicable mathematical formulation. Analysis of all egg shapes can be done using four geometric figures: sphere, ellipsoid, ovoid, and pyriform (conical or pear-shaped). The first three have a clear mathematical definition, each derived from the expression of the previous, but a formula for the pyriform profile is yet to be derived.”

In order to rectify this, the researchers introduced an additional function into the ovoid formula, developing a mathematical model to fit a completely novel geometric shape – one characterised as the last stage in the evolution of the sphere-ellipsoid, which can be used for any egg geometry. This new universal formula for egg shape is based on four parameters – the egg length, maximum breadth, shift of the vertical axis, and the diameter at one quarter of the egg length. Using this formula, scientists move forward in understanding both the egg shape itself, but also how and why it evolved as it did.

Using this formula, scientists move forward in understanding both the egg shape itself, but also how and why it evolved as it did

There are many potential applications of this research. Most obviously, if we can describe eggs, optimisation of technological parameters in the poultry sector (as well as egg incubation and selection of poultry) will be simplified. It will also aid scientists who need to describe the egg, and it could help shape future biology-inspired engineering processes. Dr Valeriy Narushin, former visiting researcher at the University of Kent, said: “We look forward to seeing the application of this formula across industries, from art to technology, architecture to agriculture. This breakthrough reveals why such collaborative research from separate disciplines is essential.”

As Prof Griffin notes: “Biological evolutionary processes such as egg formation must be investigated for mathematical description as a basis for research in evolutionary biology, as demonstrated with this formula. This universal formula can be applied across fundamental disciplines, especially the food and poultry industry, and will serve as an impetus for further investigations inspired by the egg as a research object.”