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Never mind the ubiquitous ‘which came first’ question, the hot ‘egg’ question is actually ‘why the shape’?
(of a solid or a three-dimensional surface) more or less egg-shaped.

Egg-shaped. But WHY? In an extensive paper published in the scientific journal Science* in June 2017 (which I confess to not having read very much of on account of its intensity and specificity) a collective of scientists have discredited the long held view about the reason for a bird’s eggs being, well, egg shaped.

Although birds' eggs are generally ovoid in shape, there is wide variation in the degree to which they are symmetrical, round, or bottom-heavy. Many suggestions have been put forward to explain what has driven this variation (I definitely subscribe to the ‘well, you don’t want your egg roll out of your nest’ theory). But, it seems we have all been wrong.

Scientist Mary Caswell Stoddard and her team** looked at nearly 50,000 eggs from more than 1400 species studying morphological, biophysical, and evolutionary perspectives and found little evidence to suggest that life history and nesting are decent enough explanations for egg shape. So…what is the reason?

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The paper ‘Avian egg shape: Form, function and evolution’* holds a vast body of research and data analysis and includes a number of complicated diagrams and charts but the conclusion reached (simplified to tabloid level by me) is that instead of safe nesting, flight adaptation is most likely to be responsible for the variation in egg shape. The further the flying distance, the greater the need for a streamlined and aerodynamic body, which in turn increases the need for an asymmetrical and/or elliptical egg.
It’s all about the streamlined body plan. There you have it.

* ‘Avian egg shape: Form, function and evolution’, Science, volume 356 issue 6344 p. 1249-1254

** Mary Caswell Stoddard / Ee Hou Yong / Derya Akkaynak / Catherine Sheard / Joseph A Tobias / L Mahadevan