Eggs from the Baker: Simplifying and improving on an under-appreciated oological model

Biologists have been baffled by the reasons behind, and evolutionary and ecological implications of, interspecific variations in avian egg shape. In this respect, Douglas E. Baker's mathematical model of bird eggs has been largely under-appreciated because a) the author never wrote another paper on it, b) at the time of its publication (2002) several other models were in widespread use, and c) it typically requires eight different egg measurements. Thus, the current study aimed to reduce Baker's model to a more convenient form in terms of its parameters, number of initial measurements required, compliance with the principles of geometric laws, and, finally, its mathematical transformation to a form that warrants such compliance. An experimental comparison of three modifications of the model with the contours of actual eggs that have oval, conical and pyriform shapes was performed. Results allowed us to present a new standard geometric solid of revolution of an ovoid shape, for the description of which three key egg parameters are required: length, L, maximum breadth, B, and the value of the vertical axis shift from the centre, w. In addition to the minimum set of initial measurements, this modification of Baker's model complies with the principles of the main axiom of the mathematical formula of the bird's egg and demonstrates acceptable accuracy (< 10 %) in describing the contours of real eggs. The adoption of the simplified and improved Baker model is essential for ecological and evolutionary research involving birds and their egg shapes, as well as for egg-inspired engineering.