The optimal shape of avian eggs

1. The shape of avian eggs is often explained by involving the mechanical properties of eggshell such as resistance to breakage or invoking physiological forces operating during egg development. 2. Here we take a different approach and investigate the efficient use of space. According to this approach the optimal egg shape is the one that produces the most compact fit under the incubating parent. 3. We extend the model of Andersson (1978) and use a numerical technique to investigate egg shapes in clutches of 1 to 10 eggs. In our model the shape of eggs is described by four parameters in a two-dimensional space. These parameters are free to vary - but eggs cannot be concave. 4. The optimal egg shape for each clutch size was found by a genetic algorithm. 5. The model predicts that egg shape should depend on clutch size. In particular, if the clutch consists of one egg then this egg should be spherical; whereas in clutches of two or three eggs the eggs should be biconical. In clutches of four the eggs should be pointed. The model also predicts that in clutches of over seven eggs the optimal egg shape should be approximately spherical. 6. These predictions are valuable because they point out that some of the variation in avian egg shapes may be explained solely by the efficient use of the brood patch area of the incubating parent.