Avian egg incubation period: Revisiting existing allometric relationships via surface area-to-volume ratio of an egg

The incubation period (I) for bird eggs varies among species and is used in establishing allometric relationships. Research on variations in I shed light on the evolutionary mechanisms that gave rise to the differentiation of embryonic development in distinct taxa of birds. Here, using a sampling of 444 images from 444 avian species, 89 families and 30 orders, we calculated their major geometric dimensions: volume (V) and surface area (S). An assessment of the relationship between I and the measured and calculated egg parameters demonstrated the closest and most significant correlation (R = -0.760) between I and the S/V ratio that was adopted as a conditional indicator and reflects the embryo's metabolic rate. Approximation of the values of these parameters made it possible to derive a power-law dependence for the prediction of I depending on the S/V value of a particular egg (R² = 0.757). The prediction accuracy was higher (R² = 0.783) if the eggs of the family Procellariiformes (petrels), whose I value is characterized by a longer time, were removed from the general sampling computation. We conclude that the value of the S/V ratio can characterize both the metabolism of an embryo and the conditional thermal conductivity of an egg, which aids in ensuring the temperature regime of egg incubation.