Beak morphometry and morphogenesis across avian radiations

Adaptive avian radiations associated with the diversification of bird beaks into a multitude of forms enabling different functions are exemplified by Darwins finches and Hawaiian honeycreepers. To elucidate the nature of these radiations, we quantified beak shape and skull shape using a variety of geometric measures that allowed us to collapse the variability of beak shape into a minimal set of geometric parameters. Furthermore, we find that just two measures of beak shape, the ratio of the width to length and the normalized sharpening rate (increase in the transverse beak curvature near the tip relative to that at the base of the beak), are both strongly correlated with diet, and thus indicative of how bite forces are correlated with beak shape. Finally, by considering how transverse sections to the beak centerline evolve with distance from the tip, we show that a simple geometry-driven growth law termed "modified mean curvature flow" captures the beak shapes of Darwins finches and Hawaiian honeycreepers. A surprising consequence of the simple growth law is that beak shapes that are not allowed based on the developmental program of the beak are also not observed in nature, suggesting a link between evolutionary morphology and development in terms of growth-driven developmental constraints.