Geometry and dynamics link form, function, and evolution of finch beaks

Abstract

Darwin’s finches are a classic example of adaptive radiation, exemplified by their adaptive and functional beak morphologies. To quantify their form, we carry out a morphometric analysis of the three-dimensional beak shapes of all of Darwin’s finches and find that they can be fit by a transverse parabolic shape with a curvature that increases linearly from the base toward the tip of the beak. The morphological variation of beak orientation, aspect ratios, and curvatures allows us to quantify beak function in terms of the elementary theory of machines, consistent with the dietary variations across finches. Finally, to explain the origin of the evolutionary morphometry and the developmental morphogenesis of the finch beak, we propose an experimentally motivated growth law at the cellular level that simplifies to a variant of curvature-driven flow at the tissue level and captures the range of observed beak shapes in terms of a simple morphospace. Altogether, our study illuminates how a minimal combination of geometry and dynamics allows for functional form to develop and evolve.

Beak morphometry and morphogenesis across avian radiations

“…S3). We find that the following paraboloidal profile, which was introduced as a fit to the beaks of Darwin's finches in [6], captures the upper surface of the beak for the samples in our dataset (SI Fig. S3):…”

L’évolution à petite échelle

“…Darwin a découvert la sélection naturelle en analysant les pinsons des îles Galapagos. Il s'agit d'un complexe d'espèces étroitement apparentées, diversifiées au cours des 2 à 3 derniers millions d'années sur cet archipel et adaptées à différents régimes alimentaires (graines de différentes tailles, sang d'oiseaux de mer, nectar de fleurs, insectes) via des changements de taille et de morphologie du bec (Al-Mosleh et al, 2021). Ces oiseaux ont été l'objet de nombreuses études analysant comment leurs populations répondaient aux évènements climatiques.…”

Physics of sliding on water predicts morphological and behavioral allometry in water striders

“…We expect that from among the possible linear measurements of body (width, height, length) the length is relatively more correlated with the body mass (albeit not necessarily in a linear fashion) than are body width or height as they are relatively small and differ among species relatively less than the body length. We decided not to use body length 3 (a possible alternative used occasionally in allometry) because of the elongated shape of the water striders. Leg proportions ("leg geometry") and body masses of the study species.…”

“…Understanding how laws of physics may constrain morphological and behavioral evolution of biological organisms of different body sizes is of great importance not only to biology [1][2][3] but also to the modern bioinspired engineering 4,5 . Allometry, the study of how physics and biology affect the relationships between body size and other characteristics of an organism, has a long history [6][7][8][9][10][11][12][13][14][15][16][17][18][19] .…”