  How fish modulate their fin stiffness during locomotive manoeuvres remains
unknown. We show that changing the fin's curvature modulates its stiffness.
Modelling the fin as bendable bony rays held together by a membrane, we deduce
that fin curvature is manifested as a misalignment of the principal bending
axes between neighbouring rays. An external force causes neighbouring rays to
bend and splay apart, and thus stretches the membrane. This coupling between
bending the rays and stretching the membrane underlies the increase in
stiffness. Using analysis of a 3D reconstruction of a Mackerel (Scomber
japonicus) pectoral fin, we calculate the range of stiffnesses this fin is
expected to span by changing curvature. The 3D reconstruction shows that, even
in its geometrically flat state, a functional curvature is embedded within the
fin microstructure owing to the morphology of individual rays. Since the
ability of a propulsive surface to transmit force to the surrounding fluid is
limited by its stiffness, the fin curvature controls the coupling between the
fish and its surrounding fluid. Thereby, our results provide mechanical
underpinnings and morphological predictions for the hypothesis that the spanned
range of fin stiffnesses correlates with the behaviour and the ecological niche
of the fish.
