Functional optimality underpins the repeated evolution of the extreme "saber-tooth" morphology.

"Saber teeth"-elongate, blade-like canines-are a classic example of convergence, having evolved repeatedly throughout mammalian history. Within canine teeth, there is a trade-off between the aspects of shape that improve food fracture and those that increase tooth strength. Optimal morphologies strike a balance between these antagonistic functional criteria. The extreme saber-tooth morphology is thought to confer functional advantage for more specialized predatory adaptations and optimization; however, the adaptive bases underpinning their evolution remain unclear. To determine whether saber-tooth shape reflects selection for functionally optimal morphologies, we generated a morphospace of the 3D shape of 70 non-saber and 25 saber-tooth species, a subset of which were used to quantify functional metrics of puncture performance and breakage resistance. These data were combined using a Pareto rank-ratio algorithm to evaluate optimality. We demonstrate that extreme saber-tooth morphologies are functionally optimal, occupying a localized peak in our optimality landscape. Unlike other optimal canine morphologies, extreme saber teeth optimize puncture performance at the expense of breakage resistance. This identifies functional optimality as a key driver underpinning the repeated evolution of this iconic tooth.