Odobenocetops

Odobenocetops (/ˌɒdəbiˈnɒsɨtɒps/ "walrus-face whale") was a small whale from the Pliocene. It had two tusks, and, in some fossils, one tusk was longer than the other.

Description
Odobenocetops was an early member of the dolphin superfamily, more closely related to narwhals than dolphins, with tusks projecting towards the rear of its body. It measured about 2.1 m (6.9 ft) long[1] and weighted between 150 and 650 kg. Its neck articulations show that it was very flexible, being able to turn its head over 90 degrees. This, coupled with its broad snout, similar to that of a walrus, suggests that it was a bottom feeder, searching for mollusks and sucking them out of their shells with a powerful tongue.

Tusk use
Perhaps the most striking discovery was that of a male O. leptodon skull with a tusk significantly longer than the other. On the right side of the body, the tusk was often 1.2 m (3.9 ft) long, but on the left it could only grow up to 25 centimetres (9.8 in) long.[1] Being the only male O. leptodon skull known, it is not safe to say it was present in all male individuals of the species. Being too brittle, the tusk was probably held parallel to the body. It might have been used to search out food, or as a sensory organ like narwhal tusks. Even though they are closely related to these primitive whales, the tusks were gained by convergent evolution. Tim Haines thought that the tusks could be used during the mating season in jousts over females.[1] The abstract of an influential article on an Odobenocetops species from the journal Nature helps to explain why this is so:

The recent discovery in the Southern Hemisphere (15.5 °S) of a walrus-like skull of a toothed whale (odontocete) from the Pisco Formation of southern Peru presents a startling example of convergence and specialization unprecedented among cetaceans. In contrast to other toothed whales, Odobenocetops peruvianus has no elongated rostrum but has large, ventrally directed premaxillary alveolar processes housing asymmetrical tusks. The dorsally facing orbits indicate the possibility of dorsal binocular vision which could compensate for the absence of the melon, a rostral organ involved in echolocation. Strong muscle scars on the anterior edge of the premaxillae suggest the presence of a powerful upper lip. It is this feature, together with the morphology of the deep vaulted palate devoid of maxillary teeth, that enables us to hypothesize a convergent feeding adaptation with the walrus which feeds mainly on thin-shelled bivalve molluscs, sucking out the foot and/or siphon and ejecting the shell. The structure of the face and basicranium indicates it was a delphinoid cetacean, probably related to the living beluga and narwhal (Monodontidae).[2]

O. leptodon and O. peruvianus were extremely similar but, if the single O. leptodon is not a sport and is representative of its type, O. leptodon probably had a small melon and, therefore, echolocation ability, but had reduced (or no) binocular vision.