The spell alter self says
You acquire the physical qualities of the new form while retaining your own mind. Physical qualities include natural size, mundane movement capabilities (such as burrowing, climbing, walking, swimming, and flight with wings, to a maximum speed of 120 feet for flying or 60 feet for nonflying movement), natural armor bonus, natural weapons (such as claws, bite, and so on), racial skill bonuses, racial bonus feats, and any gross physical qualities (presence or absence of wings, number of extremities, and so forth). A body with extra limbs does not allow you to make more attacks (or more advantageous two-weapon attacks) than normal.
You do not gain any extraordinary special attacks or special qualities not noted above under physical qualities, such as darkvision, low-light vision, blindsense, blindsight, fast healing, regeneration, scent, and so forth.
The racial traits of the aquatic elf says
Also called sea elves, these creatures are waterbreathing cousins to land-dwelling elves.…
- Gills: Aquatic elves can survive out of the water for 1 hour per point of Constitution (after that, refer to the suffocation rules).
Does a caster that uses the spell alter self to assume the form of an aquatic elf get gills that allow the caster to breathe water?