This word appears to have originated in "Proto-Polynesian" times - it does not seem to occur as a plant name in Fiji or further afield.
The tree to which the modern Tongan reflex of this word refers to would probably give us the best clue as to which tree, or which kind of tree, the word first referred. However, we are still investigating this as the Churchwood dictionary says only "A hardwood tree that grows at Vava'u". Similarly the Tahitian reflex is defined in Pollex as "a fragrant plant used to perfume oil". More information about that particular plant might also give clues as to the Marquesan and one of the Hawaiian reflexes. We are also making enquiries about this, so watch this space!
The Maori reflex ake refers exclusively to the tree Dodonaea viscosa (Sapindaceae), and seems to be in the "mainstream" semantically -- it is a tree with a very hard wood (in the past much used for making spears and weapons), black seeds (like most of its Hawaiian namesakes), and its leaves were used for scenting oil, thus apparently combining connotations from the Tongan and Tahitian reflexes of the original word.
The word a'e in Hawaiian refers to a close relative of the NZ ake, Sapindus saponaria ("Soapberry"), a tall, deciduous canopy tree, with black seeds much used in making leis. As you can see from the photographs, the form of the a'ea'e is quite similar to that of its New Zealand counterpart. The Hawaiian word also applies to several other species: four species of Zanthoxylum (Rutaceae), shrubs or small to medium-sized trees with aromatic leaves and a hard durable wood formerly used for making digging sticks and spears, and, on the island of Maui, Xylosma hawaiiense (Flacourtiaceae), a small tree whose fruits have black seeds.
The reduplicated form akeake, however, refers in Maori both to Dodonaea viscosa, a species found in tropical and subtropical regions round the world, and two species of Olearia (Compositae), O. traversii, originally confined to the Chatham Islands, and O. avecenaefolia, native to the South Island. Perhaps the veins on the leaves and the general (rather than specific) appearance of the Olearias in exposed locations reminded those who named them of the ake,but equally likely they were reminiscent of the Tahitian "ae", because of the scents derived from their leaves. (See the pages for ake and akeake for more information about the plants bearing these Mäori names.) On the island of Mauke, in the Cook Islands, akeake denotes the soapberry (Sapindus saponaria); in Rarotonga, according to the Savage Dictionary, it also refers to a local species of Xylosma, X. gracilis.
In Hawaiian, the reduplicated form also refers to a variegated cultivar of banana. I was very fortunate to have visited the Limahuli Garden of the National Tropical Botanical Garden on Kauai, Hawaii, where a friend of one of the curators had presented them with the plant illustrated in the photograph only a few days before. This meaning is shared with the Marquesan cognate, ake. Why this is so seems on the surface to be something of a mystery, but if you look at the shape of the leaves of the a'ea'e banana, and then at the leaves of some of the other plants which have inherited the Polynesian name, imagining that they are similar in size, perhaps the mystery may not be quite so deep.