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Question:Did the Jaredites bring swarms of bees across the ocean in their barges
Question: Did the Jaredites bring swarms of bees across the ocean in their barges?
The Book of Mormon states that the Jaredites carried swarms of bees with them to the seashore in the Old World
The Book of Mormon does not claim that the Jaredites carried honey bees to the New World. It does state that they carried swarms of honeybees with them to their encampment on the sea shore, where they spent the next four years as they built barges. This is entirely feasible.
There is only one reference to honeybees in the Book of Ether (Ether 2:3-4), and it talks of them being among the provisions that the people of Jared took with them as they traveled to the land of Moriancumer, where they spent the next four years. (Ether 2:13)
3 And they did also carry with them deseret, which, by interpretation, is a honey bee; and thus they did carry with them swarms of bees, and all manner of that which was upon the face of the land, seeds of every kind.
4 And it came to pass that when they had come down into the valley of Nimrod the Lord came down and talked with the brother of Jared; and he was in a cloud, and the brother of Jared saw him not.
5 And it came to pass that the Lord commanded them that they should ago forth into the wilderness, yea, into that quarter where there never had man been. And it came to pass that the Lord did go before them, and did talk with them as he stood in a cloud, and gave directions whither they should travel.
6 And it came to pass that they did travel in the wilderness, and did build barges, in which they did cross many waters, being directed continually by the hand of the Lord.
13 And now I proceed with my record; for behold, it came to pass that the Lord did bring Jared and his brethren forth even to that great sea which divideth the lands. And as they came to the sea they pitched their tents; and they called the name of the place Moriancumer; and they dwelt in tents, and dwelt in tents upon the seashore for the space of four years.
The Book of Mormon does not claim that the Jaredites carried honey bees to the New World
So, the Jaredites definitely carried swarms of bees with them to the place of the "great sea which divideth the lands," where they "dwelt in tents upon the seashore for the space of four years." Does this mean that the Jaredites carried the swarms of honey bees to the New World with them? The Book of Mormon does not state this. This does not preclude the possibility that they did.
Michael Ash notes,
Among the supposed Book of Mormon anachronisms is the mention of “bees” (Ether 2:3)...It should be noted firstly that the Book of Mormon's use of the term "bees" occurs in an Old World (Jaredite) setting, it is never used in connection with the New World, therefore the argument could simply end here. Did the Jaredites bring bees to the New World? We may never know. Some studies suggest, however, that bees were known in the ancient New World. Bruce Warren, for instance, notes that there “are many references in the Maya region to honey bees in ancient times, and these references occur in ritual contexts, i.e., are of native or pre-Spanish origin." Other New World scholars have observed that “not only was the domesticated bee in ancient America but that there were gods of bees and beekeepers . . . Honey was considered a real treat for the Indians. Equally important was black wax taken from the hives which was often traded for other commodities." 
- Mike Ash, mormonfortress.com