When was the last battle of the Jaredites? Various estimates have been given from 600 BC to 300 BC but no one has really pinned it down to something more specific. However, several clues are given in the Book of Mormon. First, in the book of Omni we read:
And it came to pass in the days of Mosiah, there was a large stone brought unto him with engravings on it; and he did interpret the engravings by the gift and power of God. [These engravings] gave an account of one Coriantumr, and the slain of his people. And Coriantumr was discovered by the people of Zarahemla; and he dwelt with them for the space of nine moons (Omni 1:20-22).
Here we learn that the Jaredite survivor Coriantumr was found by the people of Zarahemla, commonly known as the Mulekites. He was with them for nine lunar months. We are not told whether he was found during the lifetime of Zarahemla, but I am assuming that he was. We are not told whether he died at the end of nine months, or just left them to go off on his own. It is likely that he died.
The translation of the stone by Mosiah occurred between 279 and 130 BC. Probably closer to 130 BC as that is when the book of Mosiah begins. If they had found Coriantumr during the lifetime of Zarahemla it couldn't have been more than a hundred years earlier at the most. Therefore this would seem to date the Jaredite anihilation after about 230 BC.
Coriantumr was probably found by the Mulekites as they traveled south toward the land of Zarahemla. We learn in Alma that the Mulekites first landed in what the Nephites called “the land northward (Alma 22:30),” so it was probably while in the land northward that they encountered Coriantumr.
The second clue comes from the book of Alma wherein we read of Ammon's contact with the people of king Limhi. In an aside, king Limhi mentions an unsuccessful expedition he had sent north to look for the city of Zarahemla.
And the king said unto him: Being grieved for the afflictions of my people, I caused that forty and three of my people should take a journey into the wilderness, that thereby they might find the land of Zarahemla, that we might appeal unto our brethren to deliver us out of bondage.
And they were lost in the wilderness for the space of many days, yet they were diligent, and found not the land of Zarahemla but returned to this land, having traveled in a land among many waters, having discovered a land which was covered with bones of men, and of beasts, and was also covered with ruins of buildings of every kind, having discovered a land which had been peopled with a people who were as numerous as the hosts of Israel.
And for a testimony that the things that they had said are true they have brought twenty-four plates which are filled with engravings, and they are of pure gold.
And behold, also, they have brought breastplates, which are large, and they are of brass and of copper, and are perfectly sound.
And again, they have brought swords, the hilts thereof have perished, and the blades thereof were cankered with rust; and there is no one in the land that is able to interpret the language or the engravings that are on the plates (Mos. 8:7-11).
Farther along in his abridgement Mormon again recounts this event adding a few more details.
Now king Limhi had sent, previous to the coming of Ammon, a number of men to search for the land of Zarahemla; but they could not find it, and they were lost in the wilderness.
And they brought a record with them, even a record of the people whose bones they had found; and it was engraven on plates of ore (Mos. 21:25-27).
The date at the foot of the Book of Mormon indicates that these events occurred “about 121 BC.”
From this account we learn that the Limhi expedition had found among other things 1) a land covered with the dry bones of men and animals, 2) large breastplates made of brass and copper, 3) the rusting remains of hilt-less iron swords (the rust would indicate that these swords were made of iron). These three things can give us a rough approximation of the amount of time that had passed from the last battles of the Jaredites, to the discovery by the Limhites.
First let's discuss the bones. In a humid, wet, semi-tropical enviroment bones left on the surface of the ground tend to decompose rather quickly. If there are a lot of predators and scavengers, they tend to accelerate the process. If the soil is of volcanic origin, and therefore acidic, this also accelerates the decay.
Once again, this is for bone lying on the surface and exposed to animals, bugs, and the elements. This was the case with the Jaredite bones that the Limhites found. Bone size is also a factor with smaller bones disintegrating first and larger bones lasting longer. But the thing to note is that within 30 years the bones are all decomposing. We can safely assume that within one hundred years all evidence of the Jaredite bones which had been on the surface would have disappeared.
So if we take 121 BC as the date of the Limhite discovery, then the earliest date of the last battle would have been 221 BC. It could easily have been much later.
What is the importance of this knowledge? It suggests that there was no contact between the main body of Jaredties and the Nephites. It gives us an approximate date of the arrival of the Mulekites in Zarahemla. It gives us a reason why the land northward was open and available for Nephite settlement.
It would also be possible to use the iron swords and the breastplates to approximate the date of the Jaredite's last battle. Iron rusts quickly and will soon disintegrate if left in the elements. The hilts, which were probably of wood, had already decomposed when the Limhites found them. On the other hand, the breastplates made of brass (probably bronze) and copper were sound with no apparent corrosion.
I have not studied the corrosion rates of these metals, but it would be easy to find a time frame which fits the description given by the expedition. This would narrow the range and give a more precise date for the demise of the Jaredites.