It seems to me that the natural tree is about the Israelites and the wild branch is about the gentiles. The Gentiles were grafted into the natural tree (Israel).
Unless specified my Bible quotes are from the KJV. That is the version of the Bible we use. The JST is in the footnotes and one section dedicated to the JST.
The KJV was published in the Middle Ages. It has some grammatical and translation errors that JS had taken on for his Book of Mormon "Translation". Here are some examples from the wonderful book by J. and S. Tanner, "The Changing World of Mormonism":
KJV: he which is filthy, let him be filthy still: and he that is righteous, let him be righteous still (Rev. 22:11)
BM: they who are righteous shall be righteous still, and they who are filthy shall be filthy still (2 Nephi 9:16)
KJV: endured the cross, despising the shame (Heb. 12:2)
BM: endured the crosses of the world, and despised the shame (2 Nephi 9:18)
KJV: to be carnally minded is death; but to be spiritually minded is life (Rom. 8:6)
BM: to be carnally-minded is death, and to be spiritually-minded is life (2 Nephi 9:39) (p.119)
And here is another quote from that marvelous book (p. 124):
"I am Alpha and Omega, the beginning and the end" (Rev. 21:6).
"I am Alpha and Omega, the beginning and the end" (3 Nephi 9:18).
The words Alpha and Omega are the first and last letters of the Greek alphabet. Apostle Bruce R. McConkie acknowledges this fact: "These words, the first and last letters of the Greek alphabet, are used figuratively ..." (Mormon Doctrine, 1966, p.31).
The Greek language was used throughout the Roman Empire at the time of Christ; therefore, the New Testament was written in Greek and the words Alpha and Omega were well understood. The Nephites, however, were supposed to have left Jerusalem 600 years before the time of Christ, and therefore they would not have been familiar with these words. If Jesus had told the Nephites that He was "Alpha and Omega," it would have had absolutely no meaning to them. When the author of the Book of Mormon lifted these words from the book of Revelation he evidently did not realize that they were from the Greek language. Mormon writers maintain that the Book of Mormon "does not contain any of the numerous words in the New Testament that are of Greek origin" (Contents, Structure, And Authorship of the Book of Mormon, By J. N. Washburn, p.161). This idea is certainly incorrect.
The words Alpha and Omega are definitely of Greek origin. The Book of Mormon also contains the name Timothy (3 Nephi 19:4). Timothy is a Greek name and never appears in the Old Testament. In the same verse that we find the name Timothy we also find the name Jonas. Jonas is the New Testament name for Jonah and is found in Matthew 12:39. Joseph Smith seems to have been oblivious to the fact that the Book of Mormon contains Greek words. When it was suggested that the word Mormon came from the Greek, he stated: "This is not the case. There was no Greek or Latin upon the plates from which I, ... translated the Book of Mormon" (Times and Seasons, vol. 4, p.194). The appearance of Greek words in the Book of Mormon—especially the words Alpha and Omega—is another evidence that it is not an ancient record, but rather a modern composition.