1 Nephi 15:13

13 And now, the thing which our father meaneth concerning the grafting in of the natural branches through the fulness of the Gentiles, is, that in the latter days, when our seed shall have dwindled in unbelief, yea, for the space of many years, and many generations after the Messiah shall be manifested in body unto the children of men, then shall the fulness of the gospel of the Messiah come unto the Gentiles, and from the Gentiles unto the remnant of our seed—

Nephi begins to introduce the fact that this lineage of Israel is more than bloodlines. It is a covenant lineage. When they talk about this comparison of the House of Israel to an olive tree, it is both a literal and covenant comparison. When a branch is broken off the family tree, it maintains its identity as far as being from the olive tree (house of Israel), but it has been removed from the original covenant people. The covenant relationship is more important than the blood relationship. Christ tried to teach this principle to the Jews, but they couldn’t get it (see John 8:33–59). John the Baptist also tried to teach them, also to no avail (see Matthew 3:7–12). So Nephi, after reminding his brothers of their blood lines and that the prophesies about the house of Israel are about them, introduces this idea of a covenant lineage as well, which he refers to as the “gospel of the Messiah.” This covenant will dwindle among the Lehites, then will be re-introduced to them by the Gentiles, who have no blood inheritance of Abraham, but do have a covenant inheritance.