Recently I've been reading through B. J. Oropeza's three-volume set Apostasy in the New Testament Communities, and I found some interesting comments touching upon the nature of apostolic succession. As is well known, the replacement of Judas by Matthias (Acts 1:12-26) is a scriptural incident that has often been interpreted by Latter-day Saint thinkers as clear precedent that the Twelve was to be an ongoing body, with the death of any member requiring the selection of a new replacement so as to keep the Twelve at a full quorum. (In LDS thought, the failure to keep up this process has often been cited as a contributing factor toward the purported Great Apostasy that overtook the church.) Of course, as J. Reuben Clark, Jr., admitted, the replacement of Judas by Matthias is the only clear example we have of this in the New Testament (On the Way to Immortality and Eternal Life [Salt Lake City, UT: Deseret Book, 1953 (1948)], 34-35, 48). However, Joseph Fielding Smith advanced the argument that other members of the Twelve were likewise replaced upon their deaths by other New Testament figures designated with the title 'apostle', such as Paul (Doctrines of Salvation 3:152-153):
We know that Judas Iscariot lost his standing because of his treacherous betrayal of the Master, and Matthias was called to take his place. We know that James, the son of Zebedee, was killed with the sword not long after the resurrection of the Lord. [...] We know that it was the custom in the beginning to fill vacancies in this presiding council, for the quorum of the Twelve was to remain in the Church during its entire existence. We know that in the course of time there came a "falling away," and that the Church was taken from the earth, and that the priesthood went back to God for a season. [...] Paul was an ordained apostle, and without question he took the place of one of the other brethren in that Council.
Contrast this, of course, with Clark's statement that "there is no record that he [Paul] was ever a member of the Twelve" (35). Oropeza's findings also differ markedly from Joseph Fielding Smith's view (which is unsubstantiated by either biblical evidence or early church tradition) and support an alternative view of the Twelve (In the Footsteps of Judas and Other Defectors: The Gospels, Acts, and Johannine Letters [Eugene, OR: Cascade, 2011], 149):
Second, Jesus promised the Twelve they would sit with him on thrones "judging the twelve tribes of Israel" (Luke 22:30/Matt 19:28). The apostasy of Judas reduced the number of disciples to eleven (Acts 1:26; cf. Luke 24:9, 33) and left a vacant seat that needed to be filled if twelve disciples were to reign in the future kingdom, and so Luke includes the replacement of Judas by Matthias in the Acts narrative. Significantly no replacement is needed for James, another member of the Twelve, when he dies later on in Acts 12:1-2. His eschatological place is secure because he died a martyr. He will sit on one of the twelve thrones judging the tribes of Israel. The same could not be said of Judas; another must take his place because he will not participate in the future kingdom of God.
Oropeza's research supports the mainstream Christian tradition: that the operative factor requiring the replacement of Judas by Matthias was not Judas' death per se but rather his irrevocable act of apostasy - made irrevocable by his death. Therefore, Judas is replaced, but James and the others are not. This indicates that the Twelve was not meant to be an earthly body with a lengthy succession of members; rather, it was meant as a once-for-all eschatological quorum - and no replacement has ever been needed for any member but Judas because all of those members still hold their position in it. Naturally, the implications of this for LDS thought would be extraordinarily significant, given how overwhelmingly the LDS priesthood hierarchy is founded upon its claims that the biblical Quorum of the Twelve was just such a succession-based body.