Sorting out the heritage of Zadok and Abiathar
Acording to the scripures, Abiathar is the only living relative of Ahimelech (1 Sam 22). Ahimelech is a descendant of Aaron's son Ithamar (1 Chron 24). And, Ahimelech was the priest at Nob who gave provisions to David when he was fleeing from Saul. Saul ordered that Ahimelech's entire family be slaughtered because of David. However one person, Abiathar, son of Ahimelech survived and fled with an ephod to David's camp. David felt responsible for the deaths and told Ahimelech to remain with him for protection. At this point, Abiathar must be old enough and know enough to run to David without assistance and while in David's presence the author of Samuel calls Abiathar 'the priest.'
If I can trust the timeline in my NASB, approximately 15 years pass between the death of Ahimelech's family and the beginning of David's kingship in Hebron. David reigns as king a total of 40 years, so from the time that Abiathar enters the protection of David until Davids death, 55 years have passed. By the time of Solomon's reign, Abiathar would certainly be far too old to serve as 'the' priest since the priest is to be between 25(or 30) and 50 years old. He could however continue to assist in temple duties. When David instructs on the division of the priests at the time he appoints Solomon as king, we find that Abiathar and his son Ahimelech are mentioned but niether are listed as 'the' priest (1 Chron 24:6). This strongly suggests that Abiathar was nolonger the high priest prior to his banishment to Anathoth, and rightly so since he was essentially retired at least a decade (probably two or three decades) prior.
In 2 Samuel 8:17, we find David expanding the kingdom and Zadok son of Ahitub is mentioned as the priest along with Ahimelech the son of Abiathar. Ahimelech son of Abiathar is also mentioned in 1 Chron 24:6. Abiathar's father and his son appear to be both named Ahimelech. If the son of Abiathar has become a priest and Abiathar is not mentioned as the priest, then it is quite likely that by this time Abiathar has already retired. However a son of Abiathar named Jonathan is mentioned several times elsewhere and it still appears that Abiathar is an important priest in 2 Sam 15:35 and in 2 Sam 20:25, so 2 Sam 8:17 and 1 Chron 24:6 may contain errors. Also, 1 Kings 2:27 states that Solomon dismisses Abiathar from the priesthood. Alternatively, the usage of the name Abiathar rather than Ahimelech during Zadoks priesthood may be an error if scribes were confused by both father of Abiathar and his son having the same name.
However, the fact remains that Abiathar is very aged by the beginning of Solomons reign. One suggestion regarding the line of Zadok is that Zadok was Abiathar's uncle. Given the age of Abiathar, this senario seems extremely unlikely. Also, when David assigns the 24 divisions of the priests, Zadok is listed among those descended from Eleazar, where as Abiathar is listed as those from Ithamar. (1 Chron 24) Perhaps Zadok could be an uncle through marriage, but not by biological descent.
The presence of two priests makes a lot of sense if Zadok is younger than Abiathar. Just as when a President of the USA retires he is still called 'President' so also would it be likely to continue to call the high priest the high priest even after he has 'retired.' Perhaps a one writing about that persons life would even refer to that person as priest prior to his acquisition of that office. For example someone might write: "President Bush was in college at that time." We would know that while in college he was not president, but writer simply uses his later title out of respect. So Abiathar would be the elder, retired priest; and, Zadok would be the current chief priest during the last 30 years of Davids reign.
We would then expect that after Zadok's 30 years of service, he too would retire. In 1 Kings 4:2 we can see that before construction began on the temple, Zadok's grandson, Azariah is 'the' priest; whereas Zadok and Abiathar are simply listed as priests in 4:4.
Another twist to all this is thrown in when one writer states that Abiathar was dismissed "to fulfill the the word of YHVH, which He had spoken concerning the house of Eli in Shiloh." (1 Kings 2:27) This suggests that Abiathar was descended from Eli, yet Eli does not appear in Abiathars genealogy.
Eli's lineage is far less attested than Zadok's. Who is Eli the son of? He had two sons, Phinehas and Hophni. Is his son Phinehas the same as the Aaron's grandson? If so, then the name Eli must be short for Eleazar. However, this is very doubtful because Samuel who was a child during the priesthood of Eli's sons was contemporary with David's father Jesse. So, Eli would be contemporary with Boaz (since he was rather old when Samuel came along) during the time of the judges. Then this Phinehas son of Eli would probably have been in the generation of Obed. Phinehas son of Eleazar on the other hand lived through the Exodus hundreds of years earlier.
I really can't see how any of this implies that Zadok was a Jebusite. If Zadok's heritage is of the line of Eleazar as scripture states, then his rise to pre-eminence is fitting with the statement in Numbers 3:32 that Eleazar son of Aaron (and probably his offspring) is to be chief over the chiefs of the Levites. There were a few other points that Dr. Mariottini raised, however this is getting very long already, so I'll leave that for another post if needed.