On Ligon II, supersedence occurred when the First One (male) selected a new First One (female). The preceding First One could chose to challenge supersedence or accept the wishes of her spouse. Most older First Ones chose not to challenge for the risks were very high. In a decision of who would be First One, if a challenge was announced, the combat ended in death. If the older First One died, then her lands and possessions were given to the spouse.
There were at least two known challenges to supersedence. The first occurred roughly in 2164. The second, and best known, occurrence was in 2364 when Lutan chose Lieutenant Yar as his first against the objections of Yareena, the First Female. (TNG: "Code of Honor")