How does an alpha male lose his position?

An alpha can be displaced by a younger, stronger baboon, in which case he’s unlikely to be able to reclaim his position.  He may also fall from grace if he loses the trust or support of key members of the troop. It’s possible, but unlikely that he would be able to pull some clever social manoeuvres to get back on top temporarily.  Either way, the position of alpha is always temporary, and in baboon society, the alpha male switches out quite often – typically every 2-5 years.