Myths on Maps

In Apollodorus 3.15.1 The sons of Pandion split the inheritance where Erechtheus gets the kingdom of Athens and Butes gets the priesthood of Athena but also that of Poseidon. The problem is that in this instance Poseidon's priesthood is named the priesthood of "Poseidon Erechtheus" It is currently marked up as "Poseidon" and "Erechtheus" which kind of inplies that the priesthood of Poseidon went to Erechtheus. But in Perseus a note says that in Athens people prayed to "Poseidon Erechtheus" because poseidon was associated with Erechtheus. So, did Poseidon's priesthood go to Erechtheus or to Butes and was called "Poseidon Erechtheus"? If the later is true, should I include "Poseidon Erechtheus" as an AKA for Poseidon? Thanks ~Simon