Does Poseidon rule over all the sea gods?

Question

According to Edith Hamilton's Mythology, there are several sea gods and river gods. Since Poseidon is one of the twelve main greek god(desses), is he the ruler of or otherwise in charge of those sea and river gods?

Answer 1

According to the ever-helpful theoi.com (emphasis mine on all quotes),

Being the ruler of the sea (the Mediterranean), he is described as gathering clouds and calling forth storms, but at the same he has it in his power to grant a successful voyage and save those who are in danger, and all other marine divinities are subject to him. As the sea surrounds and holds the earth, he himself is described as the god who holds the earth (gaiêochos), and who has it in his power to shake the earth (enosichthôn, kinêtêr gas).

That just so happens to be one of the only parts of the page lacking in-line citations. Go figure. However, it later quotes Aelian, On Animals 12. 45 (trans. Schofield) (Greek natural history C2nd to 3rd A.D.):

This is the hymn: ‘Highest of the gods, lord of the sea,

On another page, it explicitly says:

The ancient Greek term for sea gods was "Theoi Halioi" or "Theoi Einalioi." These deities were commanded by the Sea-King Poseidon and his queen Amphitrite.

That said, there was an older god, Pontus, the husband/brother of Gaia. He was around long before Poseidon, and was the patriarch of all the sea/river/water gods. I don't know if/when Poseidon became dominant over Pontus, if that ever happened. However, the hymn I referenced above probably dates to a time when, in Greek mythology, Poseidon was considered to be the top marine god, as opposed to Pontus.

Answer 2

Again, I don't yet have the reputation to comment on an answer given above, so I choose to respond here.

I have uploaded and made publicly available this short, accessible paper

Poseidon the Horse God and the Early Indo-Europeans Research Reports of Ikutoku Institute of Technology 9 1985

written by Nobuo Komita in which an argument is presented that Poseidon, before being transferred to the domain of the sea, was a Proto-Indo-European horse god associated with wealth, expansion and legitimate 'kingship'. I put kingship in quotes because it's something of a standing question whether or not PIE speakers even had such a concept. 'Having the right to rule' may be a better way of describing this function. In line with C.M. Weimer's comments above, in the paper Komita argues Poseidon is a specially-adapted form of the Sky Father (i.e. Zeus) as evidenced by Poseidon's trident as compared to Zeus's lightning bolt and Poseidon's conflict with Athena over patronage of cities - on the notion that the horse god's blessing was necessary to legitimately rule.

edit: I originally got the name of this paper from the Wikipedia article, to tell the truth.