This is about a 5th c BC Greek colony in Italy, not Rome. Rome was founded about 500 BC, and the Roman navy never tried to train dolphins.
Boy am I stupid or what! ok let me go check the original in Homeric etc. Greek texts archival material for ‘boy” and “dolphin”... gotta be a clue if they made a stauette for such a strange thing if an actual thing???. This is almost like bull - jumping in Crete?
ok I found this ...
“Periandros, the man who informed Thrasyboulos of the oracle, was the son of Kypsclos, the tyrant of Corinth. The Corinthians tell a story, and the people of Lesbos agree with them, about the most amazing thing that happened during his lifetime: Arion of Methymna was carried upon a dolphin and set on shore at Tainaron.”...ff “there is a dedication by Arion at Tainaron, of a small bronze statue of a man upon a dolphin.”
source: Herodotus, “Histories”, “Book one”, 598-ff, lines 23.25; footnote 24b = Pausanias said he saw the statue six centuries later.
[I have to go back and read the original langauge and also look for more clues=] I yam havin lotsa fun!]