Over the course of the poem, the Duke reveals his obsession with control. The statue of Neptune taming a seahorse symbolizes the Duke’s persona.
The Duke boasts of his aggression toward his dead wife in an effort to gain complete mastery over her most simple pleasures. His reference to the statue of Neptune emphasizes his hunger for mastery over all of the things around him.
Just like the painting of his wife, which has become the symbol of complete submission to the Duke’s will, the statue is a symbol of captivity. The statue is an image of the seahorse being subdued to the will of Neptune. The Duke also wants to subdue others to his will.
(PLATO)