The Prym tropicalization conjecture

Let $f:C'\to C$ be an unramified double cover of smooth curves, and let $\phi:\Gamma'\to\Gamma$ be its tropicalization. Let the Prym variety associated with $f$ be the connected component of the kernel of the norm map containing the identity, and let the tropical Prym variety associated with $\phi$ be the corresponding connected component of the kernel of the induced map on tropical Jacobians.

Prym tropicalization conjecture. The skeleton of the Prym variety associated with $f$ is the tropical Prym variety associated with $\phi$; equivalently, the Prym construction commutes with tropicalization.

This is proposed as the Prym analogue of the result that the Jacobian of the skeleton of a curve is the skeleton of its Jacobian. The supplied text gives no resolution, so the conjecture remains open.