I will describe joint work with E. Gonzalez, in which we study the dependence of the moduli space of gauged pseudoholomorphic maps from a surface to a target X as the area form on the surface is varied. As an application, we get some version of the "abelianization" conjecture of Bertram et al relating Gromov Witten theory of symplectic quotients by a group and its maximal torus. This is part of a larger project which aims to develop functoriality of Gromov-Witten invariants of quotients, joint with Ziltener, Ma'u, and Ott.