  We study the scaling limit of a large class of voter model perturbations in
one dimension, including stochastic Potts models, to a universal limiting
object, the continuum voter model perturbation. The perturbations can be
described in terms of bulk and boundary nucleations of new colors (opinions).
The discrete and continuum (space) models are obtained from their respective
duals, the discrete net with killing and Brownian net with killing. These
determine the color genealogy by means of reduced graphs. We focus our
attention on models where the voter and boundary nucleation dynamics depend
only on the colors of nearest neighbor sites, for which convergence of the
discrete net with killing to its continuum analog was proved in an earlier
paper by the authors. We use some detailed properties of the Brownian net with
killing to prove voter model perturbations convergence to its continuum
counterpart. A crucial property of reduced graphs is that even in the
continuum, they are finite almost surely. An important issue is how vertices of
the continuum reduced graphs are strongly approximated by their discrete
analogues.
