  A one-dimensional interacting particle system is said to exhibit interface
tightness if starting in an initial condition describing the interface between
two constant configurations of different types, the process modulo translations
is positive recurrent. In a biological setting, this describes two populations
that do not mix, and it is believed to be a common phenomenon in
one-dimensional particle systems. Interface tightness has been proved for voter
models satisfying a finite second moment condition on the rates. We extend this
to biased voter models. Furthermore, we show that the distribution of the
equilibrium interface for the biased voter model converges to that of the voter
model when the bias parameter tends to zero. A key ingredient is an identity
for the expected number of boundaries in the equilibrium voter model interface,
which is of independent interest.
