  We consider the effects of the competition between different sources of
frustration in 1D spin chains through the analysis of the paradigmatic ANNNI
model, which possesses an extensive amount of frustration of local origin due
to the competition between nearest and next-to-nearest neighbor interactions.
An additional, non-extensive amount of topological frustration can be added by
applying suitable boundary conditions, and we show that this seemingly
subdominant contribution significantly affects the model. Choosing periodic
boundary conditions with an {\it even} number of sites not divisible by 4 and
using the entanglement entropy as a probe, we demonstrate that in one of the
model's phases, the ground state can be characterized as hosting two (almost)
independent excitations. Thus, not only do we show an intriguing interplay
between different types of frustration, but also manage to propose a
non-trivial quasi-particle interpretation for it.
