  We introduce a family of Rock-Paper-Scissors type models with $Z_N$ symmetry
($N$ is the number of species) and we show that it has a very rich structure
with many completely different phases. We study realizations which lead to the
formation of domains, where individuals of one or more species coexist,
separated by interfaces whose (average) dynamics is curvature driven. This type
of behavior, which might be relevant for the development of biological
complexity, leads to an interface network evolution and pattern formation
similar to the ones of several other nonlinear systems in condensed matter and
cosmology.
