  In a diverse population, where many species are present, competitors can
fight for surviving at individual and collective levels. In particular,
species, which would beat each other individually, may form a specific alliance
that ensures them stable coexistence against the invasion of an external
species. Our principal goal is to identify those general features of a
formation which determine its vitality. Therefore, we here study a traditional
Lotka-Volterra model of eight-species where two four-species cycles can fight
for space. Beside these formations, there are other solutions which may emerge
when invasion rates are varied. The complete range of parameters is explored
and we find that in most of the cases those alliances prevail which are formed
by equally strong members. Interestingly, there are regions where the symmetry
is broken and the system is dominated by a solution formed by seven species.
Our work also highlights that serious finite-size effects may emerge which
prevent observing the valid solution in a small system.
