Intransitivity and coexistence in four species cyclic games

► We model a four species cyclic game whose trophic network is fully connected, but with different invasion rates. ► The system is studied within the fully mixed (mean field) assumption and on a regular, square lattice. ► On the square lattice, as the invasion rates change, there is a transition from a coexistence state to one with extinctions. ► This transition is not observed within the mean field approach. ► These results indicate that for the coexistence state to persist, there must be a minimum amount of intransitivity.