Equal partners do better in defensive alliances

Abstract: Cyclic dominance offers not just a way to maintain biodiversity, but also serves as a sort of defensive alliance against an external invader. Interestingly, a new level of competition can be observed when two cyclic loops are present. Here the inner invasion speed plays a decisive role on the evolutionary outcome, because faster invasion rate provides an evolutionary advantage to an alliance. In this Letter we demonstrate that the heterogeneity of inner invasion rates makes an alliance vulnerable against a loop where group members are equal. Quite surprisingly, a loop where invasion rates are uniform can still dominate an alliance formed by heteregeneous rates even if the average speed of invasion is significantly higher in the latter group. At a specific range of parameter space, when intergroup invasion or the average inner invasion is moderate, the heterogeneous alliance with higher internal invasion speed may prevail, or the system terminates onto a novel 4- or 5-species solution.