3D triplot of the surface representing the fitness of each species (species 1 = light grey, species 2 = dark grey, species 3 = black) given the relative proportions of each species illustrating how a 3^rd species can generate coexistence between 2 species which would otherwise not coexist.

a) Shows the case where no species pairs would coexist without the third species, and is completely intransitive. In this example, species 1 replaces species 2, species 3 replaces 1 and species 2 replaces 3. b) Shows the case where species 1 and 2 would coexist in the absence of species 3 due to negative feedbacks, yet even though species 3 would coexist with neither in isolation, all three do coexist through a combination of direct and indirect negative feedbacks. c) Shows the case where the pair-wise combinations of species 1 and 2 and 2 and 3 would coexist, but even though 1 and 3 would not, all three do. Panels a, b, and c are 2D representations of the corresponding 3D plots showing the edge conditions.