Figure 1

The interactions between species 1 and 2 in mutualisms.

We assume that d₁ = 5, d₂ = 6. Species 1 plays in a seven-player game. In this first game, we choose one player of species 1 (the blue faces) to interact with six players of species 2 (the red faces). Species 2 plays a six-player game. In this second game, one player of species 2 joins and interacts with all the players of species 1. Generally, for a d₁ + 1 players' game for species 2, we choose one individual from species 2 to interact with d₁ individuals of species 1. For a d₂ + 1 players' game for species 1, we pick one individual from species 1 to interact with d₂ individuals of species 2. We do not consider intraspecific interactions within groups. It is possible to incorporate even more complexity by considering these interactions within the same species. By doing this, however, the model becomes very convoluted and beyond the scope of this paper. Figure 1 was produced with Microsoft Word. Other figures were obtained with Maple 15.