Figure 4
From: The shift between the Red Queen and the Red King effects in mutualisms
The influence of asymmetric players or rewards on the allocation of mutualistic benefits.
(1) First, we consider unequal evolutionary rates between the two mutualistic species (rx = 1/8, ry = 1). (a) For a fixed number of players of species 2 (d2 = 8), the difference between S1 and S2 depends on the number of players of species 1 (d1), where S1 and S2 represent the size of the basins of attraction of the equilibrium (C1, D2) and (D1, C2), respectively. For one-to-many interactions between the two species, S2 is larger than S1. Conversely, S1 is larger than S2 when the interactions between species are many-to-many (e.g., d1 = 4). (b) Similarly, by adjusting the intensity of reward for species 2 (w2), the Red King effect (i.e., S2 > S1) can also shift into the Red Queen effect (i.e., S1 > S2) and vice versa (the reward intensity on species 1 is fixed at w1 = 1). (2) For equal evolutionary rates between two species (rx = ry = 1), each player will receive equal mutualistic benefits when the number of players of the two species are symmetric (c) (e.g., di = 8 with i = 1,2). When the numbers of the players of the two species are asymmetric (d1 ≠8), each player will receive unequal mutualistic benefits. Similar results can be obtained for the rewards (as in (d)). We also assume that d2 = 8 in (c) and w1 = 1 in (d). The other parameters are fixed at bi = 2, ci = 1 and Mi = 1, w1 = w2 = 0 in (a) and (c) and d1 = d2 = 4 in (b) and (d).
