Limits...
The shift between the Red Queen and the Red King effects in mutualisms.

Gao L, Li YT, Wang RW - Sci Rep (2015)

Bottom Line: The Red Queen effect argues that faster-evolving species are favoured in co-evolutionary processes because they are able to obtain a larger share of benefits.Conversely, the Red King effect argues that the slower-evolving species gains a larger share of benefits.The model we propose shows that the allocations for a common benefit vary when the effect of a reward mechanism is included in the model.

View Article: PubMed Central - PubMed

Affiliation: 1] School of Mathematics and Statistics, Yunnan University, Kunming, Yunnan. 650091, P.R. China [2] State Key Laboratory of Genetic Resources and Evolution, Kunming Institute of Zoology, Chinese Academy of Science, Kunming, Yunnan. 650223, P.R. China.

ABSTRACT
Interspecific mutualisms consist of partners trading services that yield common benefits to both species. Until now, understanding how the payoffs from mutualistic cooperation are allocated among the participants has been problematic. Two hypotheses have been proposed to resolve this problem. The Red Queen effect argues that faster-evolving species are favoured in co-evolutionary processes because they are able to obtain a larger share of benefits. Conversely, the Red King effect argues that the slower-evolving species gains a larger share of benefits. The model we propose shows that the allocations for a common benefit vary when the effect of a reward mechanism is included in the model. The outcome is a shift from the Red Queen effect to the Red King effect and vice versa. In addition, our model shows that either an asymmetry in payoff or an asymmetry in the number of cooperative partners causes a shift between the Red Queen effect and the Red King effect. Even in situations where the evolutionary rates are equal between the two species, asymmetries in rewards and in participant number lead to an uneven allocation of benefits among the partners.

Show MeSH
The effects of a reward wi and the game size N on the internal equilibrium x*.We assume the numbers of players between species to be equal, i.e., d1 = d2 = d. Thus, the game size for each species is defined by N, and N = d + 1. (a) Given a relatively low reward intensity (i.e., w = 0.8), the internal equilibrium x* is above 0.5 in small groups (e.g., N = 2 or N = 3). (b) For pairwise games, the equilibrium is always above 0.5 for any reward intensity. (c) When the size of the mutualistic group is large (i.e., N = 8), the internal equilibrium can shift from a small value (below 0.5) to a large value (above 0.5) with a rise in the collective reward. The other parameters are fixed at bi = 2, ci = 1 and Mi = 1.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4316171&req=5

f3: The effects of a reward wi and the game size N on the internal equilibrium x*.We assume the numbers of players between species to be equal, i.e., d1 = d2 = d. Thus, the game size for each species is defined by N, and N = d + 1. (a) Given a relatively low reward intensity (i.e., w = 0.8), the internal equilibrium x* is above 0.5 in small groups (e.g., N = 2 or N = 3). (b) For pairwise games, the equilibrium is always above 0.5 for any reward intensity. (c) When the size of the mutualistic group is large (i.e., N = 8), the internal equilibrium can shift from a small value (below 0.5) to a large value (above 0.5) with a rise in the collective reward. The other parameters are fixed at bi = 2, ci = 1 and Mi = 1.

Mentions: In this section, we assume that the benefit bi, the cost ci, the number of players di, and the reward wi of the two species are the same. If the evolutionary rates are unequal (i.e., species 1 with rate rx = ry/8), the basins of attraction of (C1, D2) and (D1, C2) become unequal in size. In other words, the allocation of the resulting benefits is unequal between the two species (Fig. 2d, 2e, and 2f). If the game is run without any reward mechanism (with wi = 0), the basin of attraction (C1, D2) is larger than the basin of attraction (D1, C2). This implies that the faster-evolving species will receive a larger share of the benefits (Fig. 2d). This is in line with what is predicted by the Red Queen effect24. However, this effect can shift to the Red King effect when we include the reward variable in the multiplayer game. Specifically, the size of the basin of attraction of (D1, C2) increases substantially as the reward intensity wi increases (Fig. 2e). As a result, the slower-evolving species obtains a larger share of the benefits (Fig. 2f). This means that the initial Red Queen effect shifts to the Red King effect when the magnitude of the reward is over a certain threshold value (Fig. 3c). However, this reward mechanism does not allow the Red King effect to shift to the Red Queen effect (Fig. 3a and 3b). Finally, we find that the size of the reward can accentuate the Red King effect (Fig. 3b and 3c).


The shift between the Red Queen and the Red King effects in mutualisms.

Gao L, Li YT, Wang RW - Sci Rep (2015)

The effects of a reward wi and the game size N on the internal equilibrium x*.We assume the numbers of players between species to be equal, i.e., d1 = d2 = d. Thus, the game size for each species is defined by N, and N = d + 1. (a) Given a relatively low reward intensity (i.e., w = 0.8), the internal equilibrium x* is above 0.5 in small groups (e.g., N = 2 or N = 3). (b) For pairwise games, the equilibrium is always above 0.5 for any reward intensity. (c) When the size of the mutualistic group is large (i.e., N = 8), the internal equilibrium can shift from a small value (below 0.5) to a large value (above 0.5) with a rise in the collective reward. The other parameters are fixed at bi = 2, ci = 1 and Mi = 1.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4316171&req=5

f3: The effects of a reward wi and the game size N on the internal equilibrium x*.We assume the numbers of players between species to be equal, i.e., d1 = d2 = d. Thus, the game size for each species is defined by N, and N = d + 1. (a) Given a relatively low reward intensity (i.e., w = 0.8), the internal equilibrium x* is above 0.5 in small groups (e.g., N = 2 or N = 3). (b) For pairwise games, the equilibrium is always above 0.5 for any reward intensity. (c) When the size of the mutualistic group is large (i.e., N = 8), the internal equilibrium can shift from a small value (below 0.5) to a large value (above 0.5) with a rise in the collective reward. The other parameters are fixed at bi = 2, ci = 1 and Mi = 1.
Mentions: In this section, we assume that the benefit bi, the cost ci, the number of players di, and the reward wi of the two species are the same. If the evolutionary rates are unequal (i.e., species 1 with rate rx = ry/8), the basins of attraction of (C1, D2) and (D1, C2) become unequal in size. In other words, the allocation of the resulting benefits is unequal between the two species (Fig. 2d, 2e, and 2f). If the game is run without any reward mechanism (with wi = 0), the basin of attraction (C1, D2) is larger than the basin of attraction (D1, C2). This implies that the faster-evolving species will receive a larger share of the benefits (Fig. 2d). This is in line with what is predicted by the Red Queen effect24. However, this effect can shift to the Red King effect when we include the reward variable in the multiplayer game. Specifically, the size of the basin of attraction of (D1, C2) increases substantially as the reward intensity wi increases (Fig. 2e). As a result, the slower-evolving species obtains a larger share of the benefits (Fig. 2f). This means that the initial Red Queen effect shifts to the Red King effect when the magnitude of the reward is over a certain threshold value (Fig. 3c). However, this reward mechanism does not allow the Red King effect to shift to the Red Queen effect (Fig. 3a and 3b). Finally, we find that the size of the reward can accentuate the Red King effect (Fig. 3b and 3c).

Bottom Line: The Red Queen effect argues that faster-evolving species are favoured in co-evolutionary processes because they are able to obtain a larger share of benefits.Conversely, the Red King effect argues that the slower-evolving species gains a larger share of benefits.The model we propose shows that the allocations for a common benefit vary when the effect of a reward mechanism is included in the model.

View Article: PubMed Central - PubMed

Affiliation: 1] School of Mathematics and Statistics, Yunnan University, Kunming, Yunnan. 650091, P.R. China [2] State Key Laboratory of Genetic Resources and Evolution, Kunming Institute of Zoology, Chinese Academy of Science, Kunming, Yunnan. 650223, P.R. China.

ABSTRACT
Interspecific mutualisms consist of partners trading services that yield common benefits to both species. Until now, understanding how the payoffs from mutualistic cooperation are allocated among the participants has been problematic. Two hypotheses have been proposed to resolve this problem. The Red Queen effect argues that faster-evolving species are favoured in co-evolutionary processes because they are able to obtain a larger share of benefits. Conversely, the Red King effect argues that the slower-evolving species gains a larger share of benefits. The model we propose shows that the allocations for a common benefit vary when the effect of a reward mechanism is included in the model. The outcome is a shift from the Red Queen effect to the Red King effect and vice versa. In addition, our model shows that either an asymmetry in payoff or an asymmetry in the number of cooperative partners causes a shift between the Red Queen effect and the Red King effect. Even in situations where the evolutionary rates are equal between the two species, asymmetries in rewards and in participant number lead to an uneven allocation of benefits among the partners.

Show MeSH