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Impact of environmental stochastic fluctuations on the red-king effect in interspecific mutualism
Hui Zhang1,2, Yi Tao3,4, Cong Li4
1Northwestern Polytechnical University, School of Mathematics and Statistics, Xi'an, Shaanxi 710072, China.
Abstract:
Following the concept of the red-king effect proposed by Bergstrom and Lachmann [Proc. Natl. Acad. Sci. USA 100, 593 (2003)10.1073/pnas.0134966100], a stochastic asymmetric replicator equation is developed to investigate the influence of environmental stochastic fluctuations on the interspecific mutualism, where the evolutionary rate of each species is assumed to be a random variable. By the stochastic stability analysis and stochastic simulations, our results indicate that not only is the red-king effect is still true in some cases, but also the environmental stochastic fluctuations may also result in the complete reciprocity between species, that is, the so-called generosity without reservation between each other. All these results may provide a possible way to understand the evolutionary mechanism of interspecific mutualism in real nature.
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