Impact of environmental stochastic fluctuations on the red-king effect in interspecific mutualism

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.