Effects of environmental feedback on species with finite population

In an unchanging environment, natural selection always selects species with high fitness. In this study, we build a co-evolutionary system to study the interaction between stochasticity in finite populations and environmental feedback. Positive feedback between species and environment is detrimental to the invasion success, whereas negative feedback is beneficial to invasion since feedback makes population size important enough to revise natural selection's preference. In competition scenario, positive and negative feedback will benefit the initially inferior species. When selection intensity is high, negative feedback may even cause natural selection to favor the initially inferior species. All of these effects are caused by feedback that allows the initially inferior species to have greater fitness than the initially dominant species. Our results emphasize that the effects of stochasticity in evolutionary path can be reinforced by feedback with environment and then reverse the preference of natural selection.