The problem of cooperation1−8 is that defection is evolutionarily stable. If everybody in a population defects and one individual cooperates then this indi- vidual has a lower payoff and will be opposed by selection. Thus, the emergence of cooperation is thought to require specific mechanisms: for example, several cooperators have to arise simultaneously to overcome an invasion barrier9 or arise as spatial clusters10,11. This understanding is based on traditional con- cepts of evolutionary stability and dynamics of infinite populations12−16. Here we study evolutionary game dynamics in finite populations17−20 and show that a single cooperator using a reciprocal strategy3,21 can invade a population of defectors with a probability that corresponds to a net selective advantage. We specify the conditions for natural selection to favor the emergence of coopera- tion and derive conditions for evolutionary stability in finite populations.
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