A (sketchy) note on evolutionary game theory

The (Nash) equilibrium in ordinary game theory (GT) has the same relation to equilibrium in evolutionary GT (EGT) as has expectation in time and sample in statistical signal processing. That is, they are the same if the process is ergodic.

By saying this, I claim that there is some concept (call is EWWS - evolutionary WSS) in EGT that corresponds to a WSS process in statistical signal processing. I think that I am claiming that evolution is an EWSS. Or maybe it could be of interest to investigate when an evolutionary process is EWSS.

Actually, evolution is such is for sure not EWSS, since species co-evolve. Thus, there should be specific sub-branches of evolutionary processes where they are EWSS. This could perhaps also be linked to geographic location in the sense that at far enough distance evolutionary processes become disconnected  due to that there is no interaction between the individuals.