I was recently reading some literature about evolutionary game theory and I got particularly interested in Moran process linked to prisoner's dilemma as a model of evolution of two sub-populations.
Please take a look at this paper: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5701760/
I understand the model rather well yet I am missing the point of eq.(4) and (5). Why does the fitness of a single cell $f$ takes this particular form of the payoff $\pi$:
$f = 1 - w + w\pi$
I understand that $w$ is supposed to be a 'selection pressure' but why do we have the exact equation as above? why not just $w\pi$ or $1-w\pi$? This is troubling me especially it is the same equation for both strategies i.e the selection would act in the same way on both subpopulations...