Most of the formalizations of the Inclusive Fitness and Kin Selection concepts contain two highly simplifying assumptions (which actually complicate the problem): first, is that the models are described in terms of "fitness", an abstract parameter vaguely related to the population growth rate or expected reproductive success. The second is that they ignore the division between Donors and Receivers of altruism and the distribution of those roles in the population. In this paper the Inclusive Fitness and Kin Selection approaches instead of unclear fitness units, will be expressed by explicit demographic parameters describing the probability of death during focal interaction when cooperative trait can be exhibited. This will allow for more mechanistic insight into impact of the cooperative actions on the population dynamics. In addition, new framework will take into account the distribution of the roles of Donor or the Receiver in the population. This description will be used for the derivation of the population growth model describing the competition between Cooperative and Noncooperative strategies. The obtained approach will be sufficient for description of the cases when the roles are independently drawn during each interaction. However, we can imagine situations when survival and the change of the role are not correlated (such as food support for the infected individual, which keeps him alive, but cannot cure). To cover those cases, new model is extended to the case with explicit dynamics of the role distributions among carriers of different strategies, driven by some general mechanisms. In effect it is shown that even in the case when fluxes between roles are driven by selectively neutral mechanisms (acting in the same way on all strategies), the differences in the mortalities in the focal interaction will lead to different distributions of roles for different strategies. This leads to more complex rules for cooperation than the classical Hamilton's rule, that in addition to the classical Cost and Benefit contain third component weighted by difference in proportions of Donors among carriers of both strategies. Depending on the sign, this component can be termed "selfishness bonus" (when it decreases the benefit) which describes the benefit of not taking a risk related to altruist action, or "sacrifice bonus" (when it decreases the cost) which describes the benefit of sacrifice if the Receiver's survival exceeds the survival of helping Donor.