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Most of the formalizations of the Inclusive Fitness and Kin Selectionconcepts contain two highly simplifying assumptions (which actually complicatethe problem): first, is that the models are described in terms of "fitness", anabstract parameter vaguely related to the population growth rate or expectedreproductive success. The second is that they ignore the division betweenDonors and Receivers of altruism and the distribution of those roles in thepopulation. In this paper the Inclusive Fitness and Kin Selection approacheswill be expressed by explicit demographic parameters describing the probabilityof death during focal interaction when cooperative trait can be exhibited. Inaddition, new framework will take into account the distribution of the roles ofDonor or the Receiver in the population. This description will be used for thederivation of the population growth model describing the competition betweenCooperative and Noncooperative strategies. The obtained approach will besufficient for description of the cases when the roles are independently drawnduring each interaction. However, we can imagine situations when survival andthe change of the role are not correlated (such as food support for theinfected individual, which keeps him alive, but cannot cure). To cover thosecases, new model is extended to the case with explicit dynamics of the roledistributions among carriers of different strategies, driven by some generalmechanisms. In effect it is shown that even in the case when fluxes betweenroles are driven by selectively neutral mechanisms (acting in the same way onall strategies), the differences in the mortalities in the focal interactionwill lead to different distributions of roles for different strategies. Thisleads to more complex rules for cooperation than the classical Hamilton's rule.

Beyond classical Hamilton's Rule. State distribution asymmetry and the dynamics of altruism