  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
will be expressed by explicit demographic parameters describing the probability
of death during focal interaction when cooperative trait can be exhibited. 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.

Populations and Evolution;Adaptation and Self-Organizing Systems