  The new dynamical game theoretic model of sex ratio evolution emphasizes the
role of males as passive carriers of sex ratio genes. This shows inconsistency
between population genetic models of sex ratio evolution and classical
strategic models. In this work a novel technique of change of coordinates will
be applied to the new model. This will reveal new aspects of the modelled
phenomenon which cannot be shown or proven in the original formulation. The
underlying goal is to describe the dynamics of selection of particular genes in
the entire population, instead of in the same sex subpopulation, as in the
previous paper and earlier population genetics approaches. This allows for
analytical derivation of the unbiased strategic model from the model with
rigorous non-simplified genetics. In effect, an alternative system of
replicator equations is derived. It contains two subsystems: the first
describes changes in gene frequencies (this is an alternative unbiased
formalization of the Fisher-Dusing argument), whereas the second describes
changes in the sex ratios in subpopulations of carriers of genes for each
strategy. An intriguing analytical result of this work is that fitness of a
gene depends on the current sex ratio in the subpopulation of its carriers, not
on the encoded individual strategy. Thus, the argument of the gene fitness
function is not constant but is determined by the trajectory of the sex ratio
among carriers of that gene. This aspect of the modelled phenomenon cannot be
revealed by the static analysis. Dynamics of the sex ratio among gene carriers
is driven by a dynamic "tug of war" between female carriers expressing the
encoded strategic trait value and random partners of male carriers expressing
the average population strategy (a primary sex ratio). This mechanism can be
called "double level selection". Therefore, gene interest perspective leads to
multi-level selection.
