  The classical approaches to the modeling of sex ratio evolution can be
divided into two classes. The first class contains the static strategic models
related to the Dusing Fisher Shaw Mohler fitness measure, based on the
reproductive value of the offspring of the focal female. The second class
contains the population genetic models focused on the dynamics of the allele
frequencies. The approaches are not fully compatible because the strategic
models disregard the role of the male individuals as the passive carriers of
the strategy genes. In the previous two papers in this cycle, a new model
combining the strategic analysis with more rigorous genetics was presented. The
new model shows that sex ratio self-regulation is a multistage complex process
which can be regarded as an example of multilevel selection. One of the
elements of this process is the dynamic equilibrium between male and female
gene carriers associated with convergence of the dynamics to the manifold
termed the male subpopulation equilibrium (MSE). This paper attempts to explain
this phenomenon and analyze its properties. We show that the MSE phenomenon
affects every stage of sex ratio self-regulation (Lemmas 1-4). The MSE plays a
crucial role in synchronizing two levels of selection in the double-level
selection process. We show that the MSE condition can be generalized as an
interesting synergistic property allowing for the estimation of the primary sex
ratio of the entire population according to the state of some arbitrarily
chosen subpopulation (Lemma 5). We also show that the classical Dusing Fisher
Shaw Mohler fitness measure is a biased approximation of the new approach, but
that it produces compatible strategic predictions (Lemma 6).
