  The mass fraction of hot gas in clusters is a basic quantity whose level and
dependence on the cluster mass and redshift are intimately linked to all
cluster X-ray and SZ measures. Modeling the evolution of the gas fraction is
clearly a necessary ingredient in the description of the hierarchical growth of
clusters through mergers of subclumps and mass accretion on the one hand, and
the dispersal of gas from the cluster galaxies by tidal interactions, galactic
winds, and ram pressure stripping on the other hand. A reasonably complete
description of this evolution can only be given by very detailed hydrodynamical
simulations, which are, however, resource-intensive, and difficult to implement
in the mapping of parameter space. A much more practical approach is the use of
semi-analytic modeling that can be easily implemented to explore a wide range
of parameters. We present first results from a simple model that describes the
build up of the gas mass fraction in clusters by following the overall impact
of the above processes during the merger and accretion history of each cluster
in the ensemble. Acceptable ranges for model parameters are deduced through
comparison with results of X-ray observations. Basic implications of our work
for modeling cluster statistical properties, and the use of these properties in
joint cosmological data analyses, are discussed.
