  Binary populations in young star clusters show multiplicity fractions both
lower and up to twice as high as those observed in the Galactic field. We
follow the evolution of a population of binary stars in dense and loose star
clusters starting with an invariant initial binary population and a formal
multiplicity fraction of unity, and demonstrate that these models can explain
the observed binary properties in Taurus, Rho-Ophiuchus, Chamaeleon, Orion, IC
348, Upper Scorpius A, Praesepe, and the Pleiades. The model needs to consider
solely different birth densities for these regions. The evolved theoretical
orbital-parameter distributions are highly probable parent distributions for
the observed ones. We constrain the birth conditions (stellar mass, M_ecl, and
half-mass radius, r_h) for the derived progenitors of the star clusters and the
overall present-day binary fractions allowed by the present model. The results
compare very well with properties of molecular cloud clumps on the verge of
star formation. Combining these with previously and independently obtained
constraints on the birth densities of globular clusters, we identify a weak
stellar mass -- half-mass radius correlation for cluster-forming cloud clumps,
r_h / pc ~ (M_ecl / M_sun)^(0.13+-0.04). The ability of the model to reproduce
the binary properties in all the investigated young objects, covering
present-day densities from 1-10 stars pc^-3 (Taurus) to 2x10^4 stars pc^-3
(Orion), suggests that environment-dependent dynamical evolution plays an
important role in shaping the present-day properties of binary populations in
star clusters, and that the initial binary properties may not vary dramatically
between different environments.
