  We theoretically study origins of the ferroelectricity in the multiferroic
phases of the rare-earth (R) Mn perovskites, RMnO3, by constructing a realistic
spin model including the spin-phonon coupling, which reproduces the entire
experimental phase diagram in the plane of temperature and Mn-O-Mn bond angle
for the first time. Surprisingly we reveal a significant contribution of the
symmetric (S.S)-type magnetostriction to the ferroelectricity even in a
spin-spiral-based multiferroic phase, which can be larger than the usually
expected antisymmetric (SxS)-type contribution. This explains well the
nontrivial behavior of the electric polarization. We also predict the
noncollinear deformation of the E-type spin structure and a wide coexisting
regime of the E and spiral states, which resolve several experimental puzzles.
