  The commensurate and incommensurate magnetic structures of the
magnetoelectric system YMn$_{2}$O$_{5}$, as determined from neutron
diffraction, were found to be spin-density waves lacking a global center of
symmetry. We propose a model, based on a simple magneto-elastic coupling to the
lattice, which enables us to predict the polarization based entirely on the
observed magnetic structure. Our data accurately reproduce the
temperature-dependence of the spontaneous polarization, in particular its sign
reversal at the commensurate-incommensurate transition.
