  This paper considers the inverse problem of recovering state-dependent source
terms in a reaction-diffusion system from overposed data consisting of the
values of the state variables either at a fixed finite time (census-type data)
or a time trace of their values at a fixed point on the boundary of the spatial
domain. We show both uniqueness results and the convergence of an iteration
scheme designed to recover these sources. This leads to a reconstructive method
and we shall demonstrate its effectiveness by several illustrative examples.
