  This paper examines functional equivariance, recently introduced by McLachlan
and Stern [Found. Comput. Math. (2022)], from the perspective of backward error
analysis. We characterize the evolution of certain classes of observables
(especially affine and quadratic) by structure-preserving numerical integrators
in terms of their modified vector fields. Several results on invariant
preservation and symplecticity of modified vector fields are thereby
generalized to describe the numerical evolution of non-invariant observables.
