  We introduce trace definability, a weak notion of interpretability, and trace
equivalence, a weak notion of equivalence for first order structures and
theories. In particular we get an interesting weak equivalence notion for
$\mathrm{NIP}$ theories. We describe a close connection to indiscernible
collapse. We also show that if $Q$ is a divisible subgroup of $(\mathbb{R};+)$
and $\mathcal{Q}$ is a dp-rank one expansion of $(Q;+,<)$ then exactly one of
the following holds: $\mathrm{Th}(\mathcal{Q})$ trace defines $\mathrm{RCF}$ or
$\mathcal{Q}$ is trace equivalent to a reduct of an ordered vector space.
