The monadic dependence characterization of fixed-parameter tractable FO model checking

Let $d4a2$ be a hereditary class of structures. FO model checking asks, given a first-order sentence $d719$ and a structure in $d4a2$, whether $d719$ holds in that structure. The class $d4a2$ is monadically dependent if it does not interpret every finite graph via first-order formulas with a bounded number of added unary predicates.

The monadic dependence conjecture. For every hereditary class $d4a2$ of structures, FO model checking is FPT on $d4a2$ if and only if $d4a2$ is monadically dependent.

This would characterize the hereditary classes admitting fixed-parameter tractable first-order model checking in model-theoretic terms. The source presents it as an existing conjecture, and no resolution is given here.