Commensurations of $\mathrm{A}\mathrm{u}\mathrm{t}(F_N)$ and its Torelli subgroup

For $N\ge 3$, the abstract commensurators of both $\mathrm{A}\mathrm{u}\mathrm{t}(F_N)$ and its Torelli subgroup ${\mathrm{I}\mathrm{A}}_N$ are isomorphic to $\mathrm{A}\mathrm{u}\mathrm{t}(F_N)$ itself.