Reachability Query for Tree
Follow-up work by Holm, Rotenberg and Thorup [1] showed that there exists a reachability oracle for planar graphs of size $O(n)$ and query time $O(1)$. This is optimal also for trees (e.g., if the input is a star graph, then you need to know the orientation of every one of the $n-1$ edges).

[1] Holm, Jacob, Eva Rotenberg, and Mikkel Thorup. "Planar reachability in linear space and constant time." 2015 IEEE 56th Annual Symposium on Foundations of Computer Science. IEEE, 2015.