  We answer three questions posed by Bubeck and Linial on the limit densities
of subtrees in trees. We prove there exist positive $\varepsilon_1$ and
$\varepsilon_2$ such that every tree that is neither a path nor a star has
inducibility at most $1-\varepsilon_1$, where the inducibility of a tree $T$ is
defined as the maximum limit density of $T$, and that there are infinitely many
trees with inducibility at least $\varepsilon_2$. Finally, we construct a
universal sequence of trees; that is, a sequence in which the limit density of
any tree is positive.
