They are directly related. The more different trees, the more different birds because not all birds like the same trees:
Some like higher trees to build higher nests, others like lower trees, some like the leaves of some trees useful, some live in the trees that give them fruits, other in trees where many insects go, etc.
Species richness is related to the number of species living in a particular community. More the number of species present in a community more will be its species richness.
Trees provide the natural habitat for most of the birds living in this world so a higher tree species richness can provide a wide range of natural habitat for bird species.
Different species of birds rely on different source of food to reduce competition so a high species richness of trees can provide a different source of food which can support high species richness of birds.
Therefore there is a positive relationship between bird species richness and tree species richness.
