Contrary to what we used to believe, we now know that the vast majority of tree roots are in the top foot of soil. Also, they grow far beyond the drip line of the outermost leaves, grabbing up water and nutrients wherever they can find them.
That's why it's hard to grow lawns under shallow-rooted trees like maples, beeches, hemlocks, and pines. That's also why willow, maple, and poplar roots too often find their way inside our sewer pipes.
To spread and thrive, all roots need soil that's high in numerous minute microorganisms (millions of them), which facilitate the uptake of nutrients and promote good health. They go by strange names like mycorrhizal fungi and beneficial nitrogen-fixing bacteria.
How can you get these microorganisms? Where possible, let the leaves lie where they fall, to decompose and make natural compost. At least as far as your aesthetic sensibilities can stand it.
One trick: If you have ground cover, the leaves of autumn will disappear under the plants by spring and turn into compost that is a rich source of beneficial microorganisms. Compost is a rich source of beneficial microorganisms. They can also be purchased from your local nursery.
For more on tree care, consider:
Bonsai For Beginners
How To: Plant an Apple Tree
How To: Transplant Trees, Shrubs, and Perennials