Maintaining a healthy population of trees in a suburban setting shares much in common with maintaining a "woodlot" or resource forest, but there are of course a number of differences as well. The best "wooded gardens" actually have relatively few large trees, since these areas are also expected to support small trees, shrubs, garden plants, and lawns. Managing these small woodlots takes planning and a realistic sense of what woodlands look like.
Natural woodlands are bound by the laws of ecological succession, where a disturbed area (in nature disturbed by fire or storm) will first be colonized by herbaceous plants and other "pioneer species" such as fast-growing trees and shrubs adapted to sunny environments. In many regions, the mature forest will be primarily one or a few species of climax trees, and a very sparse understory of ferns, mosses, ephemeral plants, and slow-growing shrubs: an ecosystem which is too sparse and delicate for regular use as an entertainment space for humans and their pets.
Ecologically speaking, the goal in having a woodland garden is to "freeze" the ecological succession at the stage where there is a fairly extensive canopy (between 50% and 30% enclosed), which limits the amount of shade and water competition form the trees to allow us to have ornamental plants and lawns beneath. Maintaining that balance is a never-ending task, because the trees will continue to grow unless constantly suppressed. The main question is whether to prune or to cull the trees.
Culling (or "thinning")
In situations where the woodland garden was not planned in advance, there will often be decisions to be made about what trees to keep and what trees to remove. As a rule, it's best to remove trees as soon as they begin to pose a problem, because the trees will only get larger, more problematic, and more difficult to remove as they continue to grow or perhaps die (live trees are much easier to remove than dead trees).
1. Hazardous trees: Trees that pose an obvious hazard should be the first to go. Rotten trees and hollow trees are the most obvious, but a number of other factors can be just as important, such as trees from weak-wooded species, trees growing through utility lines, or even trees with dangerous fruits (such as walnuts, osage orange, or horse chestnuts and buckeyes if they are growing in an area where people, cars, or outdoor furniture is below).
2. Diseased trees: Trees with serious diseases (such as Phytophthora, Verticillium, or other fatal diseases should in most cases be removed, unless there are no other trees around that could catch the disease and the garden owner would like to maintain a snag for woodpeckers and cavity-nesting birds.
3. Invasive trees: Trees that are invasive in a particular region should in most cases be culled to protect the health of other trees and prevent seed production, although in some areas close to urban centers invasive species may represent almost all the trees present, and it may be better to keep some of them.
4. Trees with bad growth habits: When trees are not carefully managed "from the start", they can often have growth habits that are aesthetically undesirable or in many cases will eventually become hazardous. Trees that have grown up underneath larger neighbors will often lean perilously, for example, and other trees may have dangerously narrow crotches. Removing these trees reduces the competition for the trees that will be kept, and helps prevent hazards later on.
5. Overcrowded trees: The last step is to see if the healthy trees are competing with one another, and make a decision as to whether to allow them to compete, or pick the best specimens and cull the second best.
Pruning ("lightening the canopy")
After any culling has been done, or if there are no trees needing culling, the next step is to prune the remaining trees to allow light to reach the ground and reduce the water consumption of the larger trees. Limbing up is often the best option, but other methods of structural or reductive pruning can be used if low branches are desirable.
If the trees are growing in a lawn, it is generally a good idea to create tree rings around the base of the trunks to prevent damage from mowing equipment. Small rings can simply be maintained as mulched soil, or larger rings can be created and plenatd with ground covers, shrubs, or herbaceous plants adapted to competition with tree roots.