The best way to prevent weed and grass growth within the circle is to apply black landscape weed-barrier fabric. Landscape fabric is woven so it contains holes for air and water to pass through. The fabric is not only a physical barrier, but prevents light from reaching the soil beneath. Plants cannot grow without light. Landscape fabric is usually covered with bark dust or other mulch to improve appearance. After a year or two weed seeds will blow into the mulch, but they are easily controlled. Do not use ordinary black plastic as a weed barrier. It does not have holes so air and water can reach the roots.
Even without landscape fabric, a 2-inch bark dust mulch will prevent 90 percent of weed sprouting.
Weeds can also be controlled by spraying weed killers such as Roundup (glyphosate). Granular weed preventers such as Casoron or trifluralin (Preen) can also be used. Corn gluten, an organic weed preventer, is usually available only from full-service nurseries and garden stores.
Flowers planted around trees will also be competitive for water and nutrients, but not to the same extent as grass and weeds. I like to keep flower plantings at least 2 feet away from tree trunks.
Allen Wilson is a Vancouver gardening specialist. email@example.com