Native plants are critical to sustaining the wildlife we love because wildlife has adapted to them over time. If we remove the natives, we remove the wildlife. Take birds for example. Insects are a critical food source many insects of them eat plants. Native plants support astonishingly more insects than non-natives. A few power-house plants are shown below with the number of butterflies and moths supported…not including any other insect type of which there are thousands (no exaggeration).
So what’s going on here? Turns out that because native insects did not evolve with nonnative plants, most of them lack the ability to overcome the plants’ chemical defenses so cannot eat them. 
Back to making more birds and why all this matters. Insects aren’t just important for birds but 96% of our birds feed their young exclusively insects. And it takes a mind-boggling number to get those babies to fledgling stage. For example, scientists have observed that it take 6,000 – 9,000 insects to feed ONE brood of Chickadees.
As gardeners, many of us learned that bugs are bad (except beautiful butterflies and bees), but it turns out that the best food source for baby birds are caterpillars, making up the majority of baby birds diets. What a happy thing that all we have to include some native plants in our yards and we get to not only enjoy them, but all the birds we’re “making”!
Doug Tallamy in his book and on his website Bringing Nature Home says it this way:
“What will it take to give our local animals what they need to survive and reproduce on our properties? NATIVE PLANTS, and lots of them. This is a scientific fact deduced from thousands of studies about how energy moves through food webs. Here is the general reasoning. All animals get their energy directly from plants, or by eating something that has already eaten a plant. The group of animals most responsible for passing energy from plants to the animals that can’t eat plants is insects. This is what makes insects such vital components of healthy ecosystems.” 
In other words, if a particular native plant is removed from your yard, the insects that feed on that plant may also disappear from your yard. In turn, the birds that depend on the insects will no longer appear.
Tallamy encourages us to think of urban areas, like Peachtree Park, as a critical link in providing the plants that wildlife need most. 
On this site, lists of plants and trees will identify which are natives. There are native plant alternatives to non-natives. Consider planting a native instead.
References and Additional Information
 Doug Tallamy: Bringing Nature Home – Gardening For Life
 Cornell Lab of Ornithology – Nest Watch
 National Wildlife Federation Blog: Chickadees Show Why Birds Need Native Trees
 The Intown Hawk: Natives as Alternatives
 The Intown Hawk: Trees for Your Yard
 The Intown Hawk: Perennials for Your Yard
 The Intown Hawk: Plant Terminology