To a radar, birds are just large balls of water with feathers. It doesn't take many birds to produce a good signal for the radar. Insects also contain water, and since they are much smaller it takes a lot more insects to produce a signal.
Some radar sites are near concentrated nesting areas for birds. Shortly after dawn, a strong echo appears over the nesting area. This echo expands outward into a ring, as the birds fly out towards their feeding areas. At night the process is reversed as the birds fly back home.
The New Braunfels radar observes a somewhat different pattern. There, the expanding ring forms shortly after sunset, and the screen is clear by dawn. The culprit? Bats.
During the migratory seasons, the birds can essentially fill the radar volume at low levels. There may be a preferred altitude, or the birds' density may just decrease steadily upward. The reflectivity pattern will take the form of a fuzzy disk or ring, centered on the radar.
Although not all birds are going to the same place, they tend to average out to a fairly constant velocity. This velocity is, unfortunately, not zero, so if you're trying to figure out the velocity of the air (that is, the wind), you're out of luck. Insects can't fly as fast through the air. On average, their velocity tends to work out pretty close to zero, so they don't really affect the wind estimates.