Thanks for the comments.
I didn't use the AI SERVO because I don't trust it very much. There are some
techniques though that I use and feel quite useful to shoot moving birds.
first is to use my body as AI Servo, which means that I predict the moving
direction and speed of the bird and move my camera accordingly after the focus
is done.second is to wait, which means I wait for the bird to fly into my
preset focus range. third, and the most important, is to treat the birds
really well, which mean