Welcome to OPF!
I shoot nature and wildlife, birds in particular, with a 1DMk2. These cameras are very customizable via Custom and Personal Functions. Here's a few things I use in my camera that I feel help me in this type of shooting:
CF4 - set to 3. I leave the camera in AI Servo all the time, and by starting/stopping AutoFocus with the * button, I have full control over AutoFocus. I also generally shoot in Manual Exposure mode whenever feasible, but if I have it in Av, this will also allow the exposure to continue to change as the position or scene of the subject changes.
Generally I have the center AF point manually selected, and have CF17 set to 1. This allows the camera to expand to the 7 adjacent AF points when needed. This works for me well in tracking birds in flight.
On occasion, I'll have the camera set to automatically select the AF Point (so-called "ring of fire"), again using the * button via CF4, and then have the "Assist" button (to the left of the * button) set to switch to the "Registered" AF point (which I set to the center AF point). This provides significant flexibility in the appropriate circumstances.
CF20 is set to 1, again useful for birds in flight. This makes tracking a little bit easier, and helps prevent "hunting" if it briefly loses focus on the bird.
That should get you started, if you weren't familiar with these. These functions are not always completely intuitive, and can require some thought and practice to understand what they do, and how you can use them to your benefit.
Hope this helps!