We're always starving for light when shooting birds, especially action shots - but consider the potential for interaction before you drive down to a wide open aperture. As I started shooting more than a single eagle, I increased my aperture to ensure I had enough depth of field to capture the two birds. Not wanting to lower my shutter speed for an action shot, I increased my ISO to compensate (Don't be afraid to shoot at higher ISO's - it's a better alternative that an underexposed or blurry shot).
Learn to always have a feel for what your depth of field should be - pay attention to your subjects and adjust accordingly. It takes some time to build this thought process into "muscle memory" - but it's worth it. Try this online Depth of Field Calculator to help gain a better understanding of the impacts of distance, lens size and aperture. There are also some good iPhone and Android apps that allow you to take your calculations out into the field with you.
Stay in focus,
Mark