Here are the buttons mapped that will be used the most.

Sprint: Left Trigger
Bite/Eat/Hold/Mouth: Right trigger
Interact (currently sniffing only): Y
Attack: B (default) (used for flapping on a pounced target)
Sit/Sleep: D-pad up.
Jump: A (default)
Zoom in: Left Shoulder
Zoom out: Right Shoulder
Hide HUD Elements: Back button.

Here is the full list of all controls explained from the Saurian Controls menu, mapped to optimised configuration.
Horizontal input: Left stick X (default)
Vertical input: Left stick Y (default)
Jump: A (default)
Sprint: Left trigger +
Walk/Run Toggle: Left Stick Button
Interact (is now sniffing action): Y
Attack: B (default)
Lock Camera Look: Right Stick Button (default)
Sniff Action: Dpad down (does not do anything right now)
Bite/Eat/Hold/Mouth: Right trigger +
Pause the game: Start (default)
Restart the game: (nothing) (default)
Call menu: Dpad Right (does not do anthing right now)
Sit-Sleep: Dpad Up
For Camera Control: Right stick X (default)
Action0 (vertical axes camera) Right Stick Y (default)
Camera Zoom in: Left Shoulder
Camera Zoom out: Right Shoulder
Hide HUD elements: Back button

Some notable buttons mapped changed explained below:

You swiched zoom in and out, why?
This allows you to zoom in while holding your prey, for a close up screenshot.

Why is jump not on left trigger, that way pouncing prey is easier. right?
In my opinion, no. Running and attacking are the most essential controls used by your raptor. Jumping can be followed with an attack, but oftentimes there is always a need for speed during attacks.

Why is zooming mapped to the shoulders? it is not that important!
It is, currently the camera resets on many things especially certian slopes. Because the camera does not return the the position it was last calibrated, I found myself often zooming out, after the camera was forced to zoom in.