??? D80, 70-300VR, Program mode, small DOF

[Singletracklovr]

Hello,
This camera body and lens are new to me.

I typicaly use P mode when out scouting for wildlife shots.
and switch to A or S modes if I have time to setup the shot.
I prefer these modes over Auto or presets since they offer more custom setting for higher ISO, etc.

In the P (program mode) I was wondering if anyone can tell me why my camera prefers to use f5.6(shallowest DOF) for most zoomed shoots (300mm) and as brightness increases the camera chooses high and higher shutter speeds over reducing the f-stops?

The f-stop will not start decreasing until I exceed 1/2000.

The shooting conditions are outdoors, 11-2am, bright bluebird day. Other camera setting are ISO400, RAWonly, WB 5600.

Do I have something set wrong or not set at all?
In the P mode. Can I set the camera to start stoping down if the SP exceeds 1/500?

Sorry for the long winded question. I know a lot of info is required to answer this question hopefully my ramblings covered them.

-Bob