zoom lens

[reaction]

variable aperture zoom lenses.

eg 70-300 f4.5-5.6

when taking the same subject, framed to be the same size, will the DOF be the same at both ends wide open?

I ask because I assume the variable aperture is actually a fixed physical size, and it is due to the extension of the lens that the effective aperture is smaller due to that movement. Since the effective aperture is relative to the zooming, then would the DOF also be changing at the same rate?