Breathing in the desert

Factual Questions
1

My question is pretty straightforward:

Plants give off oxygen. Therefore, it would stand to reason that there would be less oxygen in a place with less vegetation (Saudi Arabia and whereabouts).

Is this the case? I understand there are wind currents, and air is more dense near the surface of the Earth, blah, blah, blah, but is there a MEASURABLE difference is the oxygen ratio in the desert?

2

Yes, there are less plants, but at the same time there are less animals USING the oxygen, so it would kind of balance out.

More to the point, most oxygen is supplied by ocean-dwelling algae, then distributed by air currents, etc. I suppose there might be an extremely small variation between desert and forest, but not enough to worry about.