Haven’t seen any studies on this, and I do know that the primary trigger to breath for most people is CO2 buildup. I am not sure if this is done on a differential basis or an absolute basis.
If it is absolute, then there should be a statistically measurable increase in the breathing rate of most people.
It may be possible that people compensate by adjusting the depth of breath, as in most people it is quite shallow most of the time.
Would be an interesting project for someone to do a Masters on, if it isn’t already well characterised.