I have noticed that I need so much fresh air while sleeping that it is not very comfortable for me to sleep with another person. I can not say anything about breath patterns but I suspect that O2 consumption has to be among those patterns.
Your body needs less O2 when sleeping and your respiratory rate slows as a result of that and many factors.
I highly doubt someone sleeping next to you is materially taking away from the O2 you're breathing in. If so, you'd be fairly out of breath in a room full of people during the day.
Unless the room you're sleeping in already has such low level of O2, you might need to look into a monitor or even using a fan to move some air.
