I strongly believe that breathing rhythm is closely associated with stride rate, and this association is not exclusive to runners. In fact, in some sports the act of breathing is determined very clearly by the rate at which the legs and/or arms are moving. Take the example of swimmers; here breathing in all strokes (except back stroke) is strictly dictated by arm turnover – you breathe in rhythm with stroke rate or take in a lot of water. In rowing and paddling, breathing is pretty nearly limited to getting a breath between strokes.
The question is how many breaths do you take per stride, or how many strides do you take per breath? Again, in counting breathing rates of elite runners, I have found that over 80% use a “2-2” rhythm most of the time, especially when running at a fairly–demanding intensity. A 2-2 rhythm means you take 2 steps (1 with the right foot and 1 with the left foot) while breathing in and 2 steps while breathing out. Some will use a 3-3 rhythm when on an easy run, and often go to a 2-1 or 1-2 rhythm when starting to work really hard toward the latter stages of a race or during a hard training session.