If the school you are applying to doesn't have rolling admissions, all of the applications gets reviewed pretty much after the deadline. As far as slots available in R1 and R2, they are very similar, so you'll have roughly equal chance of acceptance. The typical advice is to submit the applications when you think it's the best application you can present in the given time.
The advantage to applying in R1 is that you'll get feedback on your application process. So for example, you don't get interview invites, it may be a good time to either work harder on the remaining apps or apply for lower ranked schools. Alternatively, if you get invites to all of your R1 schools, you may want to consider applying to some reach schools.
Thank you for your response. If a school does have rolling admissions, what impact do the rounds have? For instance, I am interested in applying to Columbia. I see that they have rolling admissions, but they also have rounds. What's the ideal method of attack in this case?