In Claude Bouchard's Heritage Family Study Series, they did a study of 86 nuclear families, recruited and tested over 700 family members and, among other things, but them all on an interval training program in a laboratory for 20 weeks and retested them. They found that while the mean gain in VO2max was 19%, 5% gained nothing at all, and 5% gained 40-50%. Overall, they found that genetic differences explained ~40% of the variation in individual performance.
They found the maximum inherited ability to be 47%. The also found that there was no relationship between baseline VO2max, and the gain due to training:
"Hence, part of the genetic component for VO2max expresses itself only in response to an active lifestyle.
http://www.pbrc.edu/heritage/
To both Alexi Pappas and people like Malmo (who want to believe that VO2max is meaningless): You're totally full of shit. The scientific evidence here is quite clear.