The equation for Power is P = (F x d)/t, where F is force applied to the system, d is the distance over which the force is applied, and t is the time over which the force is applied. So in this case, F is strength, d is determined by the test, and t is your explosive ability -- the ability to display strength quickly. The "genetic limit for power" you refer to is determined by the ability to recruit muscle mass into contraction, and is indeed a pretty hard limit that is minimally trainable. Force production is quite trainable for many years. We can take a talented kid with a 36" SVJ who squats 275 and train him up to a 500 without having to resort to exotic means. But if we do this, what happens to his SVJ?
Not much, really. The SVJ is a test of the ability to recruit motor units into contraction rapidly, and that's all it shows us. The SVJ is a measure of your ability to generate enough force within the time it takes to perform the concentric phase of a jump, to accelerate your body's mass upward to impart sufficient velocity and therefore sufficient momentum to it, that it continues upward after the force production between your feet and the ground has stopped. The distance upward is a direct measurement of the force produced in the .25 seconds the contraction takes place, and this is more dependent on how quickly motor units are recruited than the force of the recruitment, since your body's mass is not very heavy. The bottleneck is the ability to "fire" as much of the contractile machinery in the .25 seconds, and for various reasons this is 1.) controlled by genetic endowment and is 2.) not very trainable.
It is interesting that a kid with a 36" SVJ is always stronger untrained than a kid with an 18" SVJ untrained, since the big SVJ is recruiting more muscle mass into contraction than the little SVJ. But the 36" kid is just as trainable for F as the 18" kid, and not getting him stronger is a huge mistake.
When we take the kid from 275 to 500, the algebra shows us that his P goes up, even though this does not affect his SVJ proportionally -- doubling his squat does not double his SVJ, no way, not even close. This is due to the fact that the SVJ does not depend on max force production, because you're only jumping against your bodyweight. A true 1RM force production event only occurs under a 1RM load, which is not an instantaneous power display but rather a summation event. And this time constraint is why the clean is much more influenced by an increase in strength, because it takes maybe 5-6 times as long as the SVJ and there is more time to summarize motor unit recruitment.
But power still increases because F goes up. The kid can hit you harder with a 500 than a 275, since he's not just exploding -- he's applying force after his acceleration. The tragedy here is that F is trainable and t is really not. You can radically increase the 18" kid's power even if you can't make him more explosive. Modern S&C has wasted lots of everybody's time, money, and potential with RFD "training" when College Algebra could have saved them some time.
Note: No posts from morons on the internet who say they can double your "vertical jump" or turn lead into gold will be approved.