Experiments have shown that if a subject performs bicep curls under a training program for a few weeks on just one arm, then the strength of the other arm increases as well even with no physical stimulus on it.
I’d like to hear what you all would think would happen if, say, an athlete performed only bench press over a 1 month time period. Do you reckon this would induce an increase in a squat 1RM? and if so why?
I think that yes this would happen.
Some initial thoughts that come to mind are:
-Muscles related to the squat movement are actually being trained in the bench press (e.g. core muscles)
-A psychological effect: increased confidence in handling ‘heavier’ weights
-An increase in anabolic hormones circulating in the blood stream due to the bench press training.
But, what would be really exciting is if strength training in one part of the body, could in fact increase the innervation (or at least fibres recruited) in other distant muscle groups.
This is just to review ideas and connect current training theories. I’m not for one minute suggesting that just doing the bench press is the best way to get faster! 
EDIT: Obviously, if the subject was at a high training level and had already performed squats, then the 1RM would decrease due to a ceasation of the squat exercise.
Also, any effects would be greater on an untrained individual.