Squatting is generally termed the king of exercises. No exercise, in the history of the world is used as a mainstay in so many different sports. Squatting requires mental toughness and physical strength. No amount of leg curls will prepare someone for feeling a bar on their spine; their erectors won’t be ready.
Gorsuch, et al. 2012 compared Division I college cross country runners. 10 male and 10 female runners performed their 10 rep max for 6 reps in the parallel squat and the partial squat hooked up to an EMG machine. The EMG was hooked up to the rectus femoris (for quad recruitment), biceps femoris (for hamstring recruitment), erector spinae (for back recruitment) and the lateral head of the gastrocnemius (for calf recruitment).
Interestingly, male and female runners displayed a different quad to ham ratio. As discussed previously, high school girls are far more likely to injure their ACLs in the same sports than boys because of their q-angles and the best way to prevent this is to strengthen the hamstring until the quad to ham ratio is 4:3.
Rectus femoris and erector spinae displayed much higher activation in the parallel squat compared to the partial squat while the gastrocnemius and hamstring were stimulated to similar levels. So if you are running uphill or require spinal stabilization during your running, parallel squatting should be used in your training, nor partials.
Brayton, et al. 2012 had 11 strength trained men perform squats at 50-90% of their max load at partial, parallel and full depth. The exercises were performed in a motion analysis laboratory to determine relative muscular effort. It was found that hip flexor activation increased both with load and depth. Knee extensor activation increased with depth but not load and that ankle plantar flexion increased with load but not depth.
Clearly, depth and load have a role to play in squatting and their carry over to sport. Depending on the goals of your current program, adjust appropriately. We would strongly caution though, partial squats lead to partial results- the deeper you go, the more you grow.