There are a few studies done on this and fortunately I was able to dig out a couple :). Feel free to read through the abstracts below but I'll summarize the info. here.
The 1st one shows muscle contribution broken down by the following muscle groups and their % of contribution:
23% ankle extensors
28% hip extensors
49% knee extensors
The 2nd one looks at 2 different types of jumps, the vertical jump and the broad jump. They found the following differences.
45.9% hip extensors
3.9% knee extensors
50.2% ankle extensors
40 % hip extensors
24.2% knee extensors
35.8% ankle extensors
Obviously there are differences between the 2 studies but the information does seem to verify that the more forward lean and the more the hips are pushed back (broad jump vs vertical jump), the more the posterior chain and less the quadriceps are involved.
A work-energy approach to determine individual joint contributions to vertical jump performance.
Hubley CL, Wells RP.
A work-energy approach was used to determine the contributions of the muscles crossing the hip, knee and ankle joints to the total positive work done during maximal vertical jumps. It was found that the average relative contributions of the ankle and hip muscles were approximately 23 and 28% respectively, with the remaining 49% of the work being done by the muscles acting at the knee joint. The efficiency of jumping, i.e. the ratio of potential energy gained to the net mechanical work done by the muscles acting at the three lower limb joints was nearly 1.0. These results stress the importance of all three major leg extensor muscle groups to the performance of an explosive activity such as vertical jumping. It is suggested that the work-energy approach supplies useful information concerning joint contributions without the problems associated with other techniques.
Kinetics of standing broad and vertical jumping.
Robertson DG, Fleming D.
The purpose of this study was to determine the contributions made by the leg muscle groups to the external mechanical work done in standing broad and vertical jumping. Six subjects were filmed jumping from a force platform. Linked-segment analysis and inverse dynamics methods were used to compute the muscle moments of force and power and work output created by these moments of force. Results support the principle that all three extensor moments of force summate in both types of jumping but that the sequence of contractions was not from proximal muscles to distal as is stated by the continuity principle. Instead all three extensor moments act simultaneously to produce leg extension. The contributions made by the three muscle groups were not the same for the two types of jumps. For the propulsive phase of the standing broad jump the contributions of the hip, knee, and ankle muscles were 45.9%, 3.9%, and 50.2%, respectively, whereas, for the vertical jump the contributions were 40.0%, 24.2%, and 35.8%, respectively. These results indicate that broad jumping utilizes the muscle groups differently than vertical jumping and show the importance of the hip and ankle musculature in the production of external work in jumping.