A bicycle comprises a bicycle frame and a rear wheel suspension system that is attached to the frame. The rear wheel suspension system comprises a rear wheel swingarm and a shock absorber that is coupled to the swingarm. A change in vertical wheel travel (ΔVWT) of the rear wheel is related to a change in the length of the shock absorber (ΔSL), providing a shock rate (SR). The shock rate (SR) changes throughout the vertical wheel travel of the rear wheel, such that the change in the shock rate dSR/dVWT has a change in sign as the rear wheel travels through its vertical wheel travel. In each case, the rate of change of the shock includes a change in sign, from positive to negative or from negative to positive. In some embodiments, the swingarm may be attached to the frame at a single pivot point or through a linkage system.