|Photo by Ned Harris 9/11/2015
There are two varieties of Chainfruit (aka Jumping) Cholla in the canyon (Cylindropuntia flugida var. fulgida and var. mammillata), but both generally reproduce vegetatively, i.e., a piece falls off and a new plant grows. The new plant has the same DNA, of course; therefore most Chainfruit Chollas in the same area are clones.
You'll note that the flowers are blooming right out of last season's fruits. That's typical for this cactus. The fruits generally contain sterile seeds, but it's likely that this plant has retained the ability to reproduce via seed - just look at those flowers!!