Punctuated equilibrium is a theory describing an evolutionary change that occurs rapidly and in brief geological events in between the long periods of stasis (or equilibrium). The theory is based on the stasis in fossil records, and when phenotypic evolution occurs, it is localized in rare, rapid events of branching speciation. Accordingly, the theory assumes that when there is a significant evolutionary change, cladogenesis occurs. Cladogenesis is the process where a species splits into two distinct spcies instead of one species transforming into another over time.1 The American paleontologists Niles Eldredge and Stephen Jay Gould first proposed the theory in 1972. They referred to it as punctuated equilibria.2 This theory is presented to contrast phyletic gradualism. In the latter, evolution is described to happen smoothly and continuously (anagenesis).
1 Gould, S. J., & Eldredge, N. (1977). "Punctuated equilibria: the tempo and mode of evolution reconsidered." Paleobiology 3 (2): 115-151.
2 Eldredge, N. & Gould, S. J. (1972). "Punctuated equilibria: an alternative to phyletic gradualism" In T.J.M. Schopf, ed., Models in Paleobiology. San Francisco: Freeman Cooper. pp. 82-115. Reprinted in N. Eldredge Time frames. Princeton: Princeton Univ. Press, 1985, pp. 193-223.