Final answer:
Productivity, in terms of the punctuated equilibrium model of evolution, peaks during periods of rapid environmental change, when swift adaptations can lead to the emergence of new species.
Step-by-step explanation:
According to the punctuated equilibrium model, productivity, or evolutionary change, is highest during the time of rapid environmental change. This model suggests that species evolution is characterized by long periods of little or no change (stasis), punctuated by sudden bursts of rapid change often due to significant environmental disturbances, such as a change in climate or the breakup of a supercontinent. These bursts can result in the rapid formation of new species, in contrast with gradualism, which posits a slow, steady rate of change over time.
Punctuated equilibrium is most likely to occur in small populations that experience rapid environmental changes. An example would be an island population cut off from the mainland that faces new predators, diseases, or changes in available resources, forcing rapid adaptation or speciation.