Answer:
The answer is: Scientists can tell that punctuated equilibrium occurred if they examine the fossil record and see that one organism rapidly evolved different characteristics.
Explanation:
The theory regarding "punctuated equilibrium" followed after Darwin's Theory of Evolution. According to Darwin, species evolved over time. However, evidence supporting it is lacking when it comes to fossil record. He thought that this was because the fossils were incomplete.
Darwin's idea was contradicted by evolutionary scientists, named Stephen Gould and Niles Eldrege. According to them, species change after millions of years (this phase is called "punctuated") and their change is sudden (and not gradual). This sudden change is very rapid, thus causing a fewer number of fossils being left behind. Most species who undergo speciation, occur in a different geographic location, thus leaving only a few number of fossils.
So, this explains the answer.