The Punctuated Equilibrium Hypotheses states that there are periods of time with fast rates of evolution change followed by periods of time where there is very little and slow evolution change. It is found that this typically happens where there is a newly experienced dramatic environment change such as a food source is no longer available for a species or a vast climate change occurs.
Examples:
Evolutionists do not really know how tigers got their stripes, and because of this there are two theories, one of which supports the Punctuated Equilibrium Hypothesis:
Tigers started off as solid colors with no markings or other colors in their fur. A mutation happened in some tigers that made them have stripes. These tigers were better equipped for their environment because they were able to blend in with their surroundings more, so they were able to survive better, and therefore, reproduce. These tigers produce offspring with the same mutation of stripes, and these offspring are also are able to survive and reproduce better, so in just a few generations, the tiger population became over come with the mutation of stripes because of the sudden helpful mutation.
This supports punctuated equilibrium hypothesis because the change in the tigers appearance happened very quickly over a short period of time.
Crocodiles have seemed not to change is almost two hundred million years. The rate of their evolution is actually fairly quick and in bursts due to sudden environmental changes. A study done on body size of the crocodiles and climate of their environment concluded that larger crocodiles and warmer climates spark a faster evolutionary change in crocodiles.
This supports punctuated equilibrium because crocodiles do not undergo constant change and it is only in periods of time because of a driving factor.