Structures that have reduced in size because they no longer serve an important function are called

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These structures are called Vestigial Structures.

The Vestigial Structures are those whose original function was lost during evolution. In humans, these structures are the appendix, the coccyx, the wisdom teeth and others. 

In animals, examples of vestigial structures are the wings of flightless birds, hind leg bones on whales and pythons and eyes in blind fishes. Those vestigial structures help scientists study the evolution of some species. 

Dthrough a slow process