Which would most likely cause a decrease in numbers of woodpeckers in ecosystem

The answer is: A decrease in the number of Trees

Woodpeckers are known for their use of finding food sources on the trucks of trees. They are also popularly own for beating their beaks against a tree trunk in order to provide vibrations and communicate with other woodpeckers.
Contrary to popular belief, they do not eat wood, but trees as a whole form an important part of their habitat.

Hence, the deforestation, cutting down of trees and urbanization can all lead to the decreasing number of woodpeckers in the ecosystem. 

Since the early 20th Century two species of American woodpeckers are already considered extinct.