This is the result of the twig girdler which is the long-horned wood borer. The adult female lays her eggs on the end of the branch and then where the branch is about the size of a pencil she chews around the branch leaving a notch all the way around. When a wind blows the branch breaks off and falls to the ground. The eggs hatch and the larvae feed on the branches. Insecticide is not recommended to control this. Instead pick up and dispose of the branches that fall. This will reduce the population, but these insects are strong fliers so there will still be some that come in from surrounding areas next year.