Why do I have dead spots on this row of evergreen trees?

This looks like bagworm damage. University of Memphis Director of Landscape Joellen Dimond says you should be able to see the bags the worms make. You can pick the bags off in the summer or fall and throw them away. When the crawlers are active in the spring you can spray with Bacillus thuringiensis (Bt). This will kill the caterpillars before they spin the bag. Once they are inside the bag insecticides are ineffective.

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Related Resources:
Bagworms
Bagworms on Landscape Plants
Bagworm and its control