For the first 150 million years of their evolution insects grew larger when the concentration of oxygen in the atmosphere increased. Insect respiratory systems limited their ability to sustain large bodies, so the world was never really in danger of domination by massive mantises. Still, some insects did grow wingspans as large as 70 cm (2.3 feet).
In the early Cretaceous, approximately 145 million years ago, oxygen content of the atmosphere increased, but bugs didn't get big. University of California – Santa Cruz paleobiologists found that as birds evolved and spread, insects stopped growing in response to oxygen concentration.
Big bugs may have been too slow to evade their nimble new predators.
After an asteroid did in the dinosaurs, birds continued their battle against the bugs, and were joined by a new ally, the bat, in the Eocene epoch, approximately 56 million years ago. Bats evolved to become insect-eaters par execellence, and may have caused the further reduction in insect size seen during our own Cenozoic era.
The big bugs vs. birds and bats research was published in the Proceedings of the National Academy of Science.
A blackbird eats a moth (Mick Lobb, Wikimedia Commons)