From PinataIsland.info, the Viva Piñata wiki
The food chain describes the feeding relationships between species. You have to carefully keep an eye on which predators have access to which prey in order to keep a robust garden. (While predators might not actively eat a prey, you may need to actively give up one of the prey, to be consumed for advancing a requirement.) Some pinatas may not eat each other, but they may not get along so well and fight often.
You may be able to stop a predator from eating its prey by dousing it with water, whacking it with a shovel, or keeping it behind a strong fence.
Basically, insects are eaten by birds and small mammals, which are themselves lower down the ladder than birds of prey and land predators.