How might the loss of a forest affect a food chain?

Simple, forest disappears, predators like tigers disappear due to no hunting grounds. Herbivores run out of food to eat, they die off, predators die off because there is no herbivores to hunt, we run out of food because there is neither herbivores or carnivores to eat. Nature and the food chain are two very delicate things. It doesn't take much to mess them up. Every opportunity you have to save the forest do it.