How does breaking links in an ecosystem affect the amazon rainforest, it's plants, animals and people?

By breaking the chain you most likely made something go extinct so then other creature go extict because they don't have what they need to survive, which causes more creatures to go extinct until there is nothing.

This is actually called Biodiversity ...

is the variability among living organisms from all sources, including terrestrial, marine, and other aquatic ecosystems and the ecological complexes of which they are part; this includes diversity within species, between species, and of ecosystems.

Biodiversity forms the foundation of the vast array of ecosystem services that critically contribute to human well-being. Biodiversity is important in human-managed as well as natural ecosystems. Decisions humans make that influence biodiversity affect the well-being of themselves and others.