How does a rich biodiversity enhance the ability of an ecosystem to sustain itself?

Answer 1

Checks and buffers.
Checks: A rich diversity stops any one species from growing too large. Without checks, either through competion, predators or resilant prey, the population of any one species can explode. The exploding population then destroys the surrounding ecosystem.
Buffers: Whether drought, flooding, fire, etc, there are some species better to handle the environement at any given time. Without this diversity, a signle disaster will cause much more damage to the environment.

Answer 2

Numerous ways.
The most obvious is the relationship between plants and animals - we consume oxygen and exhale carbon dioxide - the plants consume the carbon dioxide and give off oxygen. What a great and necessary piece of team work!

Other examples include the medicinal benefits we are still discovering in the rain forests and oceans from the extracts of some of the more obscure plant varieties, the birds and other creatures who defecate seeds and spread foliage which prevents erosion and runoff of the top soil, the lowly earth worms who borrow paths through the earth which allows more water to penetrate the ground before it has a chance to evaporate and feed the roots of plants, seagulls and crows and other scavengers that consume carcasses and prevent them from rotting and spreading diseases, and, I'm sure, you can think of almost endless other examples.

Answer 3

A large ecosystem has many niches to be filled, and having many species specialized to each job and each being a part of a food chain and biological pathway makes the ecosystem function.