In graduate school at SUNY-ESF, my advisor Dan Dindal taught Terrestrial Community Ecology (TCE), a course offered for undergraduate or graduate credit. I was a teaching assistant for the course for an enviable three semesters, and I say enviable as other graduate students felt lucky to have it as their T.A. for a single semester. Dr. Dindal has long since retired, yet two of his publications, Soil Biology Guide (editor) and Ecology of Compost are still in print due to their durable usefulness.
In TCE, students were supplied with a suite of tools for analyzing ecosystems. In the days before easy spreadsheets, possibly the most daunting exercise was a hand-calculated Bray-Curtis Ordination which compared communities by species abundance, and was distinguished by being a non-parametric analysis.
Among the abundance of other tools, we learned to compare communities by number of trophic levels, species diversity, population redundancy and rarity, and non-organism characteristics such as biotic and abiotic nutrient cycling, stability, ecosystem successional stages, and more.
One enduring lesson I take from that education is that an ecosystem has characteristics that are not completely dependent on current species composition.
When an ecosystem has been degraded by human activity it is not enough to cover it up with a thin layer of soil, plant grass and a few trees and call it "restored."
If an ecosystem is fully restored, it would have the same number of trophic levels as before disruption.
It would have the same diversity of species, genus, family and class, same efficiency of nutrient cycling, same ability to capture energy in biomass, and resiliency to natural disturbances.
Does it have to have identical rare species? Could be, if none other can be the keystone species for that environment. Consider that the salmon that are caught by bears become fertilizer for the forests of the Pacific Coast.
I am impatient with giving more examples, even though that is an efficient way to teach.
Let's just imagine that in a climate-changed world we'd have a better chance ourselves if the ecosystems we depend on have the resiliency that comes from diversity, even if the particular species composition of an ecosystem has changed and continues to shift.
Updated, April 22, 2013.