I read recently that if you studied botany, zoology or any such sciences twenty years ago, biodiversity would not have been a word used on the syllabus. The fact that this is now a by-word in society does not reflect badly upon scientists twenty years ago, after all, all science is a learning curve, it is to their credit and indicative of the robust methodology of science as well, that the word is accepted and studied today.
But knowing how connected everything is, is only the beginning of understanding connections. We can see and easily reason how things on this planet having evolved from a series of common roots, could be connected and how life on Earth is driven by the same scientific method -DNA (and RNA). It is not yet easily understandable how this planet is integral to the universe. We can see how it affects the solar system, through gravity, and how its pull affects the sun to a small degree and other planets in the solar system, but how the solar system interacts with other systems far away is not yet readily known but for the tantalizing fact that physics suggests particles are linked across the Universe.
But we all have come from a common root, the universe is made the same throughout, what works here will work on other planets and I am sure the biodiversity of the universe is as important to its health and well being, as our newer science is to us.