I will guarantee you one thing, that if humans didn't use technology and ultimately leave this planet and solar system most life has a lifespan that would last until a big asteroid hits the earth. The rest might last until the sun burns out.

If you want to use Darwin, why don't you think about the myriads of ways diaspora occurs among life. Many plants grow under favorable conditions, but when drought or bad conditions hit quickly propagate seeds on the wind before they die. Human life would be successful in my opinion if we used every last resource on earth (not even remotely likely) and all life on earth died in order for us to propagate to a dozen new worlds in the universe. And yes, we will/would take a healthy chunk of biosphere with us. Just in our bodies are tons of organisms on which we directly depend.

I'll admit I'm an optimist when it comes to mans use of technology. I don't really believe in limited resources for a few reasons. First, we have barely scratched the surface (literally) here on earth for resources. Second, as technology improves, and we move to nano levels of engineering, our ability to use diverse resources efficiently improves immensely. Third, there are obviously unlimited resources off planet that are just waiting for us to exploit them. Within 50 years we oculd easily start a process, that would eventually make earth as backwater as a few 1000 square miles in Africa where man started. All it would take is a space elevator, and a dash of Von Neumon self replicating machines. They would use resources off of asteroids/moons and build a Dyson swarm around the sun for us to inhabit in the (potentially) trillions. Finally, we are now in a mode of self evolving. We can now alter our own DNA. We are also creating alternative life forms (silicon based) that we are evolving. Just like colonies of ants are really a single organism and ultimately all life is a single organism (I sort of agree with an aspect of gaia here), so man is a superorganism. The whole of man is evolving as well, as more rapid communication, specialization, shared knowledge and access to same keep accelerating.

Just like we keep innovating to keep Moore's law going, man will face new problems with awesome intellectual capacity. Yes, billions of people use up unprecedented resources. But billions of minds, all connected with an internet of shared knowledge provides an awesome intellectual capacity that dwarfs any previous generation by many orders of magnitude.

Right now, so many of the kneejerk reactions of people worried about global warming are doing more harm than good. A nice example of this is the subsidizing of palm oil, "a wonder biofuel" (recent article) or even the actual costs of ethanol production from corn. This is worth another post, but subsidies are the worst thing the world economy perpetrates on markets and cause untold harm through making economies less efficient and thus less capable to solve world problems. And I mean all subsidies in total, cause we subsidize EVERYTHING.

But through everything, I remain optimistic that overall we will solve problems as they arise and things will continue to get better for most people. And I also believe ultimately that we will expand out into the universe and Earth will become an archival memory for our evolutionary successors.