A bit lazy linkage here. I went to a talk a while ago by Graeme Ackland from Edinburgh about Daisy World. It's not new, I think it's been around since the 80s, but it is quite cool. It's a really simple model of a planet where the climate conditions (here just the temperature) and the living organisms on the planet feed back to one another.
On Daisy World there are only daisies, there are a million extensions where they have forests and animals and all sorts. I think the simplest model gives the nicest story. This page gives a nice explanation and it has a java applet that you can play with - this is the best bit.
http://www.ph.ed.ac.uk/nania/nania-projects-Daisy.html
My extremely brief explanation is that there are white daisies and black daisies. White daisies cool down their environment, black daisies heat it up. If they get too hot or cold they die. Then there's a bunch of other parameters: how fast does temperature defuse, rate of daisy mutation, rates for birth and death etc. It's about as simple as it can be, and crucially is simple enough for mathematicians to come up with solutions.
The nice thing is that for reasonable parameters the system pretty much always self regulates. When things are slow to react, mutation rates are low, you get these big mass extinctions followed by regrowth. Really the best way to get a feel for it is to play with the simulations, it's very fun.
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