If we look at the species on Earth, to me it would appear that the grasses were soundly kicking everything else's butt until humans came along. Sure, the trees were winning in some areas, but the grasses managed to ruthlessly choke them out in so many places.
Why do you assume a symbiosis among things just because they can't talk? If an organism is able to reproduce itself faster than it dies, the population grows. Mice or rabbits don't suddenly stop breeding because there are enough and they realize that further reproduction will harm their habitat. Instead they reproduce until they either eat everything or the predator population catches up a bit, or a disease runs rampant through them and kill them.
Look at all the little tropical islands swarming with cockroaches and rats for a good example, or the population of house sparrows and starlings in the US, or the population of gray squirrels in the UK, not to mention zebra mussels, grass carp, kudzu, and purple loosestrife. Sure, these were introduced by people, but there is no reason to suppose that the introduction of invasive species doesn't happen naturally from time to time.