Organisms interact in many different ways, but all in all the stability of any ecosystem relies on these interactions, the specific effect on other organisms depends on the interaction.
Organisms live off of eachother... and the depletion or abondance of any one specific organism will always play some role in another that depends on it for either food or population controle. EX: The snakes that are being wrongfully released into florida have no natural enemies and therefore are reproducing at a rapid rate and are putting a small field mouse native to florida in danger of extintion... and of course there are other organism that depend on the field mouse and so on and so on, causing 'instability'.
I'm not sure if that's the kind of answer you were looking for but I hope it helps. :) By anjani!