No, organisms are never completely independant. The survival of each organisms depends/is affacted by the other organisms living around it. Therefore, we choose to say that organisms are interdependant.
This is so as a change in one population affects other populations of the community. i.e.: If the population of the small crabs living in the mud decreases, it would cause the population of the mudskippers that feed on it to decrease as well. Otherwise, the mudskipper would look for an alternative food souce; i.e.: other insects living in the same habitat, thus, causing the population of that particular alternative food source to decrease as well.
Therefore, the relative sizes of the different populations remain constant. This biological balance/equilibrium is like a web- breaking a single strand will affect the whole system.