The competitive exclusions principle says that two species cannot exist together if they compete for the same resources. One will either die out or migrate, or they will adapt to carve out separate resource niches. An example is different species of birds foraging for insects in the same tree, with each species focusing on a different part of the tree.
There are other examples of the competitive exclusion principle. This includes two species of finch found on the Galapagos Islands. It has been found the different species of finch on the islands have different size beaks. This means that they each eat different sizes of seeds so they are not competing for the same resource.
Another example comes from two birds found in American forests: the nuthatch and the brown creeper. They both seek food from the same trees, but the brown creeper travels up the trunk, while the nuthatch goes down. This means that they find and eat different insects.
Finally, there is the example of two barnacle species. The Balanus grows fast so it can smother and crush its rival, the Chthamalus. The Chthamalus survives by staying close to the shore. It is too dry there for the Balanus. Therefore, both species have a niche - the Chthamalus close to the shore where it can get dry, and the Balanus in deeper waters.