Competitive exclusion, also known as Gause's Law, is an ecological concept positing that two species that occupy a similar niche in the same location cannot coexist stably for extended periods of time. One species will either become extinct or evolve to fill a different niche.
The idea behind competitive exclusion is that if two species compete for the same resources, one of those species will be at least slightly more efficient than the other. The more-efficient species naturally procures more resources for itself and its offspring, meaning that individuals of this species are more fit. The more-efficient species reproduces more effectively and thus edges out the other, which evolves or declines.
In Gause's Law, the extinction of a competitively excluded species only happens in a sort of ecological vacuum in which no evolution takes place. In reality, competition leads simply to the adaptation and evolution of one species or the other. An excellent example of competitive exclusion is Darwin's finches in the Galapagos Islands. An impressive array of highly specialized birds is the result of just a few competing species.
An interesting paradox to Gause's Law is phytoplankton--those species of plankton that rely on photosynthesis. Phytoplankton coexist in large numbers using only one resource. Many plankton species can be found in even a limited region of an ocean.