Final answer:
Rapid speciation with little competition, known as adaptive radiation, occurs when environmental changes lead to the evolution of multiple new species from a common ancestor in a short time. Sympatric speciation and punctuated equilibrium are related concepts that describe this rapid evolutionary process driven by significant environmental changes.
Step-by-step explanation:
Rapid speciation under conditions of little competition is known as adaptive radiation. This process is a form of speciation, where one species gives rise to multiple different species in a relatively short time due to a rapid change in the environment.
The primary factor affecting the rate of speciation is environmental changes. For instance, snail fossils remain unchanged for millennia until a significant environmental shift - such as a drop in water level - isolates a small group, leading to a variation that becomes dominant due to the sharp shift in environmental conditions. In such cases, a rapid and radical form of selection occurs where the tiny, genetically varied population is poised to quickly evolve, resulting in sympatric speciation.
Another example is the East African cichlid fish which have undergone adaptive radiation in Lake Tanganyika, leading to an explosion of diverse species due to mate selection based on coloration. The rates of speciation could vary from gradual changes to bursts of rapid evolution, also known as punctuated equilibrium, often spurred by substantial environmental change.