Final answer:
The process by which one species of finch evolved into two species on the same Galápagos island is known as adaptive radiation, a type of allopatric speciation. Darwin's finches are a prime example of this evolutionary process, where different species have distinct beak shapes adapted to varied food sources.
Step-by-step explanation:
The evidence that one species of finch migrated to a Galápagos island, and evolved into two species now found on the same island, feeding on different food sources, is an example of adaptive radiation, which is a form of allopatric speciation. This process occurs when a single species evolves into multiple species, each adapting to different ecological niches. The Galápagos finches, often referred to as Darwin's finches, are iconic examples of this phenomenon. Initially, a single ancestral finch species colonized the islands and, over time, diversified into various species with distinct beak shapes and feeding habits, each suited to a different food source, thereby reducing competition and promoting survival in varying environments.