The famous radiation of Galapagos finches from the common ancestor species on the Western coast of South America is probably a result of

Adaptive evolution

Explanation:

The radiation of finches in the Galápagos archipelago is the result of the natural selection process described by Darwin as adaptive evolution. Evolution is the process for which the organisms better adapted to its environment have more chances to survive and to reproduce, thereby leaving more offspring in the next generation.  

Moreover, adaptive evolution refers to the mechanism for which species evolve by the emergence of advantageous mutations that are fixed through positive selection, thereby favoring the phenotypes that have higher adaptive fitness.