Answer:
According to Darwin's theory, natural selection is the only cause of evolution and so happened with his study about the finches on the Galapagos Islands.
There are three principles that operated among the finches on the Galapagos Islands as per Darwin's theory that includes reproductive isolation, geographic isolation, and competition.
Reproductive isolation in speciation occurs due to two main factors that include traits under divergent selection (here beak size) are same and are linked to the traits that influence mate choice and assortative mating according to the traits.
Geographic isolation in the speciation occur as one species migrate to another island and inhabit to the conditions of that island for example difference in beak shape or color.
Competition in speciation depends on the inherited characteristics that allow them to compete for limited resources as the resources for survival and reproduction are limited. Then the individual with inherited characteristic have more chances to survive than offspring with no inherited characteristics that are less able to compete.
Hence, these three evolution in the speciation of Darwin's finches on the Galapagos Islands are based on natural selection process.