Research on galapagos finches by peter and rosemary grant showed that a type of natural selection called

The type of natural selection is Directional Selection.

In directional selection, the phenotype which is more suitable to the existing environmental conditions is favored more over the other phenotypes. Thus, population of a particular phenotype increases gradually.

These birds changed from the ancestral bird in terms of the beak size, shape, etc.

The form of natural selection is called adaptive radiation