Final answer:
Charles Darwin and Alfred Russel Wallace independently proposed the theory of evolution by natural selection, with Darwin providing extensive evidence in his work 'On the Origin of Species'. Gregor Mendel's genetic discoveries later complemented their theory, and Peter and Rosemary Grant observed natural selection in action with Darwin's finches in the Galápagos.
Step-by-step explanation:
First Demonstrated Mechanism of Evolution with Evidence
Although the French naturalist Jean-Baptiste Lamarck proposed an early mechanism of how species might evolve, it was Charles Darwin and Alfred Russel Wallace who independently derived and presented the first substantiated mechanism for evolution. Their theory of evolution by natural selection was based on extensive observations made during their voyages in the middle of the 19th century. Darwin's On the Origin of Species laid out the evidence for his theory, including an extensive analysis of fossil records and the adaptive traits of organisms, found during his voyage on the H.M.S. Beagle.
Darwin's observations of finch species with varied beak shapes in the Galápagos Islands were a pivotal example of natural selection in action. Gregor Mendel's work on pea plants, although initially overlooked, eventually provided the genetic underpinnings that explained the inheritance and variation of traits that Darwin and Wallace had observed. The Grants' research on Darwin's finches further reinforced the concept of evolution by natural selection, as they witnessed it happening in real-time.