When the first of the Galápagos Islands arose from the ocean floor around 3 million years ago, they were naked, angry, lava-spewing cones devoid of life. Now, millions of years later, they are alive with some of the world’s most iconic animals. Giant tortoises.  Sea iguanas. Flightless cormorants. And those finches equipped with Swiss army knife beaks.
The Galápagos finches are probably one of the most well-known examples of evolution and will forever be tightly linked to Charles Darwin’s voyage and his theory of natural selection (although you may be surprised to learn that the Galápagos finches were not as central to Darwin’s theory as we like to think).
With their diversity of bill sizes and shapes, each species has adapted to a specific type of food; the ground-finch (Geospiza) has a thick beak adapted to feeding on a variety of crunchy seeds and arthropods, whereas the warbler finch (Certhidea olivacea) developed a slender, pointy bill to catch tasty insects hiding between the foliage.  The woodpecker finch (Camarhynchus pallidus) even uses twigs or cactus spines to pry arthropods out of treeholes. The lead photo shows the tool-using woodpecker finch probing a branch with a cactus spine on Plaza Island, Galápagos Islands, Ecuador.

Adaptive Radiation
The Galápagos finches are seen as a classic example of an adaptive radiation. This is the rapid evolution of ecologically different species from a common ancestor.
Comparisons of anatomical features of the Galápagos finches, as well as modern molecular techniques, show they are indeed more closely related to each other than to any other species. Such a group of organisms, all descended from one ancestral species, is called a monophyletic group. The variations in their DNA indicate when the different species split from one another. It also indicates that the ancestral flock likely reached the Galápagos about 2-3 million years
ago.
Origin of the finches
What did those very first finches look like? And where did they come from?
Although many of the Galápagos Islands themselves are several million years old, the oldest known fossil remains of Galápagos finches come from the Holocene period, that is, over the last 10,000 years.  These fossils are from two species of ground-finches, Geospiza nebulosi and G magnirostris, that are still living on the islands today. They thus tell us little about what the earliest finches looked like and where they might have come from.
Because of the islands’ close proximity to Ecuador (see the map), scientists have looked towards mainland South America in their search for the ancestor of the Galápagos finches. For instance, the blue-back grassquit Volatinia jacarina is a small tropical bird common throughout much of Central and South America. Based on its looks and behaviour, it was earlier thought to be the most likely direct ancestor of the Galápagos finches.
Soon, scientists started studying evolution not just from behaviour and looks, but also at the DNA level. Using evidence from DNA from the mitochondria, it was later found that another species of grassquit, Tiaris obscura, was the most likely ancestral species.

Geology and Evolution
The manner in which this species originated in Central America, but spread into South America is very interesting. About 3 million years ago, a land bridge formed between North and South America. Today it is called the Isthmus of Panama. This was a major event in the geology of the Earth and played a major role in biodiversity of the planet. This allowed animals and plants to migrate between North and South America. So also did the grassquit migrate. From South America, it made its way to the Galapagos archipelago.
Of course, this is like a detective story and there are many other clues. Even these findings are disputed. For instance, others have argued that these finches originated in the Caribbean, on the other side (east) of Panama.
Although the lack of fossils means that we don’t know much about the appearance of the first finches, we can narrow down their area of origin. The closure of the Panama land bridge altered ocean circulation, and probably brought about changes in wind strength and directions.  These changes may have facilitated the colonisation of the Galápagos Islands, especially if that area was the point of departure for a flock of adventurous finches.
Not just finches, all species of Galápagos tortoises also evolved from common ancestors that arrived from mainland South America by overwater dispersal. Galápagos giant tortoises show that in evolution, slow and steady indeed gets you places!

Compiled form various sources