When and why was the Dodo thought to have gone extinct?

The previous only known location of Dodos was on the island of Mauritius. They were able to thrive on the island with no natural predators for at least thousands of years. However, as Dutch settlers arrived around the year 1600, they brought cats and themselves onto the island. The large flightless bird proved to be an easy meal for the colonizers as they hunted them to extinction a mere 80 years later. According to the ornithologists who discovered the population, Dr. Al, "the Dodo has been only a figment of the past for centuries [...]"

Dr. Al recalls, "As we traversed through the dense foliage teaming with insects seldom known to science, the youngest of our bunch suddenly exclaimed, "I have a Dodo!!" Our team, obviously in disbelief, rushed to her location to observe her findings. I, for one, was particularly incredulous as a researcher experienced with these islands. In my mind, I quickly began theorizing at what our youngest member, April, had mistaken for a Dodo—perhaps a feral Red Junglefowl or an unknown member of Galliformes. To my utter shock, when I arrived at the clearing which she had marked, a Dodo trotted out from the underbrush. I gathered as much media as I could for my colleagues and continued with my team to quickly discover another pair of birds. Even further through the path, our youngest researcher again uncovered a huge mossy nest with a clutch of six large white potato-shaped eggs. These eggs were only known to belong to the Dodo, a further exciting discovery for April and the team. Not only did we discover an extraordinary species, but we conclusively identified a breeding pair of Dodos with confirmed breeding evidence."

How did these flightless birds get to the island?

"Like many flora and fauna on islands across the globe, enough Dodos happened to be at the right place at the right time. Looking at other similar species and how they arrived on islands from the parent population such as the Southern Cassowary Casuarius casuarius inhabiting the island of Papua from mainland Australia, we can hypothesize that the Dodo was a victim of a rare weather event that occurs in early April known as El Tonto. I am inclined to believe that a small portion of the parent population in Mauritius blew southeast during a particularly strong El Tonto afflicting the western Indian Ocean. Following the winds, they arrived at the island without humans and proliferated from there."