Learn more about Darwin in "Darwin's Secret Notebooks."

By the time I reach Carcass Island, I've learned the secret to watching penguins in the wild: You have to act nonchalant. So, arriving at Leopard Beach to find some 200 Magellanic penguins shuffling about, I simply perch myself on a sand dune and wait. Before long, the knee-high birds get used to me and fearlessly wobble past, their black-and-white, tuxedo-style plumage molting off in feathery puffs of gray.

Carcass Island, a knob of land a mere six miles long and two miles wide, sits at the western end of the Falklands, an archipelago comprising 778 islands and islets 300 miles off the east coast of Patagonia. On my way to Leopard Beach, I've wandered the isle at will, inspecting a shipwreck at Ballast Beach, climbing the fog-shrouded summit of Mount Byng, trekking along the treeless spine of the island interior. Occasionally I stop to stretch out on the spongy, heath-like diddle-dee and enjoy a silence so complete it leaves my ears ringing. As remarkable as what is found here is what's not—crowds. At times, it seems as though I have the entire island to myself.

At Leopard Beach, I realize that the longer I sit still, the more species I see: stocky, brown-gray ducks, long-billed shorebirds, buzzard-like foragers, chubby little wrens, stripe-breasted geese, some approaching me close enough to touch.

But my attention keeps coming back to the penguins. When Charles Darwin visited the Falklands 175 years ago, he noted that the Magellanic penguin was known for its habit of throwing its head back and braying like a jackass. The famous naturalist stopped in the Falklands more than a year before his visit to the Galápagos. I've come here for similar reasons, namely, to experience the wildlife, but to do so in a self-paced way that's almost impossible to enjoy in the more celebrated island chain.

On paper, the British-administered Falklands group, about the size of Connecticut, shows little advantage. It has fewer endemic animal species than the Galápagos (which sit on the Equator), a chillier climate, and no giant reptiles. What's more, the Falklands have been out of the news since the British-Argentine war fought here in 1982. Darwin himself was less than effusive, characterizing the landscape as "desolate and wretched."

But sensibilities have changed, and with upwards of 100,000 people touring the Galápagos each year, measures to lessen their impact on the land have resulted in a visitor experience that can feel almost museum-like, confined to strictly demarked walking trails. By contrast, the larger and less trammeled Falklands, which host about 700 land-based visitors a year, allow travelers the chance to wander the terrain alone with nature and open to serendipity.

I've elected to explore the Falkland Islands by jeep, ferry, and small plane, overnighting in home-stay inns. I thus avoid the cruise-ship-based day-trippers—some 63,000 of whom stop here each year en route to the Antarctic.

I began my trip three days ago in the capital of Stanley, on East Falkland Island. Stanley, population 2,115, is a tidy village of backyard gardens and painted tin roofs. It's the only real town in the islands. From there, I've island-hopped westward, stopping first at Pebble Island to see the black-necked swans and swarms of rockhopper and gentoo penguins.

Now, on Carcass Island, as the sun begins to set on Leopard Beach, I hike the shoreline back to my base—a tree-shrouded farmhouse inn run by a couple who have owned the island since 1974. Along the way, I'm shadowed by a little brown songbird that swoops and flits above me as I walk. Every time I stop, it alights nearby and cocks its head at me, as if I'm the most fascinating creature it's ever seen.