The Falkland Islands are home to roughly 500,000 sheep and about 3,000 people. That's 170 sheep for every human. You are outnumbered.
New Zealand, famously sheep-heavy, has about 5 sheep per person. The Falklands have 34 times that ratio. If the sheep ever organised, the humans wouldn't stand a chance.
The islands are about the size of Northern Ireland, sitting in the South Atlantic 400 miles east of Argentina. Wool has been the economic backbone for over a century — there's not much else to farm when your landscape is windswept grassland and not much else.
The sheep are mostly bred for fine wool rather than meat. Falkland wool is prized in the UK textile industry for its quality. The main settlement, Stanley, has a population of about 2,100 — meaning the remaining 900 people are spread across an area larger than Jamaica, mostly tending sheep.
Other contenders for "most animals per person": Mongolia with 66 horses per 100 people, and Iceland with roughly 2 sheep per person — practically a desert compared to the Falklands.