In the story "The Most Dangerous Game," how does Rainsford come to the island?

In Part I, Rainsford is reclining in a steamer chair, smoking his pipe, when he hears several gunshots. Racing up to the railing to take look out on the ocean, he accidentally knocks his pipe against a rope. Attempting to retrieve it, he is knocked overboard. Now, he is afloat in the warm, tropical waters, watching the yacht, immune to his cries and beyond his reach, disappear in the distance. He decides to swim towards the gunshots, when he hears the loud, anguished cry of an animal. Then hears a pistol shot.

Swimming determinedly, he hears water breaking on land. He manages to make it through the jagged rocks to the shore, where he falls dead asleep. When he awakes, he finds traces of a large animal killed by a 22, a relatively small weapon for such a large animal. Then, he finds prints of hunting boots and he is off to find the hunters- and food!