In the movie Cast Away with Tom Hanks the character survives 4 years on a small island. But that was a movie. It is a common cartoon image to see a single person on small island with one coconut tree, this seems unlikely to be survivable.

In real life José Salvador Alvarenga survived 14 months adrift in the Pacific Ocean.

The question What area is needed to grow enough food to sustain a person for a year? (Sister site, Sustainable Living) has answers suggesting that as little as 4,000 sf (372 m²) will support one person, but that is best case, with tools, seed and other supplies available.

Realistically, is there minimum size/configuration of an island that it is likely you could survive indefinitely?

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    The surrounding water could potentially provide enough food (fish, seaweed, etc). – StrongBad Jul 29 '16 at 16:10
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    I don't think there's going to be a generic answer. Different islands would be different. – Ben Crowell Jul 29 '16 at 17:22
  • To reinforce what StrongBad said, there are islands whose fertility on land is low, but the surrounding seas provide a lot of food. Seas at high latitudes are astonishingly fertile, as the circumpolar peoples found thousands of years ago. – ab2 Jul 30 '16 at 2:21
  • Maybe it needs to be more than one question? What would be the key differences that would define the limits? Temperature, location, something else? – James Jenkins Jul 30 '16 at 8:52
  • (a) Limit the amount or exclude the food you could get from the sea, including e.g., nesting sea-birds and walrus haul-outs; (b) include everything from the sea. – ab2 Jul 30 '16 at 10:57

...is there minimum size/configuration of an island that it is likely you could survive indefinitely?

No, at least not if you're in a location where you're not at risk of dying from exposure to the elements, but considering most uninhabited island are in the South Pacific, I think exposure is less of a worry if you're ever caught in this situation.

The determining factor is going to be the availability of fresh water (next to your abilities as a survivalist). The size of the island is irrelevant if you don't have a supply of water to drink, you'll quickly die of dehydration. You could be on a +4,000ft2 sandbar in the middle of the pacific with absolutely no water to drink, but even if water is not available on the island however, it could still potentially be collected as rain water, or distilled from seawater.

As far as island size, as long as it is an island at both low tide and high tide, then you will be safe from drowning, then the ocean can provide you with whatever else you need to stay alive. You will have access to materials to make tools and a rudimentary shelter from the sun out of shells, coral, rocks and the bones of sea creatures, and you will have a steady supply of food from all the little fish, urchins and shellfish that thrive in the reefs around small islands. It wouldn't be easy, but you could stay alive for as long as the ocean provides.

Granted, being on an island that merely spares you from death with no small measure of skill, work, and determination is hardly considered "supporting life". There's a difference between being alive and truly living. When I think of supporting life, I think of a location where life can thrive comfortably, grow and be happy, not merely surviving.

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