Fishing as a food source
We stranded on an empty island... if I learned something from all these stories about stranding: gathering some fruits and fetch some fish will increase your chance to survive. So, crab your fishing rod and get something for dinner :)
My suggestion: You can build a fishing dock. It will gather food from the ocean around your island. Like oil and other ressources the quantity of fish will decrease over the time, but it slowly regrows, if you use your fishing grounds wisely. Polluting the water to much will kill the fish and stop the regeneration. Getting too much fish will decrease the regeneration rate also. If the quantity reaches zero, you destroyed this source of food for a long time.
The easiest way to implement this is a building like the trading dock. It needs a number of workers to operate and will produce a random quantity of food. Maybe you can choose the number of fishermen (and fisherwomen of course).