Some of this is incorrect. Did you forget about the variable of "mixing your labor" with something? Anarcho Capitalists do not believe in "first come, first serve". An Ancap believes that the first person that labors into and uses a resource, owns that very specific resource. For three reasons. 1) It helps others identify your claim, 2) It prevents "claiming the whole island", and 3) thus stealing property becomes akin to slavery, as someone is necessarily stealing your labor. With the fruit tree, nobody can own the tree itself like that. They need to either own the land around it first, or cut it down, etc... But with the fruit, as long as the tree is accessible, whoever grabs the fruit and picks it could be said to be the owner of the specific fruit.