Do animals have private property rights?

Right wingers argue private property must exist as when you put labour in public property, it transforms into something new, something of a completely different value and often function. E.g. metal, glass, etc.... into smart phones.However how does this work for animals? For example, after a bird puts it's labour into making a birds nest, is it not creating private property and has a natural right to the nest? Who does the nest belong to? via /r/communism https://ift.tt/2OHB285