Ownership of the Natural World
Halacha recognizes the ability of human beings to own the natural world. In Bereishit 1:26, Hashem tells Adam
וַיֹּאמֶר לָהֶם אֱלֹהִים פְּרוּ וּרְבוּ וּמִלְאוּ אֶת הָאָרֶץ וְכִבְשֻׁהָ וּרְדוּ בִּדְגַת הַיָּם וּבְעוֹף הַשָּׁמַיִם וּבְכָל חַיָּה הָרֹמֶשֶׂת עַל הָאָרֶץ:
"And Hashem said to them you shall reproduce and grow and fill the Earth and conquer it, and rule upon the fish of the sea and the birds of the sky and in all the beasts that crawl upon the Earth."
This instruction is understood by some commentators as giving man the property rights over the Earth and all of its creatures.[1]
Ownership of the Sea
Everything in the sea and the desert is considered owner-less and free for the taking.[2] There is a dispute over the extent that people are able to own nature. Some say that while the fish in the ocean are able to be owned by whoever fish them, the sea itself cannot be owned.[3] Others say that while private individuals cannot own the ocean or the desert, governments can, because the goverment's right to property is over the whole area of a country. According to the opinion that governments have the ability to own the untamed areas of nature- governments also have the ability to sell nature to private citizens.[4]
Animals
Just as people are able to own land- so too they are able to own animals. However, if an animal rebels from the ownership of its owner it becomes owner-less. Some extend this principle to say that animals which are never fully accessible by humans cannot be considered owned on a Torah level. However on a Rabbinic level the Rabbis decreed in a series of cases that one is forbidden to steal his friend's animal, even if his friend does not own the animal on a Torah level. See Honeybee article for further reference.