God made everything. He did so timelessly eternally, and is fully responsible for everything that exists. He is not just a first cause, but an artist, author, designer and architect. It seems not unreasonable to suppose that during his eternal lifetime God has intellectual property rights to what he has made, including all biological forms of life. If so, then something like a license from God is needed to copy significant parts of creation.
A reasonable reading of Genesis tells us that God made us stewards of the non-human world around us, and in particular he has given us license to engage in agriculture, including the duplication of animals and plants. But we have not been given similarly far-reaching license with regard to humanity. We are told to be fruitful and multiply, but to be fruitful and multiply is not the same as to duplicate ourselves by any means possible. We have very good reason to think that we have license to use our reproductive organs to reproduce within a relationship designed for this purpose, namely marriage. But we have little reason to think that we have any license to reproduce outside of such a relation or that we have license to do so outside of the natural use of these reproductive organs. And the default assumption is that we have no permission to reproduce the intellectual property of another.
This line of thought generates something that is pretty much the Catholic picture of reproductive ethics. There is no permission for human reproduction outside of marriage. And reproduction needs to occur by means of human mating. Reproductive technologies, then, need to be limited to improving or repairing the reproductive potential of human mating, rather than replacing human mating by something else.
One can enhance the above story by noting that creatures have a two-fold connection with the divine artist. First, they are designed and created by him. Second, they are images of him. Some creatures are much more significantly divine self-portraits: these are persons, capable of interpersonal relationships of love. It is reasonable to think that there would be more significant restrictions on the copying of those works of art which are the divine self-portraits.
Objection 1: We shouldn't need to have Scripture to know that we may engage in agriculture and marital mating.
Response: Indeed. I think the relevant permissions are naturally "written in the heart". We intuitively grasp the difference between genetically enhancing wheat and genetically enhancing humans, and the difference between sperm banks for cattle and for humans. But the license to use new reproductive technologies is not so written in the heart.
Objection 2: Intellectual property rights are limited by society, which gets to define how long they last and to what degree they apply, and these rights are never endless.
Response: It is reasonable to think that there are such limitations for the property rights of human beings who themselves draw on centuries of culture for their creation. But God is a case apart.
Objection 3: Intellectual property rights are a matter of positive rather than natural law; they are created and modified by society.Response: I share this intuition, and that makes me not want to full endorse the line of thought in this post. But perhaps we can say that intellectual property rights of humans are a very faint reflection of divine intellectual property rights, faint because all we have and create ultimately belongs to God, and also because of the dependence of our own creative work on that of others. So in us, it's a matter of social decision whether there be rights coming from our poor ways of creating. But God is fully and truly a creator.
Objection 4: This is too cold! God is the God of love, not an IP lawyer.
Response: The story is incomplete. But art isn't something cold, nor are the "moral rights" of artists something cold and for lawyers only.