Locke assumes the law of nature is based on some kind of benevolent reason. And reason is given to nature by God.
But nature's process appears, in fact (or comprehensively supported theory, if you prefer), to be Darwinian. Life, liberty and the pursuit of happiness has little to do with it. The survival principle is the end, and adaptation, however abominable, is the means.
Darwin is not the same thing as Hobbes. Darwin's theory does not rule out cooperation. Species benefit themselves in whichever way works. It is infinitely more subtle than Hobbes, and it has far more explanatory power than Locke. Locke's thesis needs a God. Darwin's doesn't. Which is why Darwin remains controversial, of course!
For a comparable theory about the nature of society, read Adam Smith. Darwin was deeply influenced by him, and his Origin of Species has striking parallels. The fact the US Constitution was written before Darwin is why, I think, it will run into difficulty over time. It is based on an understanding of the way societies operate which lacks the flexibility evolutionary theory tells us is necessary for success over the long run. Big principles are exactly what nature disqualifies, eventually.