Nature is indifferent to the human world, for that is what we mean when we speak of "the world" - we mean the human world. We are the ones anxious over our mortality and rightly so; we are vulnerable. We were born and we must die, whereas Nature is the cycle of birth and death and the cycle is eternal.
It is not only Nature that kills, as we know. We are rather good at it too. I anticipate mankind very nearly kills itself and in so doing weakens itself to the point where Nature is able to finish it off, and thus like the deluges of religion Nature cleanses the planet of human iniquity.