I wrote this for the Times Higher last week.

In his essay, “The passing wisdom of birds”, the nature writer Barry Lopez advocates that every university establish the post of in-house naturalist, to be held in rotation by a student in his or her final year. The university naturalist would record the flora and nonhuman fauna of the campus and advise about how best to look after them. He or she would be like a university archivist, but of the outdoors.

Although I’m not a student, I should like to apply for this position. As a university naturalist I am, in CV-speak, a dynamic self-starter with a strong skill set. I’m also good at looking out of windows and spotting the seasonal shifts: like the arrival of winter on campus, with the first frost on the path and the squirrels hoarding beechmast and berries.

I teach in a building that backs on to a garden full of London plane trees. Outside one of my classrooms, there is a tree so close that you can reach out the window and almost touch its branches. The London plane is the perfect urban tree for our urban university: its knobbly bark and leathery leaves hoover up polluted air. It also sends out an early signal of autumn, shedding leaves even before Michaelmas. Yet the sheltering wall of our building – and, presumably, global warming – has, for this particular tree, held back the full force of the fall. Even now, in December, a few shrivelled, yellowish leaves cling on.

I ask my first-year students to guess how many leaves that tree had when they started their course in September. Puzzled as to why their literature class has turned into nature study, they humour me and guess a thousand. Times that by at least a hundred, I say. Look. It’s been shedding leaves since induction week, and still has some left.

We are meant to be discussing Shakespeare’s sonnets. Shakespeare never set eyes on a London plane, which is a late 17th-century hybrid. But he knew his trees, and lived in a world where they were vital – for making ships, houses, furniture, books. And while teaching the sonnets this year, something obvious has dawned on me. Shakespeare doesn’t really think in seasons, which are a human construct anyway. He thinks in micro-seasons, subtly blurring into each other.

“That time of year thou may’st in me behold,” Sonnet 73 begins, “When yellow leaves, or none, or few, do hang”. I used to think that second line was just lazily fixing up the metre, but now I love its self-cancelling order and the way it catches a precise stage of late autumn moving into early winter. Leaves in the sonnets have many states, depending on the micro-season. They are “lusty”, “fair”, “vacant”, “barren”, or “look pale, dreading the winter’s near”. And then they are gone, replaced by “old December’s bareness everywhere”.

This year, I have noticed the micro-seasons myself, perhaps because I have suddenly felt part of what the Scottish poet Kathleen Jamie calls “that rough tribe of the mortal”. And it’s not just other people who seem fragile and vulnerable. Nature feels vulnerable too, and every moment of autumn has felt like an exquisite death, a bereavement.

I’ve noted it all as the light in this afternoon seminar has slowly dimmed: the first swallows gathering on the telephone wires before their journey south; the first heavy dewfall; the first air from the Arctic; the first buzz of the gardeners’ leaf blowers in November. Meanwhile, the demands of term-time have felt more than ever like a perpetual juggernaut that acknowledges neither the seasons nor the particularity of individual lives.

Trees, our longest-living organisms, fool us into thinking that things are permanent. Alone among plants, they raise a wooden scaffolding above the ground – building, in annual increments, a frame on which to hang their leaves, while their heartwood grows hard in death and serves as a backbone. In winter, when so many other things are absent or dead, their leafless skeletons stand proud and, seemingly, immortal.

But people aren’t as sturdy as trees. As Shakespeare reminds us in the sonnets, they are more like leaves, waiting on winter. Each human life burns itself out, is “consum’d with that which it was nourished by”.

For the students – I hope – autumn is what it used to be for me: a new start, a second spring, what the French call la rentrée . Long may they feel cocooned in this illusion of continuity, that there will always be another semester, that life will go on as before.

You have to be ready to notice things – in literature as in life. When you do, they are right there in front of you, hidden in plain sight. And now life just seems too short and precious not to notice every falling leaf.