In Keepsakes, the opening section of Hiromi Kawakami’s haunting novel-in-stories, a woman describes her world. Although peaceful and orderly, it is an unsettling and strange place: people are made in factories from animal DNA, then live startlingly brief lives, growing to adulthood in a handful of years and often dying young. Memory, both personal and historical, is fragmentary and, in the case of memories of childhood, actively suppressed. Meanwhile, the society’s anxieties are focused on preserving the children the woman helps raise and the biological diversity they embody: as one of the characters declares, “If we lose the children, that’s the end of the world”.

This spectre of genetic decline and extinction stalks all 14 of the stories that make up Under the Eye of the Big Bird. In one, men – now vanishingly rare due to their genetic fragility – are assigned to breed with particular women; although they “marry” them, the question of consent is never invoked. In another, one of the characters reflects that, “as a species, we simply don’t have what it takes”.

Despite this thread the connection between the different stories is not clear at first. Instead, as they shift between characters and timeframes, each section seems to offer a glimpse of a new and newly nightmarish future. Gradually, however, a larger story begins to emerge. After a long period of falling population due to declining fertility, a last-ditch attempt has been made to save humanity by dividing us into separate communities, each under the supervision of “watchers”, raised and trained by AIs known as mothers. Within these communities “all reproductive taboos would be lifted” in the hope of jumpstarting human evolution by provoking “mutations on a far shorter timescale than in any previous evolutionary process”.

This plan works, at least for a time. Humanity begins to change, producing individuals possessed of the ability to scan and control the minds of others, as well as people with extra eyes, or the ability to breathe through gills or to photosynthesise. Meanwhile, the AIs designed to watch over us also continue to evolve, and finally merge themselves with humans and other animals.

There are moments when Under the Eye of the Big Bird’s portrait of humans evolving psychic powers in a post-apocalyptic future recalls the strand of 1960s and 70s science fiction that produced books such as Kate Wilhelm’s Where Late the Sweet Birds Sang. Similarly, the novel’s non-linear, mosaic structure is reminiscent of recent novels, such as Sequoia Nagamatsu’s How High We Go in the Dark, that have used discontinuous narratives to explore the transformation of human society by climate change and other stressors.

Yet as its queasily childlike and affectless voice – marvellously captured by translator Asa Yoneda – suggests, the novel’s real concern is not with the particularities of the worlds it depicts, but with the ways in which human nature and society shift and alter as our bodies and minds change.

Some of these transformations affect us in unexpected ways: because humans blessed with the ability to photosynthesise no longer have to compete for food they gradually lose their interest in each other and lapse into dormancy. At other times atavistic impulses take over: in one of the book’s more shocking moments, an entire strain of humanity is wiped out by a watcher who is overcome with disgust at what he considers their repulsive appearance and animalistic lovemaking. Ideas of selfhood and bodily autonomy begin to break down. In Narcissi, cloning blurs the notion of individuality in ways that challenge grammar (“We turned fifteen, and the shortest me quickly grew taller”); in other stories people learn to enter and inhabit the minds of others, with catastrophic results.

In its final stages, Under the Eye of the Big Bird bends back on itself, suggesting that this far-flung future may also be the past, or at least that the ending it conjures may in fact be a new beginning. As it does so it offers a powerful corrective to the assumption of human primacy, instead reminding us that we are not the endpoint in the process of evolution, but simply one link in a much longer chain.

• Under the Eye of the Big Bird by Hiromi Kawakami, translated by Asa Yoneda, is published by Granta (£14.99). To support the Guardian and Observer, order your copy at guardianbookshop.com. Delivery charges may apply.