[ Read: It’s a mistake to focus just on animal extinctions. ]

Rather than simply counting the numbers of extinct and endangered species, Davis instead worked out how much evolutionary history they represent. This metric, known as phylogenetic diversity, matters because not all species are equal. Some are particularly unusual and irreplaceable.

The pygmy sloth, for example, may be one of the most threatened mammal species, but it’s also one of the youngest, having diverged from its closest relative 9,000 years ago. The aardvark, by contrast, is the last survivor of a once-large group of mammals that split off from the others 75 million years ago. Losing the pygmy sloth would be like snapping off a tiny twig from the mammalian family tree; losing the aardvark would be like sawing down an entire branch.

To work out the extent of these cuts, Davis and his colleagues first built a family tree for all mammals past and present, going back 130,000 years, into the late Pleistocene. By adding up the length of all the missing twigs and branches, they calculated that prehistoric humans robbed mammals of 2 billion years of unique evolutionary history. Since the 16th century, we’ve wiped out an additional 500 million years of evolutionary history, and we stand to lose a further 1.8 billion years within the next five decades. “It is staggering,” Davis says.

Indeed, our actions have been far more destructive than if we’d just killed off species at random. That’s because, as another group showed earlier this year, we have disproportionately targeted the largest species. There used to be giant ground sloths and car-size armadillos; they’re all gone. There used to be six species of elephant-like mammals in North America alone; now there are just three left in the entire world.

And “those big things were also the most evolutionary distinct things,” says Davis. “They were often on their own branches of the tree. We don’t see that pattern in previous mass extinctions.” According to him, humans have pulled off something close to the worst-case scenario for mammalian extinctions. We could barely have destroyed more phylogenetic diversity if we’d planned to.

When the past is this grim, the future is, too. Imagine that we instigate a massive, well-funded, global conservation push that effectively saves all existing mammals from extinction. Imagine also that all the survivors produce new species at twice their highest historical rates, on a par with the African cichlid fish that are textbook exemplars of extremely fast evolution. Even in this implausibly optimistic scenario, it would take half a million years for mammalian diversity to bounce back to its Ice Age zenith.

More realistically, given how fast mammals typically evolve, and given that some living species will inevitably go extinct, the full comeback will likely take 3 million to 7 million years to stage. “That puts us on the same scale as previous mass extinctions,” says Davis. “What we are going through now could have as big an impact as the asteroid” that killed off most of the dinosaurs.