His future world is not a happy place. By his guess in about the year 3000, the population will stabilize at 11 billion. Many animals that are teetering on the brink of extinction were finally slaughtered by 11 billion people and their hunger. The sea, although thoroughly over-fished, has experienced very few extinctions have taken place. Viruses and bacteria are evolving defense against the drugs the scientists are using to cure their patients of their disease. Domesticated animals, by his standards, will survive the longest as they are altered even more by humanity's creativity and needs.
By 10 million A.D. most rats have specialized in one garbage dump or another. A time traveler ends up in one of these garbage dumps where he finds millions of species of rats, the future evolution of the pig and the snake, and is then assaulted (and presumably killed) by a horde of highly evolved crows. In the last chapter in the book we see life in the last days of habitable earth. There is so little CO2 in the atmosphere plants have to be shrubby and waxy or else they die of starvation. Animals that have been spared by humanity are now low to the ground and heavily armoured against desiccation. Species, groups, and even entire phyla are disappearing from a now inhospitable earth. Humans are still around, still working like ants to give themselves a fulfilling "life", and they will probably keep working like that till they drop dead.
This is a bit like the Morlocks in "The Time Machine" by H G Wells which carry on working because they have evolved so they want to work.