@marina_gorbunova
I’m sorry, but most of them were extinct long before food revolution.
The Neolithic revolution is just an exacerbation of a broader pattern of human-induced environmental destruction that has been going on for much, much longer. Basically what happens is that humans tend to target the largest animals in their environment when possible because they offer the highest payoff in terms of calories-to-effort ratio, and then successively “hunt down the food chain” as their previous target species disappear. Something similar has been documented with orcas “fishing down the food web”.
In fact, this is part of the reason why agriculture was invented in the first place. Eventually, as humans continue hunting species in their local environment to extinction, it gets to the point at which it’s easier for people to just try and grow their own food than keep hunting the few small-bodied species that are left. This may be part of the reason why agriculture was seemingly adopted in the Middle East earlier than in other parts of the world: most of these areas tend to be semidesert or chaparral where there are fewer natural resources1 and thus people would reach the point where they would be forced to adopt agriculture to survive faster. Compare this to, e.g., a Eurasian temperate forest or an African savannah, where there are a lot more animals and thus this practice could continue much longer.
Blaire Van Valkenburgh, a specialist researcher on Pleistocene mammals, put it this way. Most predators are in a cyclical balancing act with their prey. The best example of this is the cycle between the Canadian lynx (Lynx canadensis) and the snowshoe hare (Lepus americanus). When the predator population gets too big, prey gets scarce, and predators start to starve. This causing predator numbers to drop, prey numbers increase, and the population is brought back into balance. This works because most large predatory mammals are specialized carnivores.2
But this doesn’t work with humans. For humans, when numbers of game animals decrease, humans just switch to eating something else, usually feeding on roots, berries, or cultivated grains. However, humans never stop hunting game whenever they get the chance. This means that the human population never decreases, the populations of large mammals never recover, and you get this population of apex predators that doesn’t follow the normal rules and just refuses to die when their food disappears.
Add to this human usage of fire to clear out brush and create corridors for hunting game, and none of the environmental destruction we’re seeing now is actually new. It’s just an exacerbation of the same human patterns of behavior that have been going on since the Pleistocene. Indeed, that’s what a lot of archaeologists call it, “intensification”, and patterns of increased “intensification” of human land use have been implicated in, say, the extinction of the thylacine and Tasmanian devil on the Australian mainland 3000 ka. But this is one reason why some researchers are saying the “Anthropocene” concept doesn’t really work, because it’s really just part of a series of human-driven extinctions, habitat-destruction, and climate change that has been going on for over 500,000 years, and it’s not possible to separate more recent human-caused events from things like, say, the extinction of the Pleistocene megafauna.
But with regards to cats, there are a number of extinct cats that are thought to have been driven extinct by modern humans during the Paleolithic-to-Neolithic transition about 12,000 ka. Smilodon went extinct in North and South America about 12,000 ka. So did the American lion. Mountain lions were driven extinct in North America during the Pleistocene extinction and had to recolonize from South America. The scimitar cat (Homotherium latidens) went extinct later than 28,000 ka in Europe.
But if it’s big cats going extinct more recently you want, lions were extirpated from Europe in historical times, and this has been directly linked to human persecution and land use by post-Neolithic Revolution humans. Jaguars have been driven extinct across most of their native range, they used to be found all across North America. There’s also a number of extinct tiger populations that used to be recognized as distinct subspecies, though with the revisions to the subspecific taxonomy of Panthera tigris I’m not sure which, if any of them are considered distinct now.
1 - Specifically, populations of large mammals would be expected to be less dense, and most of those would be expected to be clustered around bodies of water like the Nile and Tigris/Euphrates Rivers. Something like this happened in ancient Egypt, where the fact that most of the wildlife was clustered around the Nile meant that over the course of the centuries most of the large mammals in Egypt were driven to extinction.
2 - Bears are similar, but a little different, in that bears rarely hunt large mammals and thus don’t apply constant predation pressure in the way that wolves, hyenas, cats, or humans do.