POD: The exact circumstance by which collared peccaries and bighorn sheep became domesticable is something of a mystery. The white lipped peccaries and the Siberian snow sheep that are the closest relatives of these animals are certainly not domesticable, the former being generally too violent and unpredictable to even tame and the latter not exhibiting the dominance behaviors seen in livestock such as cattle and goats which make it possible to herd these animals. Perhaps this change in their behavior was related, caused by the same freak wave of radiation hitting the Americas in some prehistoric time. Or perhaps time-travelling aliens reading Guns, Germs, and Steel thought it would be a good idea to give Native Americans more domestic mammals. Perhaps it was random coincidence, just a matter of the right genes activating at the right time in the separate ancestral populations of these animals. For whatever reason, though, the fact remains that in this world, the Americas found themselves with bighorn sheep that exhibit the same dominance behaviors seen in Eurasian mouflon sheep, while collared peccaries act much more like the Eurasian pig.
12,000 BC: A massive extinction occurs in the Americas as megafauna species are wiped out in their dozens. Horses, shrub-ox, mammoths, and mastodons are among the victims of a combined double-blow of humans and climate change.
Collared peccaries and bighorn sheep escape this wave of devastation. Collared peccaries remain the most widespread peccary species in the Americas, living everywhere from deserts to rain forests, although their range is reduced. The bighorns survive on the mountaintops and in the driest deserts, although the territorial habits of rams leave the species somewhat vulnerable to human predation as they are less likely to move from away from areas where human hunters take up residence.
However, the habits of human predation did change after the die off to become less destructive. Humans began to manage their environment more intensely as the easier sources of food disappeared. They used controlled burns, collected seeds, and hunted more carefully. It was these cultural changes in response to the Pleistocene die-offs that led eventually to the discovery of agriculture.