“No, the number of wolves will not grow exponentially at the local scale”
The number of animals on the same territory tends to remain stable over time
Nature is too wise for that. The wolf is an apex predator at the top of the food chain: if the wolves became too numerous, they would end up reducing the number of prey too much, threatening the very basis of their subsistence.
Instead, it works like this: wolves are organized into packs, i.e. families made up of parents (the dominant male and female) and pups. Together they occupy a very vast and exclusive territory (on average 200 square kilometres in the Alps) where they are the only ones to hunt and which they defend against intrusion from other wolves. Only the dominant pair reproduces, only once a year, and the young abandon the pack of origin and usually disperse in their 2nd or 3rd year of life. On average, one
of in four young wolves succeeds in becoming an adult in the Alps.
If there were no humans, wolves would limit their numbers by killing each other, as it happens regularly, for instance, in North America, where the anthropic pressure is lower. However, in the Western Alps, several intraspecific lethal attacks, i.e. wolves killed by other wolves, have already been documented (see for example the list reported by the Large Carnivores Centre of the Piedmont Region of wolves recovered dead with proven causes of death).