I found a new area a few years ago, killed 14 in two weekends. The area is about 10 miles north to south and about 2 miles wide on average.
Went back the next year and killed 11 more in the same area, but there were clearly not as many animals.
Went back year 3, killed 6. Definitely not as much sign or animals.
Went back year 4 killed 3. Very little sign, no howling at night
Went back year 5 killed 1. Missed 1, saw no other coyotes anywhere near. Not on the private land I couldn't hunt, and not on the public land I did hunt.
I know other people hunt this area as well, how many did they kill? I ran numbers in my head while out hunting one day, with just the number I killed, I put a serious hurt on the population. Add in the other hunters and my conclusion was that hunting had all but wiped out the population. In the non-farming west, high desert, population density is not high. Maybe around 2 coyotes per square mile, doesn't take long to clean out an area.
But, give it a couple years and it will be right back where it was.