• Coyotes limit mesocarnivore (skunks, raccoons, and foxes as well as feral cat) populations and increase bird diversity and abundance.
• Coyotes keep rodent and rabbit populations in check.
• Coyotes help control disease transmission.
• Coyotes clean up the environment.
Ways to Peacefully Coexist:
• Wildlife-proof garbage in sturdy containers with tight fitting lids.
• Don’t leave pet food outside.
• Take out trash the morning pick up is scheduled.
• Keep compost in secure containers.
• Keep fallen fruit off the ground; coyotes eat fruit.
• Keep birdseed off the ground; seeds attract rodents which then attract coyotes.
• Remove feeders if coyotes are seen in your yard.
• Keep barbecue grills clean.
• Eliminate accessible water sources.
• Clear away brush and dense weeds near buildings.
• Close off crawl spaces under decks and around buildings where coyotes may den.
• If you frequently see a coyote in your yard, make loud noises with pots, pans, or air horns, and haze the coyote with a water hose.
• Share this list with your neighbors; coexistence is a neighborhood effort.
From what I've read it's partially true. Except in the beginning its not just the alpha male and female that reproduce. They all do. It's debatable if killing them triggers a protective response to produce larger litters, or if it's simply because there are less of them so larger litters can be supported. But they do produce larger litters. If you want to effectively reduce the population its a job that requires a constant multi-year effort. It can be done but it ha to be maintained. Partially because of the larger litters, partially because yotes move in to the unoccupied territory. But at the end of the day a 2-3 year effort can substantially reduce their numbers, but if you stop after that, in 2-3 years it'll be built right back up.