I must admit, I could't fine good examples, but...

In Yellostone Nat Park, wolf population has gown recently, and since wolfs predate coyotes, coyote numbers started to dwindle. One may attribute that to coyotes being deterred by wolf's scent migrate somewhere else, but yet, if the numbers are large enough, coyotes are known to overrun the wolfs. So, here is an example of coyote not being able to face the external factors by simple reporoduction.

yes, but predator wolf hunting may not cause the same response as regular hunting would...

The much-publicized decline in coyote numbers in (some areas of) Yellowstone was a straightforward case of direct competition and intraspecifc aggression.

The state of coyote ecology before 1995, like everything with Yellowstone, is an unusual scenario. The coyotes of the park had been without competition for ~ 50 years. Animals on the northern range had responded by running in groups (~packs) and generally dominating the landscape at their trophic level. The behaviour and abundance of coyotes was influenced by (a) protection from human persecution,( b) lack of natural competition and (c) a very productive landscape.

Then, accompanied by lots of parkies, politicos and cameras, the wolves bolted from their acclimating pens (well, they actually had to be pushed out).  They immediately set about correcting this ecologically unique state of affairs:  they shredded unwary or overconfident coyotes, including excavations of dens to kill entire litters of coyote pups.

A commonly used figure in the literature is that ‘coyotes declined 50%’. This is in reference to one well-studied area of the park, not park-wide, and without going in to personality-riddled detail, I can say that figure continues to be a source of great debate.

Putting aside quantitative rigor and high drama, there was indeed a decline in coyotes following wolf reintroduction - that much is obvious. Aside from chasing and killing adults and pups with abandon, wolves hit coyotes where it really hurt – resources. The resources (speaking mostly of ungulates) that coyotes were able to control in the absence of wolves were suddenly reduced. The wolves not only killed ‘em on sight, but they ate a lot of their food! It’s hard to see coyote fecundity maintained, much less increased, under that scenario. That is likely the key to effectively reducing (but note:  still not eradicating) coyotes.

Notably, this is where we as humans have been unable to strike coyotes. We can’t deprive coyotes of a resource base because we <i> generate coyote resources wherever we go</i>. That is why they’ve expanded so much. Coyotes, much like white-tailed deer, are able to exploit the highly modified landscapes which characterize humanity. We pave the way: we remove competition, bring in yummy (and stupid) livestock species and pets, throw out garbage and create dumps.

So we arrive at the big differences between human hunting and natural competition:

1)    competing predators kill each other relentlessly:  there is no off-season, no quota, no rules of fair play. They pursue each other nonstop, day and night, 365 days a year, in places where no hunters would venture – places far from roads and in swamps and brush so thick it forces you to tunnel through on your hands and knees. We could try to seek them out across the landscape and attack them like that, but can you imagine the cost and effort? How many folks can sniff out coyote dens on the island and dig them up with a shovel?

2)    coyotes thrive in the landscapes we create for ourselves, utilizing the stuff we bring with us and the waste we throw out. No natural predator modifies the world to make life easier for its enemies. Simply by being here, we create coyote habitat.

I'm also interested in details about coyote extinctions. Even cases of experimental coyote extirpations aren't all that common, although small-scale programs have succeeded  - with unsustainably high effort (i.e, the National Bison Range in Montana). Extinctions?
The USDA is the main federal agency dedicated to coyote control through APHIS via their Animal Damage Control (or 'Wildlife Services' as it is now euphamistically known) program, although other agencies participate as well.

Several studies and agency programs have documented increased litter size and frequency in response to high coyote mortality in the midwest. Also, as trappers know, heavy pressure trapping and shooting the song dogs serve to weed out the less wary animals quickly. Sneakier critters having more babies - hence the term 'supercoyote'.

History teaches us a simple lesson, but one that's hard to swallow. Humanity, using 1800s technology, eradicated one of the most numerous animals on the planet:  the passenger pigeon. And we came frighteningly close with several virtually uncountable species of African grazer and the American bison. We removed wolves from the lower 48 rather easily. And had we not chosen to stop, most species of commercially valuable whales - some of the largest beings on the planet - would be gone.

Now, realize that the US has spent, conservatively, tens of millions of dollars (in FY 2008, WS spent $30 million on livestock protection, of which 50% is blamed on coyotes) over the last 150 years on coyotes. They've been bountied, baited, shot from the ground and the air, poisoned, set on fire, trapped and who knows what else. And yet we have never even come close to hastening the extinction of the coyote in any meaningful way. They’re arguably doing better than they were 50 years ago.

Agency trend data has revealed that, in some areas of the US, an estimated 70% of the adult population (> 1 year old) has been removed on a recurring basis with no detectable change in coyote density. Even if that's an overestimate, it's astounding.

It's certainly theoretically possible to clean them out of a localized area; maybe even an entire island. The radical effort needed is intense, long-term and astronomically costly. It simply isn't currently feasible to try to completely eradicate coyotes.

The remaining choice is to live with them. Living with any predator is a complicated but achievable balance, the nitty gritty being species-dependent (wolves, cougars, coyotes, bears). With coyotes and Newfoundland, we’ll have to keep trying and see what works best. Management tools like hunting and trapping will hopefully become more effective over time, and new options to control their numbers may become available. Overall, the best option is to use successful and cost-effective methods to control them, not throw money away trying to get rid of them.

I agree, it has been proven in other provinces and the US, that coyote numbers are kept in check by the wolf. This is just more reason to bring the good old wolf back to the Island.

Unlike the coyote which benefits from farm land, the wolf will usually avoid humans if it can.

Bring back the wolf!