Update, 1/21/2016, Petition to Prohibit Wildlife Killing Contests in Minnesota.
To keep things simple, this Petition stated its case without referring to the source literature. That's okay if you know where to find it, but here a couple of references and summaries, in case they're helpful. If I've made any errors in the summaries, those errors are mine alone, and I'll be happy to correct them.
The article about the responses of coyotes to food availability and "exploitation" (Gese 2005) describes a seven-year study by USDA Wildlife Services in southeastern Colorado. The "exploitation" was the large-scale killing of coyotes in 1987 and 1988 (44%-75% mortality) in one of the study areas. The "response" of the coyote population to the "exploitation" was that the surviving coyotes kept their same territories, but had smaller packs, younger average age, younger reproductive age, double-size litters, and more female pups than male pups. The population recovered to its original size in about eight months. There were no livestock in the study area (the favored prey of the coyotes was rabbit), so this study didn't learn about possible effects on livestock depredation.
The article about the effects of wolf-killing programs on livestock depredation (Wielgus and Peebles 2014) describes 25 years of data in Idaho, Montana and Wyoming. As expected, in years when there were more livestock or more breeding wolf pairs, there was more depredation. However, counter to the goals of the wolf-killing programs, it turned out that (unless wolf mortality caused by man was more than 25% each year) when more wolves were killed, there was *more* livestock depredation the next year. Of course, the purpose of those programs was to *lower* depredation, not increase it. But that's not what happened; go figure. Or keep reading about the predictable effects of fractured pack structure: more breeding wolf pairs, and more livestock depredation. And the expense: "mortality rates exceeding 25% are unsustainable over the long term." Programs like that cost a lot already, and stepping them up to higher levels of destruction would cost even more--financially and ecologically. So the wolf-killing programs aren't such a great idea. The authors recommend non-lethal controls backed up by targeted removals as necessary. Non-lethal controls remove attractants and add deterrents to keep predators away from livestock. They can include fencing, fladry, lights, rotational grazing, predator-resistant groups, livestock guardian animals, electronic alarms, range riders, carcass disposal, etc.
== References ==
Gese, Eric M. 2005. "Demographic and Spatial Responses of Coyotes to Changes in Food and Exploitation." In Wildlife Damage Management Conference, 271–85. USDA, APHIS, Wildlife Services.http://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1118&context=icwdm_wdmconfproc
Wielgus, Robert B., and Kaylie A. Peebles. 2014. "Effects of Wolf Mortality on Livestock Depredations." PLoS ONE 9 (12): e113505. doi:10.1371/journal.pone.0113505.http://dx.doi.org/10.1371/journal.pone.0113505