In an area where there are alot of Eagles and Hawks, they will go back into the food chain very quickly. That has been my experience when I've hunted them for Wildlife/Livestock Damage Control during the spring and summer months.
They are most likely to be picked clean by the big birds of prey if we leave them in the middle of an open field or especially on the ridge tops...........Eagles don't like to be surrounded by cover when feeding........they like to be able to see their surroundings and be able to "catch a wind" to escape.
Just as Farmers spray their crops for pests/bugs..........we Ranchers need to keep the Predators in check to protect our livestock. The majority of coyotes I've got during the spring/summer months are "belly full" of pronghorn antelope or deer......................another reason for Damage Control work.
Before we white man came to this great country, the coyote's only natural predators were the big birds of prey, wolves, bears, (and other predators sometimes when the coyotes are pups) also........starvation/mange/disease. Now, their only natural predators in most of the country; are birds of prey, some other predators and Mange/Disease. This is why they've expanded their range and can now be found in areas where they weren't in the early 1900's.
Supposedly, coyotes control their own litter size based upon the amount of food/prey available in the area and the size of their territory.......they are the ultimate survivor IMO.
Alot of people would have us (and all of America) believe that hunting non edible game should be illegal; but since we humans usually don't control our own "litter size" based on food supply and territory; hunting the hunters has become a neccessity, and maybe "those people" should look in the mirror before looking down their nose at the rest of us???????
Just my 2 cents worth.