As anyone who lives among coyotes can tell you, its a master of adaptation. Coyotes have flourished in part by exploiting the changes that people have made to the environment, but their adaptability goes back further than that.
Let's look at the coyote's skull. For a closer look at coyote skull anatomy, you can see Skullduggery here.
If you dial back 6 million years ago, (And for the record, that's not that long ago, our ancestors were just parting with chimps then,) carnivores had a lot of competition. If you jump through the various ice ages, you'll note that our modern coyotes are puny, fun sized creatures compared to their ancestors.
The wake of the climatic changes that began about 6 million years ago benefited those of the lupine lineage. The world was drying out. Forest was being replaced by scrub and savanna. The opening up of grassy plains and the prey that prospered on them also provided opportunity for fast, long legged predators.
But that doesn't mean the whole climate change thing working well for everyone. Those larger prey animals, including megafauna, are dying off.
VONHOLDT, B. M., POLLINGER, J. P., EARL, D. A., KNOWLES, J. C., BOYKO, A. R., PARKER, H., GEFFEN, E., PILOT, M., JEDRZEJEWSKI, W., JEDRZEJEWSKA, B., SIDOROVICH, V., GRECO, C., RANDI, E., MUSIANI, M., KAYS, R., BUSTAMANTE, C. D., OSTRANDER, E. A., NOVEMBRE, J. AND WAYNE, R. K.A genome-wide perspective on the evolutionary history of enigmatic wolf-like canidsIn-text: (vonHoldt et al.)
Bibliography: vonHoldt, Bridgett M. et al. 'A Genome-Wide Perspective On The Evolutionary History Of Enigmatic Wolf-Like Canids'. Genome Research 21.8 (2011): 1294-1305. Web. 24 Nov. 2015.