I was never a wildlife management major, but my academic adviser for 2 years is a relatively famous one, and I shared lab space with his students doing wildlife population modeling and took the courses on that area (and co-taught one). I also did similar enough research that I am comfortable speaking about mathematical ecology.
The logistic (S-curve) is often assumed to be a starting point to model density-dependent population growth over time. It is basically taking exponential growth (like how we know viruses take off in the body, where the more viruses there are the more can reproduce....so successive doubling makes the population start exploding).....but the exponential growth is hampered by an estimated carrying capacity (K).
Check out this S-curve here.
courses.lumenlearning.com
Now, looking at the graph, think of plotting population Vs population growth rate. That would be taking the value on the y-axis and making it the x-axis and making the y-axis the slope of the logistic growth line at that point. It looks like a snow globe where maximum population growth is in the middle where you have plenty of coyotes to reproduce (in this case) and you are relatively far from the carrying capacity.
This is called maximum sustainable yield (MSY) (figure 2). The high point on the "snow globe" is at the population where you get the really steep section on the logistic curve.
https://en.wikipedia.org/wiki/Maximum_sustainable_yield
This model makes some assumptions about boundaries (that animal migration is a net zero across the boundary). You have to make the model more complex to take into account migration as a result of various changes, hunting, etc.
Hunting will never increase their numbers beyond the carrying capacity of that particular piece of land (given everything else about it). However, if the 'yotes are to the right of that high point on the MSY curve, then killing some at some rate per year can increase their growth rate, but it will not increase their population. The trick is not confusing population size vs. population growth rate (number of new 'yotes per reproductive female). Even if the population is fenced in, killing some each each year will never increase the total population in that area. It might increase growth rate (if you are to the right of your hump on the curve) but will not increase total population. The amount you take to increase the growth exceeds the amount of increased growth.
The trick is for folks (one savage or several mini-savages) to kill enough to get to the left on that MSY curve. The coyotes are far from carrying capacity but they just don't have enough population to where doubling the population is a worry (4 going to 16 in one season is no comparison to going from 200 to 400).
Hunting coyotes in some area (a single WMA) will not increase the population within it based upon basic approaches. Will it disperse coyotes? It's definitely possible. Will that increase population outside the area you are hunting? Maybe.
I would have to dig into field research of coyotes. I just know that a writer in some hunting magazine might get some of the points I outlined wrong. The science behind predators helping ecosystems has to do largely with increasing total species diversity and not helping their prey items.