Ok so predators numbers are the same, your saying if we have more of one another fills the void. Say you decrease coyotes and bobcat fill their place, or less bear and they are replaced with say coyotes. So if this works with predators, it should also apply to prey. I know you always say I do not understand how nature works and that it is prey that controls predator numbers. So if we lose quail does this mean more grouse? Or less hare, does this give us more rabbits, or when we have less pheasants do grouse numbers go up, or less muskrat do the rabbits increase? In my lifetime all I have personally seen was a decrease in prey animals, or am I not remembering correctly, or not getting out there enough?Obviously you once again either missed the entire point or just refuse to accept anything that isn't the way to believe it should be even when all the evidence proves you are wrong. Must be those reading comprehension skills again?
The point was, and the facts are, that when coyote numbers increased the fox, raccoon, mink and weasel numbers declined. So even though you had more coyotes you had fewer of the other predators preying on small game. So, you did not end up with any more predators in the past decades than you had back in those old days. The most common predator species might have changed some but the number of predators or the amount of prey they consumed has not changed.
As for why some species appear to have declined there are many reasons for that.
First of all many of us have not seen the degree of species decline that some profess has occurred. One of the reasons is simply that people's memories just aren't as accurate as they think they are. Without keeping good records you can easily be mistake on game sightings and game harvest from the "good ole days" to today. I became acutely aware of that fact while doing annual wildlife survey routes many years ago. While doing the same route during the same time period year after year it seemed like every year I thought I was seeing less than I had seen in prior years. But, at the end of the survey period and I would be compiling the actual numbers and comparing them to prior years it was common to discover that I was mistaken and had seen about the same number or even more than I had seen in prior year. That is why I have since always kept a log of the number of hours I spend hunting in each season and what I saw. That too hasn't changed much over the past several decades for most species. Grouse and turkey are the two exceptions to that but I also know there are factors way beyond predation that have affected the populations of those two species.
As for what can be done to help improve game sightings.
The first is to start keeping an accurate log of time afield and what you actually saw verse what you think you saw and be able to compare past reality to a past remembered.
Then the second best thing you can do to improve any wildlife population is to study it, learning what habitat it needs, what is most lacking in those needs then set out to improve those most needed habitats.