Okay, I need to put up a disclaimer that I am not serious when talking about "eating" them---yak. LoL
The point I was trying to make is that: running away from predators may be ideal for an individual but not ideal for a tribe or society.
The reason humanity's natural predicators: tigers, wolfs, lions etc ceased to be any threat to us in general was because once upon a time we hunted them down, hunted them really hard, for revenge, for game, for their skins and in some cases also for meat.
If one can find an economic purpose and value for the zombies, then I am pretty sure that in next to no time, zombies will also be hunted down until they are extinct. And they would be one of the easiest things to hunt.
Thanks for bringing this up, as I was just thinking about the zombie apocalypse from a predator-prey dynamic point of view.
Humans are arguably unique in that we can be both prey and apex predator. All other animal species fill only one role when they become adults. Humans can be either, and everything in between. For example, a hunter armed with a rifle is an apex predator. A tourist lost in the woods is prey.
When we look at zombies, we could argue that their natural prey are humans, and their natural predators are also humans. Just different kinds of people. To use the Walking Dead as an example, Lori is prey, Michonne is a predator.
At the beginning of a zombie apocalypse, zombies would have plenty of prey and few predators, especially since few people would know how to deal with zombies. Thus, like all other biological organisms put into such a situation, their population explodes and they rapidly depopulate their prey.
As the ZA progresses, the prey-people die off and the predator-people survive. This means the zombies would find themselves in a situation where prey is scarce and they are more likely to run into predators than prey. Zombie population would then plateau, and one of two things would happen:
1) If zombies can eventually die of starvation, they will face the same fate as any other biological organism in this dynamic: population crash.
2) If zombies do NOT die of starvation, then their population will slowly dwindle as they are taken out by the survivors.