In short terms: They don't. However, in many cases there are clear logical deductions to make based on previous experiments or observations in similar communities. Sometimes they also do field experiments where they fence off areas, keeping the predators out and "seeing what happens".
You should also be aware that predators aren't always necessary for prey to maintain healthy populations, but rather that this can be the case in certain communities, especially ones affected by top-down control (e.g. predator numbers decline, their prey boosts in population, the plants they eat get grazed to small numbers, another type of plant gains dominance, and the plant they used to eat gets outcompeted by the new plant, the grazing animals no longer have any food and get a severe population reduction due to starvation).
false
They are not limited by natural predators
Their populations increased.
The jaws are necessary for chewing/biting food and killing prey (need for food). The limbs are necessary for ambulation (moving) (need to escape predators or find food). The teeth are necessary for defending oneself from predators and kill/eat food (need to escape predators and eat food). The eyes are necessary for evading predators and finding food (need to escape predators and find food).
One factor that can affect the populations in an ecosystem is that, if an ecosystem had owls with no predators, the owl population would increase and eat all the mice in the ecosystems. The population of the mice would decrease more and more.
The predators keep prey populations balanced.
The predators keep prey populations balanced.
The predators keep prey populations balanced.
false
They are not limited by natural predators
It is very important, because they contol the populations of their prey.
Parasites
Owls are typically the top predators in an ecosystem, eating mice, etc. Predators are needed to regulate the other populations and keep the ecosystem at equilibrium.
lacks natural predators or competitors in the new environment, leading to unchecked growth.
When the number of preys decreases, the predators can't get enough food and their population is decreasing too. During long periods of time the populations are balanced so that predators can be fed and preys don't go extinct.
Their populations increased.
Bobcats are apex predators. They usually don't have any other predators that hunt on them. However there have been known cases where large Coyote populations have affected the number of bobcats in the area. This suggests that during conflicts Coyotes can attack and even kill them.