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Predators eat their prey, prey population decreases. This results in the predator population to decrease, so less prey are consumed which causes the prey population to increase.
Therefore, if the reduction in prey population results in its increase then can this be described as negative feedback?
From my experience, "negative feedback" is more often used in the context of processes in the body which attenuate themselves or in the context of stimuli and sensors. However predator-prey dynamics could fit the general definition of the term. In general, negative feedback is just when a process or output of a system leads back into the system to attenuate itself.
Negative Feedback:
"A feedback in which the system responds in an opposite direction to the perturbation. "
In a general case of a closed-loop (feedback) control system, you've got a stimulus that gets sensed by a sensor, which sends a signal to a controller. The signal is then passed on to an effector, which can change the original stimulus. In the case of negative feedback, the stimulus is attenuated. In positive feedback, it is potentiated.
$$\begin{array}{ccc} \fbox{Stimulus}&\rightarrow&\fbox{Sensor} \\ \uparrow&&\downarrow \\ \fbox{Effector}&\leftarrow&\fbox{Controller} \end{array}$$
A common example of this would be high body temperature being detected by neurons, which send a signal to the brain to cause the body to sweat more. In this case, the sweat glands are the effectors and can lower the body temperature.
$$\begin{array}{ccc} \fbox{Change in body temp.}&\rightarrow&\fbox{Neurons} \\ \uparrow&&\downarrow \\ \fbox{Sweat Glands}&\leftarrow&\fbox{Brain} \end{array}$$
In your case, I think you could describe it with an increase of prey population being the stimulus, which is detected by the predators as they see more prey. The predators would then choose to eat the prey (I suppose this could be the controller) and then act as the effector by eating the prey (and thus, reducing the prey population). Though I'm a little iffy on this since you'd have the predator acting as both the sensor, controller and the effector. Conversely, if the prey population were lowered, the opposite would be true.
$$\begin{array}{ccc} \fbox{Change in prey pop.}&\rightarrow&\fbox{Predators sense prey} \\ \uparrow&&\downarrow \\ \fbox{Predators eat prey}&\leftarrow&\fbox{Predators choose to eat prey} \end{array}$$
Yes, in the fields population dynamics/ecology, the standard predator-prey system is routinely described in terms of a negative feedback loop. See e.g. Lewontin & Levins, 2007 for an online exemple (the term is commonly found in articles and textbooks though).
