Numbers of both predators and prey circle a singular stable point in perpetually balanced imbalance, i.e., neutral limit cycle . The degree of oscillation about the equilibrium point is a function of initial population sizes. Perturbations may eventually result in extinction of prey and predator. Assumptions Unrestricted exponential growth of the prey population in the absence of predators. Environment is homogeneous.
Every prey has an equal probability of being attacked, e.g., no age-based selection.
Prey density has no effect on the probability of being eaten, i.e., a Type 1 functional response. Predator density has no effect on the probability of a predator capturing prey. No time lags. Tanner hypothesized that under certain conditions the relative growth rates of the predator and prey will determine stability of the interactions. Unstable cycle, which leads to extinction of prey and predator.