The integration of theory and experiment in the study of predator—prey dynamics

It has been known for a long time (D’Ancona, 1926) that when the populations of two species are principally controlled by one of the species preying upon, and consequently being dependent upon, the other, both populations tend to fluctuate. While the maxima of the predator population occur somewhat after those of the prey, the intervals between maxima are approximately the same for both populations. Lotka (1920) and Volterra (1931) independently proposed the so-called Lotka-Volterra equations which appear to be the simplest plausible model for such prey-predator interactions. These equations do not have known analytical solutions, but it has nevertheless been shown by Goel et al. (1971) that the solutions are at least qualitatively correct in that they are all oscillatory, with N 1 and N 2 having the same period but out of phase.