David Peat

From Clockwork to Chaos 127but soon they are eating the vegetation as fast as it can grow. Like thepike that eat too many trout, the rabbits begin to die out.There are two competing factors at work on the population, onecausing it to expand by breeding and the other causing it to die offbecause of limited space in which to live and limited food to eat. Likethe example of the pike and trout, population size is determined by aniterative situation because young rabbits of one season become thebreeding pairs of the next. It turns out that the mathematical equationthat models this behavior is quite simple and, provided you put in avalue for the birth rate, the population can be predicted for years andyears to come.To explore this example even further we must now forget aboutreal rabbits and deal with hypothetical computer rabbits whose birthratecan be adjusted as we choose. Real rabbits don’t work in this way,unless they are given hormones, but the example itself applies to a hostof other real-life situations, from the spread of rumors and the distributionof genes in a population to certain chemical reactions and insectdamage to crops.With a low birthrate the initial pair of “rabbits” breeds and thepopulation increases until it reaches a stable level that remains staticfrom generation to generation. This population is exactly in balancewith the resources of the island. It is the stable sustainable populationfor that particular environment.With a higher birthrate the population increases more rapidly,temporarily overpopulating, then falling again, and after a time risingagain. The result is a stable oscillation in population size, a predictablesequence of fat and lean years that exactly mirrors the behavior of pikeand trout in a lake.But suppose the birthrate is higher still. The result of a mathematicalanalysis shows that within the first oscillation of fat and lean yearscan be found a second oscillation, a subcycle, a cycle within a cycle. Itnow takes four turns of the cycle to come back to the starting point.Increasing the birthrate even further means that new oscillationsare added. Now it is a case of wheels within wheels within wheels, oroscillations within oscillations within oscillations. The situation becomesincreasingly complex; population scientists would have to gather