Regulation of Populations with Nonoverlapping Generations by Microparasites: A Purely Chaotic System

Consider a plant or animal population with discrete, nonoverlapping generations whose density is regulated by a lethal pathogen that spreads in epidemic fashion throughout each generation before the reproductive age is attained. Surprisingly, this simple and deterministic system has no stable point and no stable cycles, but rather exhibits chaotic dynamics (in other words, the map relating the magnitude of the population in generation t + 1 to that in generation t has a truly ergodic invariant measure). The model has pedagogic interest as an example in which simple and natural assumptions lead to purely chaotic dynamical behavior. This population model, with its relatively transparent dynamics, also helps us to understand how the frequency- and density-dependent effects that pathogens can introduce in the population genetics of host-parasite associations can be exceedingly complicated, and can lead to polymorphisms that vary chaotically.