How do the behavioural interactions between individuals in an ecological system produce the global population dynamics of that system? Wepresent a stochastic individual–based model of the reproductive cycle of the mite Varroa jacobsoni, a parasite of honeybees. The model has the interesting property in that its population level behaviour is approximated extremely accurately by the exponential logistic equation or Ricker map. We demonstrated how this approximation is obtained mathematically and how the parameters of the exponential logistic equation can be written in terms of the parameters of the individual–based model. Our procedure demonstrates, in at least one case, how study of animal ecology at an individual level can be used to derive global models which predict population change over time.