Monte Carlo Simulation of Age-Dependent Host-Parasite Relations

The death of a biological population is an extreme event [1] which we investigate here for a host-parasitoid system. (Parasites let the host survive, parasitoids eventually kill the host. In the following both are called parasites.) For seasonal hosts (plants or animals) the parasites can survive only if they parasitise the right developmental stage (egg, larva, pupa, imago) of their host. Therefore they have to attack their host at the right time, i.e. at the right age of the host or the respective right month of the year [2]. Earlier the host has not yet accumulated enough resources, unsuitable for an attack of a parasite. Biological evolution thus should ensure that the parasites “know” what the proper age of the host or time of the year is. The present note aims to check if such an evolutionary self-organization can be simulated; we do not deal with the process how the parasites recognise the age of the host or the month of the year. One example are diversified host-parasite-systems: Endoparasites deposit their eggs in the interior of the host animal, and thus in case of young host larvae for example they have to wait until the host has developed enough. Then they compete with ectoparasites attacking the host animal from the outside. Thus the consideration of the age of the individuals is important, similar to the ’just in time’ philosophy in logistics. We will simulate both fluctuations in equilibrium (normal case), and possible extinction (extreme event) and thus will find the border between extinction and survival. We use the standard asexual Penna ageing model of mutation accumulation, with reproduction starting an age of 8 time intervals, using a “genome”