Discrete event versus continuous approach to reproduction in structured population dynamics

The governing equations are derived for the dynamics of a population consis ting of organisms which reproduce by laying one egg at the time, on the bas is of a simple physiological model for the uptake and use of energy. Two li fe stages are assumed, the egg and the adult stage where the adults do not grow. These assumptions hold true, for instance, for rotifers. From the mod el for the life history of the individuals, a physiologically structured po pulation model for a rotifer population is derived. On the basis of this di screte event reproduction population model a continuous reproduction popula tion model is proposed. The population model together with the equation for the food result in chemostat equations which are solved numerically. We sh ow that for the calculation of the transient population dynamic behaviour a fter a step-wise change of the dilution rate, an age structure suffices, de spite the size and energy structure used to describe the dynamics of the in dividuals. Aggregation of the continuous reproduction population model yiel ds an approximate lumped parameter model in terms of delay differential equ ations. In order to assess the performance of the models, experimental data from the literature are fitted. The main purpose of this paper is to discu ss the consequences of discrete event versus continuous reproduction. In bo th population models death by starvation is taken into account. Unlike the continuous reproduction model, the discrete model captures the experimental ly observed lack of egg production shortly after the step change in the dil ution rate of the chemostat. (C) 1999 Academic Press.