TY - JOUR
T1 - Discrete event versus continuous approach to reproduction in structured population dynamics.
AU - Kooi, B.W.
AU - Kooijman, S.A.L.M.
PY - 1999
Y1 - 1999
N2 - The governing equations are derived for the dynamics of a population consisting of organisms which reproduce by laying one egg at the time, on the basis of a simple physiological model for the uptake and use of energy. Two life 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 model for the life history of the individuals, a physiologically structured population model for a rotifer population is derived. On the basis of this discrete event reproduction population model a continuous reproduction population model is proposed. The population model together with the equation for the food result in chemostat equations which are solved numerically. We show that for the calculation of the transient population dynamic behaviour after a step-wise change of the dilution rate, an age structure suffices, despite the size and energy structure used to describe the dynamics of the individuals. Aggregation of the continuous reproduction population model yields an approximate lumped parameter model in terms of delay differential equations. In order to assess the performance of the models, experimental data from the literature are fitted. The main purpose of this paper is to discuss the consequences of discrete event versus continuous reproduction. In both population models death by starvation is taken into account. Unlike the continuous reproduction model, the discrete model captures the experimentally observed lack of egg production shortly after the step change in the dilution rate of the chemostat.
AB - The governing equations are derived for the dynamics of a population consisting of organisms which reproduce by laying one egg at the time, on the basis of a simple physiological model for the uptake and use of energy. Two life 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 model for the life history of the individuals, a physiologically structured population model for a rotifer population is derived. On the basis of this discrete event reproduction population model a continuous reproduction population model is proposed. The population model together with the equation for the food result in chemostat equations which are solved numerically. We show that for the calculation of the transient population dynamic behaviour after a step-wise change of the dilution rate, an age structure suffices, despite the size and energy structure used to describe the dynamics of the individuals. Aggregation of the continuous reproduction population model yields an approximate lumped parameter model in terms of delay differential equations. In order to assess the performance of the models, experimental data from the literature are fitted. The main purpose of this paper is to discuss the consequences of discrete event versus continuous reproduction. In both population models death by starvation is taken into account. Unlike the continuous reproduction model, the discrete model captures the experimentally observed lack of egg production shortly after the step change in the dilution rate of the chemostat.
U2 - 10.1006/tpbi.1999.1416
DO - 10.1006/tpbi.1999.1416
M3 - Article
SN - 0040-5809
VL - 56
SP - 91
EP - 105
JO - Theoretical Population Biology
JF - Theoretical Population Biology
ER -