The effect of the organisms' body size and energy reserves in models for population dynamics

We present two models suitable for describing dynamics of a population of unicellular organisms residing in chemostat. These models are based on biologically motivated Dynamic Energy Budget (DEB) theory and take into account the dynamics of mean energy reserves and body length of organisms in the population. The difference between the models is in the construction of the reproduction rate. In model A it is the ordinary reproduction rate used in DEB theory. In model B it is adjusted to take into account a saturation effect in the dynamics of mean body length. Our modeling approach is illustrated by considering population of E. coli developing in the chemostat. We consider realistic situations of growth of population of E. coli at fixed and varied environmental and biological factors. We show that unlike model B in model A the dynamics of body length does not affect directly population development. Nevertheless, taking such dynamics into account is essential in both models since it provides additional constrains to population development. The models can be easily extended to include description of individual characteristics other than body size (e.g., reproduction rate, mortality rate). The models predict two types of transient dynamics: one type is similar to that in a logistic model; the other type is damped oscillations. The essential difference between the models is that model B better predicts the extinction threshold of the population.

Duke Scholars

Author Alexander Kulminski Social Science Research Institute

Author Kenneth G. Manton Trinity College of Arts & Sciences

Author Igor Akushevich Social Science Research Institute

Author Anatoli I. Yashin Social Science Research Institute