Theoretical investigation of the dependence of population parameters on initial population size

Abstract

In a series of experiments with yeast, classical dynamical models were fitted to populations that differed only in their initial population size (Pylvänäinen 2005). The results revealed a surprising dependence between estimated growth rate and initial population size. Perceived as an artefact, this undesired relationship was tentatively removed by an ad-hoc procedure. This strategy reflects the usual approach of population models in which parameters are not considered to depend on initial conditions. However, our analysis reveals that the observed relationship between estimated growth rate and initial population size is unavoidable when the dimension of a system is reduced. For the present case, the two-dimensional food-yeast system was reduced to a model for yeast only. The consequence of system reduction questions our conception of one-dimensional population models.

Keywords: Logistic model; Parameter estimation; System dimension; System of differential equations.