Abstract: Often when modelling population processes the initial state is not known with certainty. Here we outline a general method for incorporating random initial conditions in population models where a deterministic model is sufficient to describe the dynamics of the population. For a large class of models we show that the overall variation is composed of variation due to random initial conditions and variation due to random dynamics, and thus we are able to quantify the variation not accounted for when random dynamics are ignored. We begin by reviewing some results of Tom Kurtz, which allow one to quantify variation in density-dependent population models.
This is joint work with Anthony Dooley (ARC Centre of Excellence for Mathematics and Statistics of Complex Systems, and The University of New South Wales) and Joshua Ross (University of Warwick, United Kingdom)
Acknowledgement: This work is supported by the ARC Centre of Excellence for Mathematics and Statistics of Complex Systems
Last modified: 4th July 2007