Numerical methods and parameter estimation of a structured population model with discrete events in the life history
Kelpin F.D.L, Kirkilionis M.A, and Kooi B.W.
Numerical methods and parameter estimation of a structured population model with discrete events in the life history.
J. Theor. Biol. 207: 217 - 230
We consider two numerical methods for the solution of a
physiologically structured population (PSP) model with multiple life
stages and discrete event reproduction. The model describes the
dynamic behaviour of a predator-prey system consisting of rotifers
predating on algae. The nitrate limited algal prey population is
modelled unstructured and described by an ordinary differential
equation (ODE). The formulation of the rotifer dynamics is based on a
simple physiological model for their two life stages, the egg and the
adult stage. An egg is produced when an energy buffer reaches a
threshold value. The governing equations are coupled partial
differential equations (PDE) with initial and boundary conditions. The
population models together with the equation for the dynamics of the
nutrient result in a chemostat model. Experimental data are used to
estimate the model parameters. The results obtained with the explicit
finite difference (FD) technique compare well with those of the
Escalator Boxcar Train (EBT) method. This justifies the use of the
fast FD method for the parameter estimation, a procedure which
involves repeated solution of the model equations.