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Individual-based models: formulation of development equations and computational aspects
Giuseppe Buffoni, Sara Pasquali
ENEA - Santa Teresa
giuseppe.buffoni@santateresa.enea.it(Abstract received 03/08/2005 for session A)
ABSTRACT
The individual-based models (IBMs) track all the individuals in a population. In this Lagrangian modelling approach, the dynamics of the overall population is obtained by performing numerical simulations of the life histories of the individuals. The status of an individual (the individual state variable) is individuated by a physiological age which can be defined in terms of biometric descriptors (such as a characteristic length, a weight) or by the percentage of development. The model equations describe the time evolution of the status of an individual, i.e. its life history, which is assumed completely determined by the main biological processes. We assume that the individuals belong to a stage -structured population, where the stages are defined by sharp biological events and address our analisys only to the main biological processes of development (growth), reproduction, and mortality. The individual state variable, i.e. the physiological age of an individual, considered as a stochastic process, is defined as the percentage of development in a stage. The development of an individual is regarded as an accumulation of small increments of physiological age over time. These increments are given by the contributions of a deterministic term, due to the stage-specific mean development rate, and of a stochastic term, due to the variability of development time among the individuals. When regression effects are not allowable in the development process, the stochastic term must assume only non negative values. Different formulations of the development equations of an individual are illustrated. They are based on various distributions (normal, gamma, beta) of the stochastic term. A comparison of the development schemes is performed, by means of theoretical analysis and numerical experiments. Some computational aspects regarding the choice of time step, probability distribution and averaging procedures of the realizations of the overall population dynamics are illustrated.
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2005 LAPCOD Meeting, Lerici, Italy, June 13-17, 2005