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Abstract
A stochastic model for the dynamics of a single species of a stage
structured population is presented. The model (in Lagrangian or
Monte Carlo formulation) describes the life history of an individual
assumed completely determined by the biological processes of
development, mortality and reproduction. The dynamics of the overall
population is obtained by the time evolution of the number of the
individuals and of their physiological age. No other assumption is
requested on the structure of the biological cycle and on the
initial conditions of the population. Both a linear and a nonlinear
models have been implemented. The nonlinearity takes into account
the feedback of the population size on the mortality rate of the
offsprings. For the linear case, i.e. when the population growths
without any feedback dependent on the population size, the balance
equations for the overall population density are written in the
Eulerian formalism (equations of Von Foerster type in the
deterministic case and of Fokker-Planck type in the stochastic
case). The asymptotic solutions to these equations, for sufficiently
large time, are in good agreement with the results of the numerical
simulations of the Lagrangian model. As a case study the model is
applied to simulate the dynamics of the greenhouse whitefly, Trialeurodes vaporarioum (Westwood), a highly polyphagous pest
insect, on tomato host plants.
Mathematics Subject Classification: 92D25.
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