Populations characterized by either a continuous physiological age structure or by a discontinuous stage structure are illustrated. The dynamics of these populations is described in terms of the main biological processes determining the life history of an individual: development, reproduction and mortality. In general, the average values and the standard deviations of the rates of these processes depend on time through the environmental variables (temperature,...) and food; furthermore, some of them may depend on the overall population size, which gives rise to a feedback on the population growth. Both deterministic and stochastic models for the population dynamics can be formulated in Eulerian or Lagrangian approachs.
In the Eulerian formalism, balance evolution equations are written for the physiological age distributions (Von Foerster equations in the deterministic case, and Fokker-Plank equations in the stochastic case).
In the Lagrangian formalism (random flights, Monte Carlo formulations) the dynamics is obtained by means of a model, in general stochastic, describing the time evolution of the life history of an individual. The dynamics of the overall population (i.e. the time evolution of the  stage-physiological age distributions) is obtained by performing numerical
simulations of the life histories of all the individuals.
Comparisons of the dynamical responses of the models are obtained from the analysis of the results of the numerical simulations, for different situations of the biological system, depending on environmental conditions and food. Numerical results obtained by means of Lagrangian models are supported by a theoretical analysis of Eulerian equations.

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