Qualitative behavior of stage-structured populations: application to structural validation

The transient behavior of a class of nonlinear differential systems representing stage-structured populations is studied. The qualitative dynamics are described in terms of succession of extrema for the state variables, or for the integrated difference between two trajectories. The rules giving the possibilities of extrema are derived, they characterize the classical stage-structured models. These rules can be compared with experiments to validate the structure of the model. An explanation for the disagreement of this transition scheme with some experiments could be an unexpected interaction with another variable. A new model taking the interaction into account thus engenders new transition rules, which are to be compared with experiments. These results are illustrated with experiments on copepods, showing how the qualitative experimental features can help the construction and the validation of the models.