Title: Population dynamics, from qualitative modelling to experimentally validated models
Abstract: To model population dynamics, structured population equations have been developed and know a long-lasting interest in the mathematical community for more than sixty years. They describe a population dynamics in terms of well-chosen traits, assumed to characterize well the individual behaviour. More recently, thanks to the huge progress in experimental measurements, the question of estimating the parameters from individual-based or population measurements also attracts a growing interest, since it finally allows to compare model and data, and thus to validate - or invalidate - the "structuring" character of the traits. However, the so-called structuring variable may be quite abstract ("maturity" replacing age), and/or not directly measurable (such as a complex network of proteins), whereas the quantities effectively measured may be linked to the structuring one in an unknown or intricate manner. We can thus formulate a general question: is it possible to estimate the dependence of a population on a given variable, which is not experimentally measurable, by taking advantage of the measurement of the dependence of the population on another - experimentally quantified - variable? In this talk, we give first hints to answer this question, and as a telling example we apply it to the growth and division of bacteria, for which we review three types of models: the timer model / age-structured equation, the sizer model / growth-fragmentation / size-structured equation, and the adder model / "increment of size"-structured equation.
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