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Structured Population Modeling

Biology Master, ENS
Coordination : David Claessen, ENS, Bernard Cazelles, UPMC
Hours : 60 h
Credits : 6 ECTS
Semester : 1st semester
Number of students : 20 max.

Aims : Acquiring the biological and mathematical principles to model the dynamics of structured populations. Applying these principles to the construction and analysis (mathematical, numerical) of models motivated by specific biological questions.

Themes : The physiological or developmental state of individuals is an intrinsic cause of structuring in all populations. When physiological or developmental differences between individuals translate into differences in their birth and death rates, the temporal and spatial dynamics of the population as a whole cannot be understood without taking that structure into account. This course presents the biological concepts and mathematical tools needed to model the dynamics of structured populations. The emphasis is set on structure defined by body size (individuals move across the population structure by growth) or infectious stage (individuals move across the population structure as they interact with a pathogen). Specific notions addressed in the course are : dynamic energy budget, allometries and metabolic theory of ecology, consumer-resource dynamics, escalator boxtrain model, SEIR models, disease prevalence, epidemics and R0 threshold theory.
Computer-based sessions will provide an introduction to simulation tools such as the EBT software and to Bayesian inference methods as MCMC. A significant fraction of classroom time will be devoted to hands-on, individual projects. Enrolled students are expected to have some experience with population and community modeling.

Organization : Two-week intensive course, mornings and afternoons included.
Lecture-style presentations will be complemented by computer-based tutorials. About 50% of the course time will be devoted to individual projects (under the instructors’ supervision) involving the design and numerical implementation of simple models.
Evaluation will be made on the basis of the presentation of the individual projects at the end of the course period.

Teaching team :
David Claessen (ENS, Paris)
Bernard Cazelles (UPMC, Paris)
Eric Edeline (UPMC, Paris)
Nicolas Loeuille (UPMC, Paris)