# Seminar "Modelling in biology" - Vincent Calvez

The next ** "Modelling in biology"** meeting will take place **the 27th of January at 4pm**. This time the seminar will held in the salle des thèses.

The speaker will be Vincent Calvez from the maths lab of the ENS:

## Quantitative methods for population dynamics

"I will present three case studies in population dynamics for which we have developed quantitative methods based on the theory of large deviations.

1) Concentration waves of swimming bacteria. I will briefly explain how we can compute the speed and the velocity distribution of chemotactic waves of bacteria in a dedicated kinetic model.

2) Accelerated propagation of an invasive species as a consequence of dispersal evolution (and spatial sorting). Here, we couple ecological and evolutionary aspects in the same model for an invasive species over large time scales. We compute the rate of expansion which occurs faster than linearly, contrary to classical models for invasive species.

3) Maladaptation of an age-structured population in a changing environment. We focus on the interplay between demography and evolution in a simple model for an age-structured population. The phenotypical trait acts on the mortality rate, and it is age-specific. Moreover, the optimal trait moves linearly in time, due to environmental change. In the case of an age at onset, we show that there is a critical speed for the optimal trait which characterizes complete maladaptation.

I will emphasize the methodological aspects. I will show how the analysis of the three problems rely on similar mathematical tools."