Besançon Meeting on Probability, Ecology & Evolution 2026

Liste des Contributions

6. Heuristics of the speed of invasion in an advancing population

Several studies have investigated systems of reaction-diffusion partial differential equations (PDEs) in expanding domains with two distinct propagation speeds, one faster than the other. While the faster speed is straightforward to compute, determining the slower one remains challenging. Several PDEs works rigorously establish the so-called ”following travelling wave” speed. The objective...

7. Markov processes forced on a subspace by a large drift, with applications to population genetics

We consider a sequence of Markov processes $X^1,X^2,\ldots$ with state space $E$, where $X^N$ is subject to a strong drift towards a subset $D\subseteq E$, and where $\Phi(X^N)$ evolves on a slower timescale for a suitable map $\Phi:E\to D$. Using the method of martingale problems, we prove a limit theorem showing that, as $N\to\infty$, $\Phi(X^N)\Rightarrow Z$ in the space of càdlàg paths,...

4. On a Branching Annihilating Random Walk

We consider a discrete-time branching annihilating random walk (BARW). Within a
time step, each particle, before dying, produces a random number of offspring which are
then randomly and independently displaced in space. If, after the displacement, a site is
occupied by several particles, all particles at that site are annihilated. This can be thought
of as a very strong form of local...

8. SIR model with immune-escape mutations: recurrent emergence and persistence of the epidemic

We study an individual based SIR-model where the pathogen acquires immune-escape mutations at rate $N^{\alpha}$ per capita, where $N$ is the population size and alpha in $(0,1)$.
In this regime, even when the population is closed and immunity to a strain is permanent, the epidemic can persist thanks to the accumulation of sufficiently many mutations. We derive conditions for persistence of...

9. Slow-fast dynamics of stochastic particle systems arising in telomere biology

The ends of linear chromosomes, called telomeres, shorten at each cell replication, eventually driving the cells to a senescent state when they become too short. The enzyme telomerase, present in cancerous cells and some unicellular organisms, elongates the telomeres and allows cells to continue replicating. Recent experiments show that if this enzyme is inactivated some rare survivors (ALT),...