7 problems

Champagnat–Bovier's dimorphic-state conjecture. As $(K,\mu_K,\sigma_K)\to(+\infty,0,0)$,

Champagnat–Bovier's fast-branching conjecture. If $\partial_{22}f(x^*,x^*)>\partial_{11}f(x^*,x^*)>0$, then there is fast evolutionary branching: for some $\varepsilon_0>0$, every…

Mutation-scale conjecture. The assumption $\sigma \ll K^{-(2+\varepsilon)}$ is too restrictive and can be weakened to

Unique convergence-stable diffusion-rate conjecture. For each advection rate

Consider the model's functions $\beta_{m,n}$, with $\delta,C,\alpha,\tau,\kappa$ and $\sigma$ fixed and $p\in(0,\tfrac{1}{4})$. The observed qualitative behaviours include cyclic b…

The model describes bacterial populations with mutation, dormancy and transfer, in which traits that can become unfit are also capable of entering dormancy. Evolutionary suicide is…

Let $u=u(t,x,\mathbf y)$ be a population density structured by a phenotypic trait $\mathbf y\in\Omega\subset\mathbb R^k$, with $k\geq1$, satisfying … Here $\rho$ is the total popul…