10 problems

No-surfing conjecture. In the presence of a strong Allee effect, a result analogous to the theorem asserting no gene surfing of deleterious mutations should hold; in particular, de…

Let $\theta_{\textup{min}}$ and $\theta_{\textup{max}}$ be the minimum and maximum Allee thresholds, let $\alpha$ be the mutation parameter, and consider the critical case … Extinc…

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…

Let $\theta_{\textup{min}}$ and $\theta_{\textup{max}}$ satisfy … and let $\alpha$ be the mutation parameter. The outcomes are classified as “E. or P.” when both extinction and per…

Let $(u(x,t),v(x,t))$ be a solution of the reaction-diffusion benthic-drift model, and let $(H1)$ and $(h1)$ denote the conditions defined in the paper. Global extinction conjectur…

Predator-extinction conjecture. The only feature of the dynamics is predator extinction. Numerical simulations suggest this behavior, but its validity remains an open problem.

Consider a one-dimensional reaction-diffusion model with strong Allee effect in which a protection zone has fixed total length $2L$. The connected design is $(-L,L)$, while a separ…

Let $\{x_n\}$ be a positive solution of equation (4ab), and assume that condition (fxp0) holds. Consider its even subsequence $\{x_{2n}\}$ and odd subsequence $\{x_{2n-1}\}$. Parit…

Let $x_0$ and $x_1$ be the initial values of a solution of equation (4a), and let $x^{\ast}$ be the positive fixed point specified in the preceding discussion. Extinction means con…

Consider a system of interacting patches in which each patch is either in state $0$ (empty) or state $1$ (at carrying capacity), and suppose that all patches are connected, so the…