Critical-selection conjecture for interacting Wright–Fisher diffusions

Consider the system of interacting Wright–Fisher diffusions on $\mathbb Z^d$ with $N=1$ and parameter $\mu>1$, where $s$ is the selection parameter and coexistence refers to long-term coexistence of the two types. Critical-selection conjecture. There exists a critical value $s_0\geq 0$ such that there is coexistence for $s>s_0$ and non-coexistence for $s<s_0$. The conjecture concerns balancing selection and is motivated by an existing large-selection coexistence result, while the full resolution remains open according to the authors.