Concavity conjecture for the dispersal-induced growth transition curve

Assume $\bar{r}_1<0$, $\bar{r}_2<0$, and $\chi>0$, and let $m^*>0$ be the threshold from the sink-sink result. For $m\in(0,m^*)$, let $\omega_{crit}(m)$ denote the transition frequency at which the relevant Floquet exponent vanishes, so that dispersal-induced growth occurs below this curve. Concavity conjecture. The function

$$\omega_{crit}:(0,m^*)\rightarrow(0,\infty)$$

is concave. The curve is the numerically observed upper boundary of the dispersal-induced growth region; its concavity is not established analytically in the source.