Johnson's conjecture on realizability of critical points

Let $\Lambda=\{\lambda_1,\dots,\lambda_n\}\subset\mathbb{C}$ with $n\ge 2$ be a list, let

$$p(z)=\prod_{i=1}^n(z-\lambda_i),$$

and let $\Lambda'=\{\mu_1,\dots,\mu_{n-1}\}$ be the list of zeros of $p'$. A list is realizable if it is the spectrum of an entrywise nonnegative matrix. Johnson's conjecture. If $\Lambda$ is realizable, then $\Lambda'$ is realizable. This conjecture asks whether realizability is inherited by the list of critical points of the polynomial whose roots form a realizable list. Its resolution is not indicated in the supplied text.