Let $\text{JSD}(P\mid\mid Q)$ be the Jensen-Shannon divergence (https://en.wikipedia.org/wiki/Jensen-Shannon_divergence) between two probability distributions $P$ and $Q$.
Question: Is $\text{JSD}(P\mid\mid (1-\alpha)P+\alpha Q)$ a monotone increasing function of $\alpha$ for $0\le\alpha\le 1$?
My numerical simulations seem to suggest so, but is this a well-known result? Or is there a counterexample?