Figure B1.

The first and last local minima of $F_{\mathrm{ST}}$ as functions of the frequency M of the most frequent allele, for $K\ge 3$ subpopulations. (A) Relative positions within the interval $\left[i/K,\left(i+1\right)/K\right)$ of the first and last local minima, as functions of K. The position $x_{min}\left(i\right)$ of the local minimum in interval $I_i$ is computed from Equation B1. If K is odd, then this position is $x_{min}\left[\left(K-1\right)/2\right];$ if K is even, then it is $x_{min}\left(K/2\right).$ The position of the last local minimum is $x_{min}\left(K-2\right).$ Dashed lines indicate the smallest value for $x_{min}\left(i\right)$ of $1/2,$ and the limiting largest value of $2-\sqrt{2}.$ (B) The value of the upper bound on $F_{\mathrm{ST}}$ at the first and last local minima, as functions of K. These values are computed from Equation 5, taking $\lfloor KM\rfloor =i$ and $\left\{KM\right\}=x_{min}\left(i\right),$ with $x_{min}\left(i\right)$ as in part (A). Dashed lines indicate the limiting values of 1 and $2\sqrt{2}-2$ for the first and last local minima, respectively.