## Supplemental Material for Huang et al, 2019

Material S2: The simulation computer program to obtain the numerical solutions of genotypic and phenotypic frequencies of zygotes and the genotypic frequencies of gametes. The program can be run on Windows platforms and requires the .Net Framework V3.5 runtime library.

Material S3: The C++ source code of the genotypic and phenotypic frequencies of polysomic inheritance under double-reduction. The prefix of functions is GFZ (genotypic frequencies of zygotes), GFG (genotypic frequencies of gametes), PFZ (phenotypic frequencies of zygotes), or PFG (phenotypic frequencies of gametes). An example that is the function in the second case (i.e. G = AAAB) in Equation (A4) is given by

double GFZ4_iiij(double a1, double pi, double pj)

{

double pi2=pi*pi;

return (8*(-1+a1)*pi2*(-3*a1+2*(-1+a1)*pi)*pj)/pow(2+a1,2);

}