In the article by J. A. Woolliams, P. Bijma and B. Villanueva (Genetics 153: 1009–1020) entitled “Expected genetic contributions and their impact on gene flow and genetic gain,” the following text is added to the end of Appendix C:

First, c_q(t) and b_q(t) are calculated according to Equations 11. Then the following iterative scheme is applied, where c* and b* are the solutions from the previous iteration: cq(t)=∑qXq−1Xpgpq(cp∗(t−age(p))+bp∗(t−age(p))dpq) bq(t)=∑qXq−1Xp(gpqλpq)cp∗(t−age(p))+∑pXq−1Xp(gpqπpq)bp∗(t−age(p)).

This is repeated until convergence.

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