Competitive gene flow does not necessarily maximize the genetic gain of genomic breeding programs in the presence of genotype-by-environment interaction

National and international across-population selection is often recommended and fairly common in the current breeding practice of dairy cattle, with the primary aims to increase genetic gain and genetic variability. The aim of this study was to test the hypothesis that the strategy of truncation selection of sires across populations [i.e., competitive gene flow strategy (CGF)] may not necessarily maximize genetic gain in the long term in the presence of genotype-by-environment interaction (GxE). Two alternative strategies used to be compared with CGF were forced gene flow (FGF) strategies, with 10 or 50% of domestic dams forced to be mated with foreign sires (FGF10%, FGF50%). Two equal-size populations (N-dams = 1,000) that were selected for the same breeding goal trait (h(2) = 0.3) under GxE correlation (r(g)) of either 0.9 or 0.8 were simulated to test these 3 different strategies. Each population first experienced either 5 or 20 differentiation generations (G(d)), then 15 migration generations. Discrete generations were simulated for simplicity. Each population performed a within-population conventional breeding program during differentiation generations and the 3 across-population sire selection strategies based on joint genomic prediction during migration generations. The 4 G(d)_r(g) combinations defined 4 different levels of differentiation degree between the 2 populations at the start of migration. The true rate of inbreeding over the last 10 migration generations in each scenario was constrained at 0.01 to provide a fair basis for comparison of genetic gain across scenarios. Results showed that CGF maximized the genetic gain after 15 migration generations in 5_0.9 combination only, the case of the lowest differentiation degree, with a superiority of 0.4% (0.04 genetic SD units) over the suboptimal strategy. While in 5_0.8, 20_0.9, and 20_0.8 combinations, 2 FGF strategies had a superiority in genetic gain of 2.3 to 12.5% (0.21-1.07 genetic SD units) over CGF after 15 migration generations, especially FGF50%. The superiority of FGF strategies over CGF was that they alleviated inbreeding, introduced new genetic variance in the early migration period, and improved accuracy in the entire migration period. Therefore, we concluded that CGF does not necessarily maximize the genetic gain of across-population genomic breeding programs given moderate GxE. The across-population selection strategy remains to be optimized to maximize genetic gain.