Summary - Asymptotic genetic gains and lags are derived in French beef cattle breeding schemes for an objective including direct and maternal effects on growth. A simple general
method using matrix algebra is presented to simultaneously calculate asymptotic genetic
gains and lags, whatever the population structure. The heterogeneity of use of artificial
insemination (AI) in selection herds is considered. At the same overall rate of AI use, larger
asymptotic genetic gains can be obtained by concentrating AI in only a fraction of the herds
instead of keeping the same lower rate in all herds. An application concerns the Limousin
selection nucleus, where 23% of calves are bred by AI in only 50% of the herds. When an
aggregate breeding objective for growth is considered, positive annual asymptotic genetic
gains are expected in both direct (+ 0.13 genetic standard deviation) and maternal effects
(+ 0.05 genetic standard deviation) on growth, despite the negative estimates (around
- 0.2) of genetic direct-maternal correlations. The major part of the genetic gains in direct
and maternal effects are due to AI sire selection and dam selection respectively. Taking into account sampling uncertainty in estimates of preweaning genetic parameters leads
to the conclusion that the predicted asymptotic response in maternal effects is positive
with a very high probability. Nevertheless, strongly negative (around -0.6) estimates of
correlations between direct and maternal effects lead to negative responses in maternal
effects.