  We study the asymptotic behavior of stationary solutions to a quantitative
genetics model with trait-dependent mortality and sexual reproduction. The
infinitesimal model accounts for the mixing of parental phenotypes at birth.Our
asymptotic analysis encompasses the case when deviations between the offspring
and the mean parental trait are typically small. Under suitable regularity and
growth conditions on the mortality rate, we prove existence and local
uniqueness of a stationary profile that get concentrated around a local optimum
of mortality, with a Gaussian shape having small variance. Our approach is
based on perturbative analysis techniques that require to describe accurately
the correction to the Gaussian leading order profile. Our result extends
previous results obtained with an asexual mode of reproduction, but using an
alternative methodology.
