We study the asymptotic behavior of stationary solutions to a quantitative genetics model with trait-dependent mortality and a nonlinear integral reproduction operator with a parameter describing the deviation between the offspring and the mean parental trait : the infinitesimal model. It accounts for the mixing of parental phenotypes at birth.
Our asymptotic analysis encompasses the case when the parameter is typically small. 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 linear reproduction operator corresponding to asexual reproduction, but using an alternative methodology.