  We study the long-time behavior of solutions to a model of sexual populations
structured in phenotypes. The model features a nonlinear integral reproduction
operator derived from the Fisher infinitesimal operator and a trait-dependent
selection term. The reproduction operator describes here the inheritance of the
mean parental traits to the offspring without variability. We show that, under
assumptions on the growth of the selection rate, Dirac masses are stable around
phenotypes for which the difference between the selection rate and its minimum
value is less than 1/2. Moreover, we prove the convergence in some
Fourier-based distance of the centered and rescaled solution to a stationary
profile under some conditions on the initial moments of the solution.
