  This paper is devoted to the analysis of the long-time behavior of a
phenotypic-structured model where phenotypic changes do not occur. We give a
mathematical description of the process in which the best adapted trait is
selected in a given environment created by the total population. It is
exhibited that the long-time limit of the unique solution to the nonlocal
equation is given by a Dirac mass centered at the peak of the fitness within or
at the boundary of the region where the initial data is positive. Specially, If
the peak of the fitness can't be in the support of the solution, then the
infinite time blow-up of the solution occurs near the boundary of the region
where the solution is positive. Moreover, our numerical results facilitate a
deeper understanding of identifying the position of the centers.
