Nonlocal Lotka-Volterra models have the property that solutions concentrate as Dirac masses in the limit of small diffusion. Is it possible to describe the dynamics of the concentration points and of the mass of the Dirac? We will explain how this relates to the so-called 'constrained Hamilton-Jacobi equation' and how numerical simulations can exhibit unexpected dynamics well explained by this equation. Our motivation comes from 'populational adaptive evolution' a branch of mathematical ecology which models the darwinian evolution.