  We consider a integro-differential nonlinear model that describes the
evolution of a population structured by a quantitative trait. The interactions
between traits occur from competition for resources whose concentrations depend
on the current state of the population. Following the formalism of\cite{DJMP},
we study a concentration phenomenon arising in the limit of strong selection
and small mutations. We prove that the population density converges to a sum of
Dirac masses characterized by the solution $\phi$ of a Hamilton-Jacobi equation
which depends on resource concentrations that we fully characterize in terms of
the function $\phi$.
