In this paper, we present entropy satisfying schemes for solving an integro-differential
equation that describes the evolution of a population structured with respect to a continuous trait.
In [P.-E. Jabin and G. Raoul, J. Math. Biol., 63 (2011), pp. 493–517] solutions are shown to converge
toward the so-called evolutionary stable distribution (ESD) as time becomes large, using the relative
entropy. At the discrete level, the ESD is shown to be the solution to a quadratic programming
problem and can be computed by any well-established nonlinear programing algorithm. The schemes
are then shown to satisfy the entropy dissipation inequality on the set where initial data are positive
and the numerical solutions tend toward the discrete ESD in time. An alternative algorithm is
presented to capture the global ESD for nonnegative initial data, which is made possible due to the
mutation mechanism built into the modified scheme. A series of numerical tests are given to confirm
both accuracy and the entropy satisfying property and to underline the efficiency of capturing the
large time asymptotic behavior of numerical solutions in various settings.