We propose a general numerical approach that can be used to study the invasion fitness of a mutant in evolutionary models and to determine evolutionary singular strategies when the competitive exclusion principle holds. We illustrate this method with a mass-structured individual-based chemostat model. We assume that the mutations are rare and that the resident population is large, in which case the mutant population can be viewed, on a short time scale, as evolving in a constant environment. Both deterministic and stochastic models can be proposed to describe such a problem. We exploit a previously derived mathematical relationship between these models to derive a general method for analyzing the invasion fitness of stochastic models. Our method is based on a deterministic reduced model for which it is straightforward to determine the feasibility of invasion and the convergence-stable evolutionary singular strategy.