We consider an integro-differential model describing the evolution of a population in space and along a phenotypic trait. This type of models can be used to study e.g. biological invasions or the effect of global warming on species’ range. From this structured population model, we recover through asymptotic analysis a classical model from evolutionary biology, introduced by Kirkpatrick and Barton. This asymptotic analysis allows us to generalize this latter model to study the effect of pollen dispersion on species’ dynamics. (Notice that the time is one hour earlier for this week because of the mathematical analysis minicourse, see the full program at http://www.imperial-analysis.org.uk/ )