Hybrid zones are narrow regions in which two distinct types of individuals reproduce and produce offspring of mixed type. Some mathematical models conclude that hybrid zones of populations with asymmetric selection against heterozygotes evolve, when correctly rescaled, as mean curvature flow plus a constant flow. This conclusion rests on modelling the density of a particular allele as the solution of a partial differential equation in the euclidean space, proving the result in that deterministic setting and finally showing the presence of genetic drift does not disrupt the conclusion. In this talk, I will sketch the main ingredients to adapt this result to capture an effect one would see in a real-life population; the presence of barriers. Barriers refer to environmental obstacles that prevent individuals from invading certain zones. Mathematically this translates into studying the dynamics in a subset of the euclidean space with reflecting conditions on the boundary. We show that in a particular family of domains there is a phase transition; if the domain presents an “opening bigger” than an explicit constant there is an invasion of the fittest type, but if the opening is smaller than said constant then there is coexistence between the two types of individuals. We also mention how the presence of genetic drift (modelled by a Spatial-Lambda-Fleming Viot type process) may affect these results. This is work under the supervision of Alison Etheridge.