Evolutionary dynamics of nationalism and migration

•Evolution of nationalism and assimilation is modeled using replicator dynamics (RD).•I study the existence of asymptotic or neutral stability in the state space.•RD takes into account own population effects when an enclave of immigrants exists.•In one set-up, evolution may depend on initial conditions and basins of attraction.•Enclave makes assimilation less likely and allows for equilibria with polymorphism.

I present a dynamic evolutionary game model to address the relation between nationalism against immigrants and assimilation of the latter into the host country culture. I assume a country composed of two different large polymorphic populations, one of native citizens and the other of immigrants. A native citizen may behave nationalistically or may welcome immigrants. Immigrants may have an interest in learning the host country language or not. Evolution is modeled using replicator dynamics (RD). I also account for the presence of an enclave of immigrants in the host country. In the RD, the latter represents the immigrants’ own population effect, which contribution to fitness is controlled using a parameter ρρ, 0≤ρ≤10≤ρ≤1, that represents the enclave size. In line with the empirical literature on migration, the existence of an enclave of immigrants makes assimilation less likely to occur. For large values of ρρ, complete assimilation may not occur even if immigrants and natives share very close cultures and norms. Government policy regarding nationalism is modeled both exogenously and endogenously. A single or multiple asymptotically stable states exist for all cases studied but one in which the dynamics is similar to that found in the predator–prey model of Lotka–Volterra for competing species.