External bias in the model of isolation of communities

We extend a model of community isolation in the d-dimensional lattice to a case with an imposed imbalance between the birth rates of competing communities. We provide analytical and numerical evidences that in the asymmetric two-species model there exists a well-defined value of the asymmetry parameter when the emergence of the isolated (blocked) subgroups is the fastest, i.e., the characteristic time t(c) is minimal. The critical value of the parameter depends only on the lattice dimensionality and is independent of the system size. A similar phenomenon is observed in the multispecies case with a geometric distribution of the birth rates. We also show that blocked subgroups in the multispecies case are absent or very rare when either there is a strictly dominant species that outnumbers the others or there is a large diversity of species. The number of blocked species of different kinds decreases with the dimension of the multispecies system.