External bias in the model of isolation of communities

TL;DR

This paper investigates how imbalances in birth rates affect community isolation in lattice models, revealing a critical asymmetry parameter that optimizes the formation of isolated groups.

Contribution

It extends existing community isolation models to include birth rate imbalances and identifies a critical asymmetry value that maximizes community isolation speed.

Findings

Existence of a critical asymmetry parameter depending on lattice dimension.

Blocked subgroups are rare when a dominant species exists or diversity is high.

Number of blocked species decreases with system dimensionality.

Abstract

We extend a model of community isolation in the d-dimensional lattice onto the case with an imposed imbalance between birth rates of competing communities. We give analytical and numerical evidences that in the asymmetric two-specie 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 tc is minimal. This critical value of the parameter depends only on the lattice dimensionality and is independent from the system size. Similar phenomenon was observed in the multi-specie case with a geometric distribution of the birth rates. We also show that blocked subgroups in the multi-specie case are absent or very rare when either there is a strictly dominant specie that outnumbers the others or when there is a large diversity of species. The number of blocked species of different kinds decreases with the dimension of the multi-specie system.