An inhomogeneous contact process model for speciation

TL;DR

This paper introduces an inhomogeneous contact process model to study speciation and extinction, highlighting how phase transition depends on the asymptotic ratio of birth to death rates.

Contribution

The model incorporates spatially inhomogeneous contact rates and analyzes the critical conditions for phase transition in speciation dynamics.

Findings

Phase transition existence depends on the limit of the birth/death rate ratio.

The model links spatial inhomogeneity to speciation-extinction dynamics.

Critical thresholds are identified based on the asymptotic behavior of rates.

Abstract

We propose the following model for speciation and extinction. Birth and deaths occur according to spatially inhomogeneous contact rates. We assume that the ratio of the birth rate over the death rate at a site converges to some limit as the site goes to infinity. We show that the existence of a phase transition depends critically on the value of this limit.