Immigration-induced phase transition in a regulated multispecies birth-death process

TL;DR

This paper investigates how population regulation causes a phase transition in multispecies birth-death-immigration models, disrupting power-law distributions and leading to dominant high-population species, with implications for biological diversity modeling.

Contribution

It introduces a global regulation mechanism in a neutral BDI model, revealing a phase transition that alters species count distributions and challenges mean-field approximations.

Findings

Power-law distributions are destroyed by regulation.

A phase transition occurs with decreasing immigration rate.

An accurate species abundance estimate is derived via a Moran process.

Abstract

Power-law-distributed species counts or clone counts arise in many biological settings such as multispecies cell populations, population genetics, and ecology. This empirical observation that the number of species $c_{k}$ represented by $k$ individuals scales as negative powers of $k$ is also supported by a series of theoretical birth-death-immigration (BDI) models that consistently predict many low-population species, a few intermediate-population species, and very high-population species. However, we show how a simple global population-dependent regulation in a neutral BDI model destroys the power law distributions. Simulation of the regulated BDI model shows a high probability of observing a high-population species that dominates the total population. Further analysis reveals that the origin of this breakdown is associated with the failure of a mean-field approximation for the expected species abundance distribution. We find an accurate estimate for the expected distribution $\langle c_k \rangle$ by mapping the problem to a lower-dimensional Moran process, allowing us to also straightforwardly calculate the covariances $\langle c_k c_\ell \rangle$. Finally, we exploit the concepts associated with energy landscapes to explain the failure of the mean-field assumption by identifying a phase transition in the quasi-steady-state species counts triggered by a decreasing immigration rate.