Immigration-induced phase transition in a regulated multispecies birth-death 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 $⟨c_k⟩$ by mapping the problem to a lower-dimensional Moran process, allowing us to also straightforwardly calculate the covariances $⟨c_k{c}_{\ell }⟩$. 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.

arXiv comment22 pages, 8 figures, accepted to J. Phys. A

References in corpus (12)

• Stochastic Dynamical Structure (SDS) of Nonequilibrium Processes in the Absence of Detailed Balance. II: construction of SDS with nonlinear force and multiplicative noise
• Stochastic Models of Evolution in Genetics, Ecology and Linguistics
• Demographic noise can reverse the direction of deterministic selection
• Extinction Rates for Fluctuation-Induced Metastabilities : A Real-Space WKB Approach
• Fluctuating fitness shapes the clone size distribution of immune repertoires
• Exact Solution of the Multi-Allelic Diffusion Model
• Stochastic self-assembly of incommensurate clusters
• Landscape Paradigms in Physics and Biology: Introduction and Overview
• Population Genetics with Fluctuating Population Sizes
• Evolutionary Dynamics with Fluctuating Population Sizes and Strong Mutualism
• A mapping of the stochastic Lotka-Volterra model to models of population genetics and game theory
• Two-timescale evolution on a singular landscape

Cited by in corpus (3)

• Diversity in Biology: definitions, quantification, and models
• Phenomenology and dynamics of competitive ecosystems beyond the niche-neutral regimes
• A Random-Line-Graph Approach to Overlapping Line Segments