Giant number fluctuations in microbial ecologies

TL;DR

This paper investigates the occurrence of Giant Number Fluctuations (GNF) in various microbial ecological models, demonstrating analytically and conceptually that GNF can arise in processes like mutation, lysogeny, and horizontal gene transfer.

Contribution

The study extends the understanding of GNF to multiple microbial ecological processes, showing their emergence in models of mutation, viral infection, and gene transfer.

Findings

GNFs occur in bi-directional mutation processes at large times

Lysogeny under viral manipulation maps to mutation processes exhibiting GNF

Horizontal gene transfer can also lead to GNF in microbial populations

Abstract

Statistical fluctuations in population sizes of microbes may be quite large depending on the nature of their underlying stochastic dynamics. For example, the variance of the population size of a microbe undergoing a pure birth process with unlimited resources is proportional to the square of its mean. We refer to such large fluctuations, with the variance growing as square of the mean, as Giant Number Fluctuations (GNF). Luria and Delbruck showed that spontaneous mutation processes in microbial populations exhibit GNF. We explore whether GNF can arise in other microbial ecologies. We study certain simple ecological models evolving via stochastic processes: (i) bi-directional mutation, (ii) lysis-lysogeny of bacteria by bacteriophage, and (iii) horizontal gene transfer (HGT). For the case of bi-directional mutation process, we show analytically exactly that the GNF relationship holds at large times. For the ecological model of bacteria undergoing lysis or lysogeny under viral infection, we show that if the viral population can be experimentally manipulated to stay quasi-stationary, the process of lysogeny maps essentially to one-way mutation process and hence the GNF property of the lysogens follows. Finally, we show that even the process of HGT may map to the mutation process at large times, and thereby exhibits GNF.