Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India.
J Theor Biol. 2012 Sep 7;308:96-104. doi: 10.1016/j.jtbi.2012.05.030. Epub 2012 Jun 7.
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 Delbrück 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.
种群大小的统计波动可能非常大，具体取决于其潜在随机动态的性质。例如，在资源不受限制的纯生育过程中，微生物种群大小的方差与平均值的平方成正比。我们将这种方差随平均值的平方而增长的大波动称为巨数波动（GNF）。Luria 和 Delbrück 表明，微生物种群中的自发突变过程表现出 GNF。我们探讨了 GNF 是否会在其他微生物生态系统中出现。我们研究了通过随机过程演化的某些简单生态模型：（i）双向突变，（ii）噬菌体对细菌的裂解-溶源，以及（iii）水平基因转移（HGT）。对于双向突变过程的情况，我们在大时间上精确地证明了 GNF 关系成立。对于细菌在病毒感染下发生裂解或溶源的生态模型，我们表明如果可以通过实验操纵病毒种群使其保持准稳定状态，那么溶源过程本质上映射到单向突变过程，因此溶源菌具有 GNF 属性。最后，我们表明即使是 HGT 过程也可能在大时间上映射到突变过程，从而表现出 GNF。
