Abstract
Abstract Introduction According to the empirical regularity called Taylor's law, the variance of population density in samples of populations is a power of the mean population density. The exponent is often between 1 and 2. Our experiments investigated how genetics, evolution, and environment shape Taylor's law. Methods Genetically different strains (wild type and hypermutator) of the bacterium Pseudomonas fluorescens evolved and were assayed under different environmental conditions (with and without antibiotic rifampicin and bacteriophage SBW25φ2, separately and in combination). Results Experimental treatments altered the exponent b, but not the power law form, of the relation between variance and mean population density. Bacterial populations treated only with rifampicin had a narrow range of mean population densities and exponent b = 5.43. Populations exposed to rifampicin plus phage had b = 1.51. In ancestral, control, and phage-exposed populations, mean abundance varied widely and b was not significantly different from 2. Evolutionary factors (mutation rate, selection) and ecological factors (abiotic, biotic) jointly influenced b. Conclusions Taylor's power law relationship accurately and robustly described variance as a function of mean population density, with overall exponent b = 1.89. These and other experiments with different factors acting on bacterial population size support the relevance of models that predict 'universal' patterns of fluctuation scaling.
Highlights
According to the empirical regularity called Taylor’s law, the variance of population density in samples of populations is a power of the mean population density
If virus resistance arose from heritable mutations, their theory showed, the distribution of the number of resistant bacteria under given conditions would not be described by the Poisson distribution, which has variance equal to mean, but would be described by an over-dispersed distribution, with variance significantly larger than the mean
The experimental replicate populations of P. fluorescens were seeded from four different strains of bacterial cells: wild type WT/Rif(Rainey and Bailey 1996), hypermutator MutS/Rif- (Pal et al 2007), rifampicin-resistant wild type WT/Rif+, and rifampicin-resistant hypermutator MutS/Rif+
Summary
According to the empirical regularity called Taylor’s law, the variance of population density in samples of populations is a power of the mean population density. If virus resistance arose from heritable mutations, their theory showed, the distribution of the number of resistant bacteria under given conditions would not be described by the Poisson distribution, which has variance equal to mean, but would be described by an over-dispersed distribution, with variance significantly larger than the mean. They counted the numbers of resistant bacteria and reported the raw counts, means, and variances in series of eight similar cultures in their Table 2. They remarked (Luria and Delbrück 1943, page 504): ‘... in every experiment the fluctuation of the numbers of resistant bacteria is tremendously higher than could be accounted for by the sampling errors, ... in conflict with the expectations from the hypothesis of acquired immunity’ and in support of the alternative hypothesis of heritable mutations
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