Distributions of the asymmetry coefficient a.
The value of a represents the proportion of damage partitioned by a mother bacterium to its new daughter. Asymmetry requires that a < ½. If a = ½, the partitioning is symmetrical. Distributions are illustrative representations except for (A), which was derived from the experiments of Stewart et al. . (A) Stochastic variation for observed values of a estimated from experimental E. coli data. Distribution mean = .4845, variance σS2 = .0004557, and sample size n = 128. (B) Distribution of a when the partitioning of damage is stochastic but symmetrical with a mean of ½. A Gaussian distribution with a variance of σS2 = .0004557 is assumed for illustration. (C) Distribution of the proportion of damage allocated to the daughter that gets less damage when partitioning is stochastic but symmetrical. Because symmetrical partitioning is random with respect to whether a daughter is old or new, polarity can be ignored and all the daughters can be re-categorized into ones that get less and ones that get more damage. If only the lesser daughters are considered, the resulting distribution is the half- or folded normal of the Fig 3B distribution. The mean of the half-normal is ½—√(σS2 • 2 / 3.141593…), which equals .483 (●). (D) Gaussian distributions representing four populations: a of new daughters (mean = .48; var = σS2 = .00046; a of old daughters (mean = 1 –.48 = .52; var = σS2 = .00046); a population made by pooling the new and old daughters; and daughters produced by a stochastic but symmetric mother where the variance is increased to σS2 + D2/4 = .00046 + .00042/4 = .00086 and mean = ½.