On the Choice of a Mathematical Model to Represent Normal Bacterial Growth

Abstract

Theproblem considered is that of constructing a stochastic process (not necessarily of the Markov type) to represent the growth of a bacterial colony in the absence of mortality and mutation. The importance of the distribution of fission-times is emphasized, and an approximate relation between the coefficient of variation of the fission-times and the asymptotic coefficient of variation of clone-size is discussed. Rahn's model of the fission process, a rather different model put forward by the author in 1948 and a more general model (of which the other two are special cases) are examined in relation to the problem of estimating “the number of genes” in bacteria. Reasons are given for supposing that existing estimates of this number (Finney & Martin, 25; Kendall, 20) may be too low. The need for further experimental work (including an experimental determination of clone-size fluctuations) is stressed.