Choosing probability distributions for modelling generation time variability

Abstract

This paper explores the variation in generation time of bacterial systems growing at suboptimal temperatures. Generation time generally has a distribution with a long right-hand tail, suggesting a model with variance proportional to the second or third power of its mean. Suitable non-normal probability distributions include the ‘gamma’ and ‘inverse Gaussian’, with the modelling being carried out by ‘generalized linear regression’. The procedure is illustrated with replicated data on Pseudomonas fluorescens obtained using a gradient temperature incubator with nutrient broth as the growth medium. The results show that the ‘gamma’ distribution is a suitable stochastic assumption when modelling generation time. This enables one to predict, for example, a mean generation time of 615 min at 2·4°C, and that 0·1% of the observed values will fall below 471 min and one in a million below 405 min. Use of an unreplicated set of data gave less conclusive results but favoured the ‘inverse Gaussian’ distribution as the stochastic model.