A secondary model for the effect of pH on the variability in growth fitness of Listeria innocua strains

Variability in microbial growth is a keystone of modern Quantitative Microbiological Risk Assessment (QMRA). However, there are still significant knowledge gaps on how to model variability, with the most common assumption being that variability is constant. This is implemented by an error term (with constant variance) added on top of the secondary growth model (for the square root of the growth rate). However, this may go against microbial ecology principles, where differences in growth fitness among bacterial strains would be more prominent in the vicinity of the growth limits than at optimal growth conditions.This study coins the term “secondary models for variability”, evaluating whether they should be considered in QMRA instead of the constant strain variability hypothesis. For this, 21 strains of Listeria innocua were used as case study, estimating their growth rate by the two-fold dilution method at pH between 5 and 10. Estimates of between-strain variability and experimental uncertainty were obtained for each pH using mixed-effects models, showing the lowest variability at optimal growth conditions, increasing towards the growth limits. Nonetheless, the experimental uncertainty also increased towards the extremes, evidencing the need to analyze both sources of variance independently. A secondary model was thus proposed, relating strain variability and pH conditions. Although the modelling approach certainly has some limitations that would need further experimental validation, it is an important step towards improving the description of variability in QMRA, being the first model of this type in the field.