Maximum Likelihood Estimators For Colony Forming Units

There is a recognized need to measure the abundance of microbes in hospital environments, in the sanitation industry, and in food preparation. Doctors, microbiologists, and food safety experts have been addressing this need by using serial dilution methods to grow bacterial colonies in small enough numbers to count and, from these counts, to infer bacterial concentrations measured in Colony Forming Units (CFUs). There are two primary types of such methods: plating bacteria on a growth medium and counting their resulting colonies or counting the number of tubes at a given dilution that have growth. Traditionally, these types of data have been analyzed separately using different analytic methods. Here we build a direct correspondence between these approaches, which allows one to extend the use of the Most Probable Number (MPN) method from the liquid tubes experiments, for which it was developed, to the growth plates. We also discuss how to combine measurements taken at different dilutions, and we review several ways of analyzing colony counts, including the Poison and truncated Poison methods. For all methods, we discuss their relevant error bounds, assumptions, strengths, and weaknesses. We provide an online calculator for these estimators.