Modeling the Relationship Between

9 Most probable number (MPN) and colony-forming-unit (CFU) estimates of fecal 10 coliform bacteria concentration are common measures of water quality in coastal 11 shellfish harvesting and recreational waters. Estimating procedures for MPN and 12 CFU have intrinsic variability and are subject to additional uncertainty arising from 13 minor variations in experimental protocol. It has been observed empirically that the 14 standard multiple-tube fermentation (MTF) decimal dilution analysis MPN proce15 dure is more variable than the membrane filtration CFU procedure, and that MTF16 derived MPN estimates are somewhat higher on average than CFU estimates, on 17 split samples from the same water bodies. We construct a probabilistic model that 18 provides a clear theoretical explanation for the variability in, and discrepancy be19 tween, MPN and CFU measurements. We then compare our model to water quality 20 samples analyzed using both MPN and CFU procedures, and find that the (often 21 large) observed differences between MPN and CFU values for the same water body 22 are well within the ranges predicted by our probabilistic model. Our results indicate 23 that MPN and CFU intra-sample variability does not stem from human error or 24 laboratory procedure variability, but is instead a simple consequence of the proba25 bilistic basis for calculating the MPN. These results demonstrate how probabilistic 26 models can be used to compare samples from different analytical procedures, and 27 to determine whether transitions from one procedure to another are likely to cause 28 a change in quality-based management decisions. 29