Calibrating and validating bacterial water quality models: a Bayesian approach.

Water resource management decisions often depend on mechanistic or empirical models to predict water quality conditions under future pollutant loading scenarios. These decisions, such as whether or not to restrict public access to a water resource area, may therefore vary depending on how models reflect process, observation, and analytical uncertainty and variability. Nonetheless, few probabilistic modeling tools have been developed which explicitly propagate fecal indicator bacteria (FIB) analysis uncertainty into predictive bacterial water quality model parameters and response variables. Here, we compare three approaches to modeling variability in two different FIB water quality models. We first calibrate a well-known first-order bacterial decay model using approaches ranging from ordinary least squares (OLS) linear regression to Bayesian Markov chain Monte Carlo (MCMC) procedures. We then calibrate a less frequently used empirical bacterial die-off model using the same range of procedures (and the same data). Finally, we propose an innovative approach to evaluating the predictive performance of each calibrated model using a leave-one-out cross-validation procedure and assessing the probability distributions of the resulting Bayesian posterior predictive p-values. Our results suggest that different approaches to acknowledging uncertainty can lead to discrepancies between parameter mean and variance estimates and predictive performance for the same FIB water quality model. Our results also suggest that models without a bacterial kinetics parameter related to the rate of decay may more appropriately reflect FIB fate and transport processes, regardless of how variability and uncertainty are acknowledged.

An assessment of fecal indicator bacteria-based water quality standards.

Fecal indicator bacteria (FIB) are commonly used to assess the threat of pathogen contamination in coastal and inland waters. Unlike most measures of pollutant levels however, FIB concentration metrics, such as most probable number (MPN) and colony-forming units (CFU), are not direct measures of the true in situ concentration distribution. Therefore, there is the potential for inconsistencies among model and sample-based water quality assessments, such as those used in the Total Maximum Daily Load (TMDL) program. To address this problem, we present an innovative approach to assessing pathogen contamination based on water quality standards that impose limits on parameters of the actual underlying FIB concentration distribution, rather than on MPN or CFU values. Such concentration-based standards link more explicitly to human health considerations, are independent of the analytical procedures employed, and are consistent with the outcomes of most predictive water quality models. We demonstrate how compliance with concentration-based standards can be inferred from traditional MPN values using a Bayesian inference procedure. This methodology, applicable to a wide range of FIB-based water quality assessments, is illustrated here using fecal coliform data from shellfish harvesting waters in the Newport River Estuary, North Carolina. Results indicate that areas determined to be compliant according to the current methods-based standards may actually have an unacceptably high probability of being in violation of concentration-based standards.

Modeling the relationship between most probable number (MPN) and colony-forming unit (CFU) estimates of fecal coliform concentration.

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

Rapid taste responses in the gustatory cortex during licking.

Rapid tastant detection is necessary to prevent the ingestion of potentially poisonous compounds. Behavioral studies have shown that rats can identify tastants in approximately 200 ms, although the electrophysiological correlates for fast tastant detection have not been identified. For this reason, we investigated whether neurons in the primary gustatory cortex (GC), a cortical area necessary for tastant identification and discrimination, contain sufficient information in a single lick cycle, or approximately 150 ms, to distinguish between tastants at different concentrations. This was achieved by recording neural activity in GC while rats licked four times without a liquid reward, and then, on the fifth lick, received a tastant (FR5 schedule). We found that 34% (61 of 178) of GC units were chemosensitive. The remaining neurons were activated during some phase of the licking cycle, discriminated between reinforced and unreinforced licks, or processed task-related information. Chemosensory neurons exhibited a latency of 70-120 ms depending on concentration, and a temporally precise phasic response that returned to baseline in tens of milliseconds. Tastant-responsive neurons were broadly tuned and responded to increasing tastant concentrations by either increasing or decreasing their firing rates. In addition, some responses were only evoked at intermediate tastant concentrations. In summary, these results suggest that the gustatory cortex is capable of processing multimodal information on a rapid timescale and provide the physiological basis by which animals may discriminate between tastants during a single lick cycle.