Exploring the effects of natural stressors on indicators and pathogens in surface waters with persistence modeling

Introduction: Surface waters are challenged by a variety of conditions that may influence the persistence of microbial and viral species of concern. Water monitoring and management practices rely on indicator organisms, and thus it is important to understand how common stressors affect the persistence of indicators and pathogens comparatively. Persistence has traditionally been assumed to follow first-order decay kinetics, but this assumption is potentially over-simplifying a process that is known to be more dynamic than the assumed linear profile. Previous reviews and analyses have identified two and three-parameter models that have been shown to more frequently provide a good fit to persistence data than the exponential model (Mitchell & Akram, 2017; Dean et al., 2020). To explore the applicability of these models for targets persisting in natural surface waters, a systematic literature review and meta-analysis were conducted to assess the availability of datasets for modeling, and to explore the relationship between the observed persistence and the documented experimental conditions. The implications of the first-order decay kinetics assumptions were evaluated by completing factor analyses that relied on only the exponential model to describe persistence, and factor analyses informed by the best fitting models from the tested suite. Methods: A systematic literature review was conducted to identify all available datasets pertaining to indicators and pathogens in natural surface waters that documented the following factors: water type, water temperature, sunlight presence, predation presence, and method of detection. The targets fell into five main groups including fecal indicator bacteria (FIB), bacteriophages, pathogenic bacteria, viruses, and protozoa. Over 650 datasets were identified, extracted or digitized for the meta-analysis. Five models, the exponential (Chick 1908; Watson, 1908), exponential damped (Whiting & Buchanan, 2001), Juneja and Marks 1 (Little, 1968), Juneja and Marks 2 (Juneja, Marks, & Mohr, 2003), and double exponential (Shull et al., 1963), were fit to the datasets. Bayesian Information Criteria (BIC) values were used to identify the best fitting model(s), and goodness of fit was determined with normalized root mean square errors (nRMSE). If more than one model provided a good fit to the dataset, model-averaged metrics were calculated using the BIC value as a weighting value (Dean et al., 2020; Haas et al., 2014). To evaluate the effect of considering alternative persistence models, T90 and T99 values were calculated for each dataset with the exponential model (EP-calculated) and using the models determined to provide the best fit by the BIC and nRMSE values (BF-calculated). The EP-calculated and BF-calculated T90 and T99 values were then used as dependent variables in an exploratory factor analysis using correlation coefficients, Kruskal-Wallis tests, and basic linear models. The performance and predictive power of the linear model method were evaluated by fitting the models to training and testing datasets to calculate RMSE values. Results: The exponential model provided a good fit to only 15% of the tested datasets and the distributions of EP-calculated T90s and T99s had a higher variance than those of the BF-calculated distributions. In particular, the exponential model calculated a higher range of T90 values for FIB, bacteriophages, bacteria, and viruses, as shown in Figure 1. The exponential model also predicted higher average T99s for all target groups, suggesting that the impact of model selection becomes more pronounced after the first log-reduction. The discrepancy between T99s was greatest for the protozoa targets as shown in Figure 2. The T90 and T99s predicted by the different persistence modeling methods were treated as dependent variables in a variety of factor analyses. When only the exponential model was used to calculate the dependent variables, sunlight had inflated importance as indicated by the correlation and Kruskal-Wallis coefficients. Interestingly, the linear model fit to EP-calculated decay metrics had more significant interactions than the model fit to the BF-calculated decay metrics. Significant interactions were observed between sunlight and water type, sunlight and method, temperature and predation, and water type and method. The BF-calculated linear model only identified a significant interaction between sunlight and method. However it is important to note that the linear models fit to both the EP-calculated and BF-calculated decay metrics had relatively poor performance with RMSE values greater than 14 days. The predictive power was better for the T90 linear models (~ 11 days) than the T99 (~14 days). Conclusions: Traditionally applied first-order decay kinetics only provided a good fit to 15% of the tested datasets and there was greater variance in the calculated T90 and T99 distributions when the exponential model was fit to the data. These results indicate that fitting two-parameter and three-parameter persistence models can potentially reduce the uncertainty associated with target decay. The differences between the EP-calculated and BF-calculated metrics were greater for the T99 data than the T90 data, suggesting that the importance of using more accurate persistence models increases as later time points are considered. This is especially important when considering the reliance on natural decay in a number of surface water uses and applications. Notably, the differences between the persistence models fit were more prominent for target groups like viruses and protozoa, which are pathogen groups of high concern in surface waters. The factor analyses conducted herein indicate that the reliance on the exponential model may be potentially overestimating the effect of sunlight on decay in natural surface waters. The linear models fit in the factor analysis, however, were found to have poor performance on the datasets as a whole. This suggests that there may be factor-decay relationships that are nonlinear in nature and that other methods may be more appropriate to explore the dynamic behaviors of indicators and pathogens in diverse water quality and environmental conditions. The results of this analysis have implications for the fields of water management and risk assessment, as narrowing the uncertainty associated with indicator and pathogen decay in surface waters is a critical component of human health-related decision making for surface waters.