Evaluating stressor response relationships

1. Evaluating stressor response relationships Brian Haggard and Thad Scott Arkansas Water Resources Center UA Division of Agriculture UA Division of Agriculture Arkansas Water Resources Center

2. What is stressor response? Biological response varies across a range of nutrient concentrations We can describe theses relationships using statistical tools Dependent Independent

3. What relationships are important in setting nutrient criteria? • The state decides which relationships are important based on • Water body type • Designated use • Response variables often linked to nutrients include • Algal biomass • Water clarity • Biodiversity

4. How do we evaluate stressor response relationships? Regression Tree Regression Changepoint

5. Regression: What is it? Dependent • Treats one variable as a function of another • Results in an equation that can be used to predict a response • Linear, multiple linear & non-linear fits possible y= 0.03X + 0.39 R2=0.4 p<0.01 Independent

6. Regression relationships require ‘desired’ endpoint Haggard & Scott 2010

7. Change-point analysis: What is it? Dependent • Identifies a threshold where a change in the response variable occurs • Useful for identifying specific nutrient concentrations where shifts occur Independent

8. Regression tree analysis: What is it? Dependent Dependent • An extension of change-point analysis • Secondary analysis on data subsets • Quantifies thresholds in multiple independent variables in hierarchy Independent 1 Independent 2

9. Regression tree analysis: What is it? Dependent • Also allows one independent variable to be split multiple times Independent

10. Change-points and Impairment Here, we see the variability change in the biological response at a given nutrient concentration... But, it is apparent that not all sites express impact or impairment above this nutrient concentration. Biological Response Nutrient Concentration

11. Change-points and Impairment Here, we see the variability change in the biological response at a given nutrient concentration... But, it is apparent that sites above this change-point always show impact or defined impairment. Biological Response Nutrient Concentration

12. Multiple Change-points and Impairment Here, we see the variability change in the biological response at multiple nutrient concentrations… The first change-point might served as a threshold, and the second change-point might show impact or defined impairment. Biological Response Nutrient Concentration

13. How do we select the best analysis? • Goodness of fit and significance • Visual comparison • Statistics indicate the strength of the relationship • AIC or other model selection techniques • Each tool has pros and cons that can be balanced based on attributes of the dataset and desired output

14. What do we want the analysis to tell us? • Regression analysis provides predictive models, but can be complex and difficult to evaluate • Change-point analysis yields a specific, easily interpreted stressor value, but requires large data sets • Regression tree analysis identifies multiple values in one stressor, or hierarchical splits in multiple stressors; but requires large data sets

15. How does this work in the real world? • The analytical tools described here have previously been employed in the Red River Basin • We’ll share some findings from the Red River Basin next…