1. Claire Ferguson 1, Adrian Bowman 1, Marian Scott 1 and Laurence Carvalho 2 1 University of Glasgow 2 Centre for Ecology & Hydrology A Case Study of Loch Leven http://www.tulbol.demon.co.uk/art/banatvewe.jpg Additive and Varying-Coefficient Models

2. Dataset: 1968 - 2002 150 variables measured, covering… Physics Lake chemistry Lake biology Weather Loch Leven

3. Loch Leven – the Data

4. The EC Water Framework Directive (WFD) 2000 states that there should be good status in all shallow waters by 2016. Research: Investigating statistical techniques to explore the combined impacts of climate and nutrients on water quality. Motivation

5. chlorophyll a Response year, month, SRP, Daphnia, water temp, NO 3 -N Covariates Additive Model 1988 - 2002

6. Chlorophyll

7. Should a covariate be linear as opposed to nonparametric? Is a nonparametric covariate significant? Additive Models - Inference

8. VariableF-Test linear effect p-value F-Test no effect p-value year 0.6320.634 month -0.212 log(SRP) 0.0680.016 log(Daphnia) 10.951 water temp 0.0590.090 log(NO 3 -N) 0.6510.153 Inference

9. Mainly linear relationships between variables. Little evidence of trend and seasonality. Important ecological relationships identified. The nature of trends and relationships can be explored simultaneously. For chlorophyll a (in this time period)- Summary of Additive Models

10. Linear Regression Model Varying-coefficient Model (VCM) VCM – Case Study