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 Additive and Varying-Coefficient Models

Dataset: variables measured, covering… Physics Lake chemistry Lake biology Weather Loch Leven

Loch Leven – the Data

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

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

Chlorophyll

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

VariableF-Test linear effect p-value F-Test no effect p-value year month log(SRP) log(Daphnia) water temp log(NO 3 -N) Inference

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

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