t Models for Ecological Systems

Summary Ecological systems comprise physical, chemical and biological parameters which are gen- erally interrelated and consequently many of the variables are potentially both responses and covariates within the system. In order to explore relationships fully and make appro- priate inferences about such a system it is necessary to identify all the important forms of dependence. Multivariate models are, therefore, required to model multiple responses and covariates. Ferguson, Bowman, Scott and Carvalho (2007) outlined univariate ad- ditive and varying-coe-cient models for a lake ecosystem highlighting that relationships between variables change throughout the year. A multivariate varying-coe-cient model is presented here to explore changing relationships, whilst accounting for dependence between responses. Techniques are applied to data from Loch Leven, Kinross, Scotland.