Dimension reduction techniques in community ecology : with applications to spatio-temporal marine ecological data
The aim of this PhD-thesis is to develop techniques which can be used to analyse spatio-temporal ecological data sets. Central questions are: A. What are the relationships between species abundances and spatial environmental variables in a particular year? What are relationships between species? B. How do these species-environmental relations and species interactions change from year-to-year? What is the effect of global environmental variables on these year-to-year variations? The thesis is divided into two parts. In Part I, we concentrate on the first question. We discuss the state-of-the-art technique canonical correspondence analysis (CCA). Using assumptions which are unlikely to hold in practice, Ter Braak (1986) showed that CCA estimates certain parameters of the 'restricted Gaussian response (RGR) model'. This model describes species abundances as a unimodal, symmetric function along a gradient. The key feature in CCA and RGR is that the gradient is a linear combination of environmental variables. Using numerical optimisation routines, we show that the parameters of the RGR model can easily be estimated. This has considerable advantages over CCA, because all parameters are estimated in a regression context, without making doubtful assumptions. RGR is applied on various data sets. A model validation indicates that for some species the model is inappropriate. For this reason, we develop a smoothing model in which the covariate is a linear combination of environmental variables. It is called restricted generalised additive modelling (RGAM). In Part II, we concentrate on question B. We develop a new technique, called dynamic generalised additive modelling. For each species a smoothing function and a stochastic trend are estimated.