Applications of mixed models in ecology
Statistics is a science that deals with variability in data. The presence of variation in natural processes means that statistics has a central role within a discipline such as ecology. Thus, any technique that determines the sources of variability will play a prominent part in the statistical modelling of ecological data. My thesis addresses one popular approach, a mixed model analysis. The practical use of mixed models in ecological research had at one time been limited to occasions in which experiments involved balanced data. Given the infrequent occurrence of such events, there were few practical applications of mixed models in the ecological literature. The development of methods for fitting mixed models to unbalanced data and the wider availability of the software to fit them were the seeds for the now growing trend in mixed model analysis among ecologists. During my PhD I focused on the development and novel application of mixed models in ecology. The work presented in this thesis was motivated by four examples, each involving unbalanced data with complex correlation structures. The intention of each example, motivated by specific questions of interest, was to explore the extent to which mixed model methodology could be practically applied in ecology. Features of a mixed model analysis were manipulated in each example to address a number of general issues in ecological statistics: how to develop efficient sampling designs; the effect of using estimated variances in power calculations; ways to handle correlated explanatory variables in a regression analysis and how to correctly model reproductive success. An additional issue concerned the estimation of a change point location in a simple change point model.