Aims: The aim of this guide is to provide practical help for ecologists who analyze data from biodiversity–ecosystem functioning experiments. Our approach differs from others in the use of least squares-based linear models (LMs) together with restricted maximum likelihood-based mixed models (MMs) for the analysis of hierarchical data. An original data set containing diameter and height of young trees grown in monocultures, 2- or 4-species mixtures under ambient light or shade is used as an example.
Methods: Starting with a simple LM, basic features of model fitting and the subsequent analysis of variance (ANOVA) for significance tests are summarized. From this, more complex models are developed. We use the statistical software R for model fitting and to demonstrate similarities and complementarities between LMs and MMs. The formation of contrasts and the use of error (LMs) or random-effects (MMs) terms to account for hierarchical data structure in ANOVAs are explained.
Important Findings: Data from biodiversity experiments can be analyzed at the level of entire plant communities (plots) and plant individuals. The basic explanatory term is species composition, which can be divided into contrasts in many ways depending on specific biological hypotheses. Typically, these contrasts code for aspects of species richness or the presence of particular species. For significance tests in ANOVAs, contrast terms generally are compared with remaining variation of the explanatory terms from which they have been ‘carved out’. Once a final model has been selected, parameters (e.g. means or slopes for fixed-effects terms and variance components for error or random-effects terms) can be estimated to indicate the direction and size of effects.