Joshi, J., Matthies, D.& Schmid, B. (2000) Root hemiparasites and plant diversity in experimental grassland communities 88, 634-644. Appendix 2 Skeleton analysis of variance/deviance for the measured parameters in the experiment. The treatment model consisted of the effects of the number of species (species richness), the number of functional groups, the presence of legumes and the effect of the Rhinanthus treatment and its interactions with the previously listed factors. The final model was found by backward elimination of factors of minor interest. These were defined as factors that did not reach an F-value > 2 . Because the different species assemblages within each diversity level were randomly selected from the species pool , their mean square was used as the appropriate error term to test the effects of the diversity treatments (number of species and number of functional groups). The interaction term Rhinanthus x assemblage served as error term to test the interaction between the effects of Rhinanthus and the diversity treatments. Because the different aspects of diversity, number of species (A) and number of functional groups (B), were partly confounded we fitted these terms in alternative sequences (in generalised linear modelling terminology the sequence A + B corresponds to "A ignoring B" and "B eliminating A" and the sequence B + A corresponds to "B ignoring A" and "A eliminating B"; the interaction AxB was always omitted from the analyses because of its low F-values). If the combinations of the partial factorial A crossed with B are considered as a major factor "diversity treatment", the above approach is equivalent to forming different sets of orthogonal contrasts within this major factor . Incidentally, this approach is similar to the type-IV sum-of-squares approach in the statistical package SAS where contrasts within a partial factorial design are chosen arbitrarily (SAS, 1990). The preferred sequence of contrasts was in most cases B + A. Thus, for the sake of clarity we only present the results of the analyses in which the number of functional groups (B) preceded the number of species (A). The main effect of the Rhinanthus treatment was tested against the residual variation among the two quadrats within individual plots. The block and subblock effects were used to eliminate spatial variation within the experimental site.

Notes: random effects (error model) in italic letters, fixed effects (treatment model) in roman letters; effects are always adjusted for effects that precede them.